Research ArticlePhase Clustering Based Modulation Classification Algorithmfor PSK Signal over Wireless Environment

Qi An1 Zi-shu He1 Hui-yong Li1 and Yong-hua Li2

1Electronic Engineering Department University of Electronic Science and Technology of China Chengdu China2Air Force Airborne Academy Guilin China

Correspondence should be addressed to Qi An sunnycaroline163com

Received 18 April 2016 Accepted 14 July 2016

Academic Editor Laurence T Yang

Copyright copy 2016 Qi An et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Promptitude and accuracy of signalsrsquo non-data-aided (NDA) identification is one of the key technology demands in noncooperativewireless communication network especially in information monitoring and other electronic warfare Based on this backgroundthis paper proposes a new signal classifier for phase shift keying (PSK) signals The periodicity of signalrsquos phase is utilized as theassorted character with which a fractional function is constituted for phase clustering Classification and the modulation order ofintercepted signals can be achieved through its Fast Fourier Transform (FFT) of the phase clustering function Frequency offset isalso considered for practical conditions The accuracy of frequency offset estimation has a direct impact on its correction Thusa feasible solution is supplied In this paper an advanced estimator is proposed for estimating the frequency offset and balancingestimation accuracy and range under low signal-to-noise ratio (SNR) conditions The influence on estimation range brought bythe maximum correlation interval is removed through the differential operation of the autocorrelation of the normalized basebandsignal raised to the power of 119876 Then a weighted summation is adopted for an effective frequency estimation Details of equationsand relevant simulations are subsequently presented The estimator proposed can reach an estimation accuracy of 10minus4 even whenthe SNR is as low as minus15 dB Analytical formulas are expressed and the corresponding simulations illustrate that the classifierproposed is more efficient than its counterparts even at low SNRs

1 Introduction

With the development of science and technology wirelessnetwork has become the main media of information trans-mission in recent decades and it plays an important rolein the field of communication field of military and otherfields Satellite wireless network communication technologymeets the requirements of time and place for informationtransmission with its wide coverage good broadcastingability and the unlimited character of different geographicalconditions at any time or place In the field of electronicsurveillance and electronic countermeasures multiple sen-sors can make each combat unit share their reconnais-sance information through effective collaborative workingsystems and generate an overall situation with high precisionand reliability via information fusion Thus the technologyof cooperative reconnaissance network based on multiple

sensors has become a hot issue in the field of electronicwarfare

As one of the main modulation methods in wirelesscommunication networks PSK including multiple phase-shift-keyed (MPSK) and other converted forms such as 1205874differential quadrature phase-shift-keyed ((1205874)DQPSK) isalso one of the most common carrier transmission modesin wireless digital communications It has high spectrumutilization ratio and strong anti-interference ability moreimportantly it is also relatively simple in circuit imple-mentations Because of the remarkable spectrum characterand multiple demodulation methods (1205874)DQPSK is widelyused in satellite communication networks and mobile com-munication systems The nonbalanced quadrature phase-shift-keyed (UQPSK) is a modulation mode transferringtwo different types and rates of binary bit stream datawhich is established by different power distribution of two

Hindawi Publishing CorporationMobile Information SystemsVolume 2016 Article ID 2398464 11 pageshttpdxdoiorg10115520162398464

2 Mobile Information Systems

orthogonal components of the carrier In recent years it hasbeen widely used in satellite digital communication networksor transmission and tracking systems between aircraft andgrounded processing systems

The present algorithms of PSK signalsrsquo modulation recog-nition are mostly based on decision theory and statisticpattern [1ndash3] The former [1] is usually analyzed via themaximum likelihood function A sufficient statistic for clas-sification is obtained and simplified and then a suitablethreshold is chosen for comparing with this statistical param-eter to achieve the modulation classification Based on thisgeneral principle some improved algorithms such as Quasi-Log Likelihood Ratio [4 5] (qLLR) Average Log LikelihoodFunction [6] (ALLF) Sequential Probability Ratio Test [7](SPRT) and other improvements were proposed by homeand abroad scholars However these methods require a lotof known parameters have a sensitive touch of symbolsrsquo syn-chrony andmodemismatch and lead to a huge computationwhich limit its own practical application heavily

According to different statistical classification charac-teristics the statistic pattern recognition methods can bedivided into a number of branches which are mainly basedon instant information in time domain or other transformingdomains spectral correlation [8] (eg high order cumulant)constellations chaos theory and fractal theory and otherproperties Extracted from the instant information of thereceived signal in time and frequency domains severalparameters are adopted in Traditional Digitally ModulatedSignal Recognition Algorithm [3] (DMRA) This methodhas a large correct recognition set which makes it suitablefor real-time data analysis However since each thresholdis heavily dependent on SNR DMRA cannot be effectivelyaccomplished in practice especially in the situations with lowSNR The algorithm derived from wavelet transform [9ndash11]can extract the signalsrsquo instant phase accurately Yet it is onlysuitable for pulse shaping signals and deteriorates seriouslyfor other kinds of signals Based on spectral correlationhigh order cumulant [12 13] has a great property of anti-noise However it is limited to its exponentially increasingcomputation as the signalsrsquo modulation order is bigger-than-equal eight and cannot achieve online real-time data analysiswhich limits its practical application heavily Besides themethods based on constellations [14 15] and fractal theory[16] and any other methods are restricted to various extentsto apply in practice

Inspired by data mining and image processing somenovel algorithms are proposed in the recent one or two yearsin noncooperative communication The approach based onclustering algorithms is a new trend inAutomaticModulationClassification (AMC) for digital modulations An advancedmethod derived from 119870-means algorithm is proposed byWeber et al [17] for Quadrature Amplitude Modulation(QAM) and PSK signals In this paper a novel utility functionwhich indicates the best fitting constellation diagram isdefined for the AMC decision Simulations and measure-ments in a real monitoring environment demonstrate itseffectiveness Xu et al [18] proposed a new method for phaseclustering Originated from mountain cluster algorithm [19]this technique can achieve multiple peaks in only one

Preprocessing Processing DemodulatorInputdata

Basebanddata

Outputdata

AMC

Algorithms Identifier

Figure 1 Receiver model

calculation process and avoid repeated peak cutting Onthe other hand it has about seven times computation timethan high order cumulant due to its principle of repeatedsearching Moreover the author did a fault analysis at thecondition of frequency offset existence Both the algorithmsabove are formulated in the following section as objects forperformance comparison

In view of these above problems this paper proposesan effective classifier The structure is as follows In thesecond part one traditional and two novel methods of recentworks on the PSK signal classification are formulated andtheir shortcomings are pointed out respectively In the thirdpart an improved method is proposed and elaborated forclassification Furthermore a robust estimator for frequencyoffset is presented and described in detail in the subsequentpart Necessary comparisons and simulations are performedand shown in the fifth part which demonstrate the feasibilityand effectiveness of proposed methods in this paper

2 Recent Works

AMC is a significant step after signal detection in a radiomonitoring environment and is fatal to the following processsuch as signalsrsquo demodulation and other stepsThe simplifiedblock diagram of the receiver is depicted in Figure 1 Afterseries of preprocessing the received signal in the receiveris transformed into a baseband signal It is identified forsignal modulation recognition which leads to a more effec-tive signal processing such as demodulation and decodingsubsequently

From the beginning of requirement in electronic mon-itoring and countermeasures lots of researches are studiedby home and aboard scholars Their proposed algorithmsand methods develop and improve the performance of NDAAMC of intercepted signals A traditional algorithm highorder cumulant and two novel methods advanced119870-meansalgorithm and phase clustering method are introduced andelaborated in this section They are adopted as the compari-son objections

21 High Order Cumulant Assume that the signal to beprocessed 119909(119899) is a 119896 order stationary random process withzero mean According to the basic theory of stochasticprocesses the 119896 order cumulant and 119896 order moment of 119909(119899)are both relative to time delay yet irrelevant to the 119899th timespot

Mobile Information Systems 3

For complex stationary random signal119883(119905) its high ordermoment can be unitedly expressed as

119872119901+119902119901

= 119864 [119883119901

(119883lowast

)119902

] (1)

where 119901 and 119902 are the index number of 119883 and 119883lowast respec-tively Several high order cumulants commonly used can berepresented by high order moment as follows

11986220

= 11987220

11986221

= 11987221

11986240

= 11987240

minus 31198722

20

11986241

= 11987241

minus 311987221

11987220

11986242

= 11987242

minus100381610038161003816100381611987220

10038161003816100381610038162

minus 21198722

21

11986260

= 11987240

minus 151198724

11987220

minus 301198723

20

(2)

In theory the algorithm of high order accumulation cancompletely eliminate the effect of Gaussian noise and bean ideal tool for signal processing under Gaussian noiseHowever this method is not suitable for online real-timesignal processing due to its amount of calculation Thehigher modulation order the intercepted signal has the morecomputation which increases exponentially it costs

22 Advanced K-Means Method The 119870-means algorithm isan optimal method for hard clustering when the number ofclusters 119870 in the input data 119909 is known Equation (3) is thecost formula where 119894 is the index and 119873 is the length of theinput data 119909

119869 =

119873

sum

119894=1

1003816100381610038161003816119909119894 minus 11991111989411989611987511987010038161003816100381610038162

(3)

The variable 119911119894119896

is the membership indicator which isequal to unity if the input data 119909

119894

belongs to the cluster 119896 andzero otherwise The membership indicator 119911

119894119896

is calculatedbased on the shortest distance of the input data 119909

119894

to theprototypes 119875

119870

as given in (4) where 119908119894

represents the index119896 of the winning prototype 119875

119896

for the input data 119909119894

120596119894

= argmin119875119870

(1003816100381610038161003816119909119894 minus 119875119870

1003816100381610038161003816) (4)

The 119870-means algorithm iteratively solves the clusteringproblem stated in (4) by alternating between a competitiveand a learning step In the competitive step the allocation ofthe input symbols 119909

119894

to the prototypes 119875119870

is carried out insuch a way that 119869 in (3) is minimised In the learning stepthe prototype positions are updated by calculating the meanvalue of the corresponding input symbols 119909

119894

A novel utility function 119865 is proposed byWeber that indi-cates the best fitting constellation diagram to the calculatedprototypes of the clustering algorithm

119865 = 1198652

1

(119862119878119870

) lowast 1198652

(119862119878119870

)

1198651

(119862119878119870

) =1

1 + 119869119862119878119870119870

1198652

(119862119878119870

) =1

1 + (1119870)sum119870

119896=1

1003816100381610038161003816119862119896 minus 1198751198961003816100381610038161003816

sum119870

119896=1

Φ(119875119896

)

119870

Φ (119875119896

) =

1 for119873

sum

119894=1

119911119894119896

gt 0

0 else

(5)

where 119869119862119878119870

is the result of the cost function in (3) for a specificconstellation pattern 119862

119878119870

of the considered modulation pool119872

119878119870

The variable119870 represents the number of prototypes orthemodulation order of119862

119878119870

and 119878 represents themodulationscheme 119862

119870

are the specific symbol positions of the constel-lation pattern 119862

119878119870

and 119875119870

are the calculated prototypesGenerally the first term of the utility function 119865

1

(119862119878119870

)

indicates the minimisation of cluster variances and thesecond factor119865

2

(119862119878119870

) evaluates the position of the calculatedprototypes 119875

119870

to the given constellation pattern 119862119878119870

andthe assignment of the input symbols 119909

119894

to the prototypesTo conclude the utility function 119865 = 1198652

1

(119862119878119870

) lowast 1198652

(119862119878119870

)

evaluates if all prototypes are covered by the input samplesand if the variance of the clusters and the EVM can beminimised For this reason this algorithm is named thehighest constellation pattern matching (HCPM) algorithm

A real monitoring environment is employed for field trialinWeberrsquos paper Eight signals including 4 kinds of QAM andMPSK signals respectively are introduced for identificationcapability demonstration Two-Threshold Sequential Algo-rithmic Scheme (TTSAS) [20] fuzzy algorithm [20] and the119870-centre algorithm are adopted for performance compari-son Simulations andmeasurements show the effectiveness ofthe proposed method than the other three counterparts

The idea gives a new direction for signal recognitionWhat is better it can be extended to the application of QAMsignal detection and identification However the simulationrunning time it needed is too long that is to say it isnot relatively suitable for real-time signal processing thansome other methods The simulation time of this method isdisplayed in the table in Simulation which shows that it hasa larger weakness as it compares to its counterparts

23 Phase ClusteringMethod Anothermethod based on datamining is phase clustering method proposed by Xu et al [18]Inspired by subtractive clustering method a novel clusteringfunction is derived for signalsrsquo classification Because themethod proposed in this paper is an improvement of thismethod the specific process is no longer described here

The carrier frequency offset is also considered in XursquospaperThe premise is that the received signal has been timingsynchronized When the carrier frequency offset Δ119891 satisfies

4 Mobile Information Systems

Δ119891119879119887

le 015 an approximate exact complex sequence can beobtained from [21] and the phase sequence can be expressedas

120593119903

(119896) = 120593119909

(119896) + 2120587119896Δ119891119879119887

+ 120593119899

(119896) (6)

where 119879119887

is the symbol period and 119896 = 1 119873 is the samplespot where 119873 is the sample number of each data package120593119899

(119896) is the noisersquos phase and the phase of received signal120593119909

(119896) is

120593119909

(119896) isin 2120587119898

119872+ 120579

0

119898 = 0 1 119872 minus 1 (7)

In order to eliminate the influence of frequency offset asmuch as possible a new sequence can be obtained by makingdifference to 120593

119909

(119896) that is

1205931015840

119903

(119896) = 120593119903

(119896 + 1) minus 120593119903

(119896)

= 120593119909

(119896 + 1) minus 120593119909

(119896) + 2120587Δ119891119879119887

+ 120593119899

(119896 + 1)

minus 120593119899

(119896) = 1205931015840

119909

(119896) + 1205931015840

119899

(119896)

(8)

where

1205931015840

119909

(119896) isin 2120587119898

119872+ 2120587Δ119891119879

119887

119898 = 0 1 119872 minus 1 (9)

The major idea of Xursquos method for reducing the influenceof frequency offset is to employ the difference of phase of thebaseband signal 1205931015840

119903

(119896) as the signal to be processed the sameas the condition without frequency offset to get the correctsignal modulation order A significant premise mentionedin his paper is that 1205931015840

119909

(119896) is a uniform distribution objectHowever in this case the effective part (9) is no longer subjectto uniform distribution which directly leads to the phaseclustering algorithm invalid

Four commonMPSK signals are introduced for classifica-tion performance in XUrsquos paper The correction classificationprobability is adopted as the measure index

In order to enhance the recognition efficiency this paperproposes an improved method for phase clustering whichcan effectively reduce the signal processing time withoutdegrading the classification performance In addition in viewof the carrier frequency offset this paper also gives a feasiblesolution for its estimation and correction

3 Proposed Method

In order to achieve a better NDA classification performancefor signals an improved phase clusteringmethod is proposedin this paper Then a robust estimation method is proposedfor frequency offset correction

31 Advanced Phase ClusteringMethod The received wave ofmodulated PSK signal can be generally expressed as

119903 (119905) = sum119899

119886119899

119892 (119905 minus 119899119879119904

) 119890119895(2120587119891119888119905+1205790) + 119899 (119905) (10)

where 119886119899

isin exp(minus119895(2120587119898119872)) 119898 = 0 1 119872 minus 1 is thesymbol sequence 119872 is the modulation order 119892(119905) is the

shaping pulse of shaping filter 119879119904

is the sample period 119891119888

isthe carrier frequency and 120579

0

is the carrier phase (Figure 3)119899(119905) is the white Gaussian noise with zero mean and 119873

0

varianceRoot Raised Cosine (RRC) filter is generally adopted for

signal shaping in wireless communication networks It is alsoconsidered in this paper Under the premise of carrier andtiming synchronization the output baseband signalrsquos phaseafter matching filter can be written as

120593119903

(119896) = 120593119909

(119896) + 1205790

+ 120593119899

(119896) 119896 = 1 2 119873 (11)

where 120593119909

(119896) denotes the phase sequence of transmittedsignal 120593

119899

(119896) denotes the phase sequence of noise and 119873 isthe sample number of each data package For PSK signalits phase 120593

119909

(119896) expressed as follows commonly obeys touniform distribution which means that there are 119872119873sample spots intensely around each constellation point if119872-order modulated signal is sampled at119873 points

120593119909

(119896) isin 2120587119898

119872 119898 = 0 1 119872 minus 1 (12)

In order tomeasure the radian distance between the phaseof sampled point and reference phase a distance function119863(120576) is defined with independent variable 120576 isin [0 2120587) here

119863 (120576) =

|120576| |120576| le 120587

2120587 minus |120576| |120576| gt 120587(13)

An advanced clustering function is proposed for phaseclustering and expressed as fractional form which has aremarkable reduction on computation as comparing to theindex form as

V119903

(120579) =

119873

sum

119896=1

1

1 + (119873120587)119863 (120593119903

(119896) minus 120579) (14)

where 120579 isin [0 2120587) denotes the phase variable as the referencephase

A division set of 120579 is installed as the reference phasefor phase clustering As is shown in formula (14) all thephase to be processed need to measure the distance to eachreference phase 120579 before clustering In fact the clusteringprocess is similar to a repeated search process Just because ofthis the computational quantity of phase clustering is totallydetermined by the division set of 120579 A suitable division cannot only reduce the calculation amount of this method butalso enhance the correction rate of clustering The uniformdistance from 0 to 2120587 is a commonmethod of reference phasesegmentation

For simplicity an approximation is used to reduce calcu-lation amount When119863(120593

119903

(119896) minus 120579) ge 9120587119873

1

1 + (119873120587)119863 (120593119903

(119896) minus 120579)le 01 (15)

And it can be regarded as

1

1 + (119873120587)119863 (120593119903

(119896) minus 120579)asymp 0 (16)

Mobile Information Systems 5

When a baseband PSK signal is to be processed the advancedphase clustering (APC) function can be expressed as

V119903

(120579) =

119873

sum

119896=1

1

1 + (119873120587)119863 (120593119909

(119896) + 1205790

+ 120593119899

(119896) minus 120579) (17)

Assume that 120593119909

(119896) is distributed independently and hasan equal occurrence probability Since 120593

119899

(119896) is a stationaryGaussian phase noise formula (17) can transform into

V119903

(120579)

asymp119873

119872

119872minus1

sum119898=0

1

1 + (119873120587)119863 (2120587119898119872 + 1205790

+ 1205931015840119899

(119898) minus 120579)

(18)

Note that the necessary condition of the upper equationis the uniform distribution of the transmitted signal phasewithout noise In the ideal constellation there are approxi-mate119873119872 sample points distributed on the location of eachconstellation if the sample number of the received signalwhich has119872 modulation order is 119873 Otherwise the aboveequation is not established anymore

Due to the particularity of the distance function 119863(120576)has a periodicity of 2120587 On the other hand the independentvariable 120579 in the clustering function (14) is only related to thedistance function which leads to the fact that the clusteringfunction also has the periodicity of 2120587

The character of periodicity of formula (14) is given indetail When 120579 + 2120587119872 lt 2120587 the periodicity of clusteringfunction is formulated and elaborated in formula (19) It alsocan be proved as the sameway that V

119903

(120579+2120587119872minus2120587) = V119903

(120579)if 120579 + 2120587119872 gt 2120587

V119903

(120579 +2120587

119872) =

119873

119872

sdot

119872minus1

sum119898=0

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus (120579 + 2120587119872))

=119873

119872(

1

1 + (119873120587)119863 (120601 minus (120579 + 2120587119872))

+

119872minus1

sum119898=2

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus (120579 + 2120587119872))

+1

1 + (119873120587)119863 (2120587119872 + 120601 minus (120579 + 2120587119872)))

=119873

119872(

1

1 + (119873120587)119863 (2120587 + 120601 minus (120579 + 2120587119872))

+

119872minus2

sum119898=1

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus 120579)

+1

1 + (119873120587)119863 (120601 minus 120579)) =

119873

119872

sdot

119872minus1

sum119898=0

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus 120579)= V

119903

(120579)

(19)

The expression of clustering function V119903

(120579) is a periodicalfunction with

119879V =2120587

119872 (20)

Since the periodic signal has special spectral propertiesin frequency domain the period of clustering functioncan be extracted easily through Fast Fourier Transform(FFT) 119881

120579

(120596) = FFT[V119903

(120579)] The certain frequency whichis corresponding to the place of maximum value of itsFourier transform result indicates 119879V Modulation order 119872can be calculated through the above equation then signalsrsquoclassification is achieved More favorably carrier phase 120579

0

is irrelevant to this method for 119879V which means that thisproposed method is also robust to signalrsquos constellationrotation

If deep recognition requirements are needed for PSKsignals with the same modulation order lots of statisticsparameters can be chosen and employed For examplethere are two sets of data 4PSK and OQPSK 8PSK and(1205874)DQPSK Envelope entropy of differential phase of thebaseband signals can be introduced to distinguish themrespectively The recognition performance is certainly deter-mined by the introduced statistics parameters yet regardlessof the APC method

The APC method has several advantages

(1) Since it is derived from the coding characters ratherthan statistical properties the direct influence of SNRis reduced

(2) As an optimization algorithm of multiple peakssearching it achieves all the peaks in one calculationprocess and avoids repeated peak cuttings

(3) Fraction is used instead of exponential function inthe clustering function so that the calculation processis simplified which leads to a much lower computa-tional quantity

32 Frequency Offset Correction In the digital communica-tion system the carrier frequency offset is often introducedby the difference between the receiver and the transmitteroscillator and also caused by the Doppler frequency shiftwhich is brought by the channel nonlinearity and phase noiseIn the wireless network especially the electronic monitor-ing and other noncooperative communication systems theaccuracy of frequency offset estimation directly affects theperformance of the receiver

6 Mobile Information Systems

In Xursquos method mentioned in last section phase cluster-ing algorithm is directly adopted with the difference phase ofreceived signal However the difference phase of the effectivepart of signal which carries messages is no longer uniformdistribution Only frequency offset estimation and correctioncan be considered in this case to eliminate the impact offrequency offset as much as possible

The frequency offset estimations of the Fitz and LampRalgorithms are directly achieved via the weighted summationof the autocorrelation of the signal This means that thesetwo algorithms and the improvedmethods based upon themare all heavily affected by the correlation interval on theestimated range unless the correlation interval achieves itsmaximum value of sampled number 119873 However in thiscase the calculation amount increases dramatically especiallywhen 119873 is large For this particular reason most of theimproved methods are derived from Kayrsquos algorithm Theautocorrelation function of the processing signal is used inthe MampM algorithm used in Kayrsquos and LampWrsquos algorithmsfor weakening the influence brought on by phase noiseHowever the addition operation of the autocorrelationrsquosphase introduces the phase folding problem An objectionphase of the baseband signal which has a real value near minus120587or120587may be changed to a completely different value under theinfluence of noise and this leads to an error in the frequencyoffset estimation result The WNALP algorithm is derivedfrom the MampM algorithm which solves the phase foldingproblem and broadens the estimation range remarkablyHowever the signal in real noncooperative environmentsis usually intercepted under a low SNR due to its specialcondition which causes great difficulties in subsequent signalprocessing

In order to reduce the thresholdsrsquo effect and improvethe unbalance between estimation accuracy and estimationrange of frequency offset under low SNR an advancedNDA estimator based on the weighted summation of thedifferential phase of the autocorrelation is proposed in thispaper

Assume that timing synchronization is accomplishedThe baseband signal sequence with frequency offset 119909(119896) isexpressed as

119909 (119896) = 119888119896

exp119895(2120587119891Δ119896119879119904+120579) + 119899 (119896) (21)

where 119888119896

(119896 = 1 2 119873) is the modulated symbol sequencefrom the transmitting end 119873 is the number of samplingpoints of the selected signal segment in the receiving end119891Δ

is the unknown frequency offset to be estimated 119879119904

isthe sample period and 120579 is a random initial carrier phasewhich follows the uniformdistribution in the range of [0 2120587)Usually the channel noise of the communication system119899(119896) is considered to be random complex additive Gaussiannoise with zeromean and bilateral spectral density119873

0

2 Wenormalize its amplitude as

(119896) =119909 (119896)

|119909 (119896)| 119896 = 1 2 119873 (22)

Then under the hypothesis of 119899(119896) ≫ 1 for a large enoughSNR

(119896) ≃ 119890119895(2120587119896119891Δ119879119904+120579+

120573(119896))

(23)

where (119896) is also a Gaussian process with zero meanThe autocorrelation is defined as

1198770

(119898) =

119873

sum

119896=119898+1

(119896) lowast

(119896 minus 119898) 119898 = 1 2 119871119903

(24)

where (119896) = 119876

(119896) is the normalized baseband signalraised to the power of 119876 and 119871

119903

is the set maximumcorrelation interval Using the same principle as above theautocorrelation function can be continuously transformed as

1198770

(119898) ≃ 119890119895(2120587119898119891Δ119879119904+(119898)) (25)

where (119898) is also a Gaussian process with zeromeanWe seethat

ang1198770

(119898) 119877lowast

0

(119898 minus 1) = 2120587119891Δ

119879119904

+ (119898) + (119898 minus 1)

2 le 119898 le 119871119903

(26)

We define Δ1205930119877(119898)

≜ ang1198770

(119898)119877lowast

0

(119898minus 1) According to theprinciple of Kayrsquos algorithm an objective function can be setas

J0

= (Δ1205930 minus 2120587119891Δ119879119904e)119879Cminus1 (Δ1205930 minus 2120587119891Δ119879119904e) (27)

where Δ1205930 = [Δ1205930119877(1) Δ1205930119877(2) Δ1205930119877(119871119903)]119879 The estimated

value of the frequency offset Δ

is obtained when theobjective function J

0

obtains its minimum value So thenormalized weighted correlation linear estimator proposedcan be expressed as

Δ

=1

2120587119876119879119904

sdot

119871119903

sum119898=2

1205960

(119898) sdot arg [1198770

(119898) 119877lowast

0

(119898 minus 1)] (28)

where 1205960

is the weight of the differential phase

1205960

(119898) =3 [(119873 minus 119898) (119873 minus 119898 + 1) minus 119871

119903

(119873 minus 119871119903

)]

119871119903

(41198712119903

minus 6119871119903

119873 + 31198732 minus 1) (29)

The normalized baseband signal is considered to bethe signal to be processed which effectively weakens theperformance loss resulting from the nonlinear operation ofraising to a power of 119876 The weighted summation of thedifferential phase of the autocorrelation also decreases theinfluence of noise effectively compared to the method ofargument operation after weighting the conjugate differenceof the autocorrelation Thus it provides a better estimationaccuracy and is described in Kayrsquos paper [5]The difference ofautocorrelation is a great improvement which can make theestimation range independent of the maximum correlationinterval 119871

119903

and solve the phase folding problem comparedto Fitzrsquos and the LampR algorithm and the improved methodsbased upon them Meanwhile the proposed method in this

Mobile Information Systems 7

Table 1 Simulation time for order classification

Simulation time (s)HOMmethod 00158AKMCmethod 04523PC method 00720APC method 00345

paper has the same estimation range as its counterpartWNALP algorithm Importantly the large estimation vari-ance of the WNALP algorithm under low SNR conditionsis improved which effectively balances the trade-off betweenestimation accuracy and estimation range under low SNR inthe process of frequency offset estimation

4 Simulation

Computer simulations are performed to test the performanceof the methods proposed in this paper Considering thebackground of electronic monitoring and countermeasurein satellite communication and wireless communication net-works the simulation set contains six common modulationtypes of PSK signals BPSK QPSK 8PSK 16PSK OQPSK(1205874)DQPSK and UQPSK Each simulation result is theaverage of 1000 independent runs Because of the specialenvironment we assumed no a priori knowledge of inter-cepted signal is assumed for all the experiments

Regular communication equipment and environment areadopted for these simulations The signals are shaped byraised root cosine filter with its roll-off factor 120572 = 022 Thereceived intercepted signal is sampled 119873 = 512 points fortest with Sample frequency 119891

119904

= 20MHz We suppose thatthe symbol rate119873

119904

has been estimated accurately by a certainalgorithm and the sample number in per symbol period is119873119887

= 119873119904

lowast 119873119891119904

= 32 Additive white Gaussian noise isconsidered in this situationMoreover channel effects such asfading andmultipath propagation are ignored andwe assumethat perfect time and frequency synchronization have beenachievedThe SNR in this paper is defined as119864

119904

1198730

where119864119904

is the energy per symbol and1198730

is the power spectral densityof the Gaussian noise

A common method based on four-order cumulant(HOC) and two new ways derived from data miningadvanced 119870-means clustering (AKMC) and phase clustering(PC) are adopted for performance comparison of signalclassification Classification capabilities and simulation timesin a single run of the subroutines are shown in Figure 2 andTable 1 respectively

The same set of signal data to be processed are introducedin four subroutines respectively for classification perfor-mance and simulation time comparison Except for four-order cumulant the other three methods present obviouscorrect classification rate trends and a large SNR tolerancefor all the involved signals The 16PSK signal can be correctlyclassified from approximate 2 dB and the other six signalshave larger SNR tolerances less than minus5 dB Even so they aredistinguished clearly via simulation time table It is shown inTable 1 that PC method and AKMCmethod both cost two or

more times simulation time than APC method proposed inthis paper If the modulation order of signal to be processedis 16 the order needs to be chosen as 16 for accumulation inHOC algorithm However the computation amount of thisalgorithm increases exponentially It is a predictable resultthat its simulation time could be bigger than or equal tothe time of APC method Due to the instability of the APCalgorithm at the low SNRs few wrong judgements of thesignalrsquos modulation order appear That is the reason why theorder of 16PSK signal gets 17 during 1sim2 dB

In summary APC method proposed in this paper hasa better classification capability than its counterparts andgives a new guidance for practical signal processing Orderclassification result and correct classification rate by APCmethod are separately displayed in Figures 4-5

Frequency offset directly impacts on the performance ofsignal classification In order to verify the effectiveness ofthe proposed NWALPmethod theWNALP algorithm fromwhich the proposed method in this paper is derived wasselected for comparison in this paper

Let us assume that the signal to be processed is a QPSKsignal with additive Gaussian noise The number of samplepoints is set as 119873 = 256 and the sampling frequency isnormalized to the unit as 119891

119904

= 1 The correlation intervalof autocorrelation is set as 119871

119903

= 1198732 Each simulation ofestimation accuracy and estimation range for the frequencyoffset was run at least 100 times The estimation varianceis adopted as the measure of estimation accuracy TheMCRLB [22] is also calculated as an absolute measure of thetheoretical optimal valuation

MCRLB = 3

21205872119873(1198732 minus 1)sdot1

119864119904

1198730

(30)

The performance of the proposed method compared tothe abovementioned methods is shown in Figure 5 under anormalized frequency offset 119891

Δ

= 0001 as the SNR changeswithin the range ofminus15sim20 dB by 1 dB steps It can be seen thateven when the frequency offset is set at a smaller value theWNALPalgorithm still shows a poor estimation performanceof about 10minus2 under low SNRs This means that when thefrequency offset is small the error of the algorithm may beof the same order of magnitude as the frequency offset itselfSuch a large estimation error leads to a complete failure ofthe algorithm However it can be obviously seen that theestimation accuracy of the proposed method remains steadyin the vicinity of 10minus4 under low SNR conditions and hasan improved estimation accuracy of at least two orders ofmagnitude compared to the original WNALP algorithm Onthe other hand the estimation error of the proposed methodrapidly decreases to a magnitude near the MCRLB Even asthe SNR increases it remains steady at approximately 10minus7due to the SNR threshold effect

The estimation range of the carrier frequency offset isusually observed under large SNRs in order to obtain widerand more accurate bounds When SNR = 15 dB the esti-mated ranges of the chosen algorithms were simulated asshown in Figure 6 As can be seen the proposed NWALPmethod can achieve the same frequency offset estimation

8 Mobile Information Systems

0 5 10 15 20 25minus5SNR (dB)

0

02

04

06

08

1

CORR

CORR by 4-order cumulants CORR by advanced K-means clustering

CORR by phase clustering

0 5 10 15 20 25minus5

SNR (dB)

0

02

04

06

08

1

CORR

CORR by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5

SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

minus5 5 10 15 20 250SNR (dB)

0

02

04

06

08

1

CORR

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 2 Comparison of correct order recognition rate

range asWNALP which has proved to be a better choice for alarge estimation range than other algorithmsThis estimationrange cannot be increased even if the SNR increases It canbe seen that the proposed method in this paper can achieve alarge frequency offset estimation range

Figure 7 vividly shows the difference of constellationchanges before and after frequency offset correction bytwo distinct colors Signal with frequency offset make itsconstellation is displayed as a blue ring which cannot catchany constellation point However the approximate originalappearance is displayed after frequency offset correction withred It can be seen that the proposedmethod in this paper hasa remarkable effectiveness under 0 dB

5 Conclusion

This paper presents a robust classifier for NDA recognition innoncooperative wireless environment Nonsupervised clus-tering of the signal phase is achieved bymeasuring the radian

distance between each signal phase and the reference phaseThis method proposed optimizes the clustering functionand reduces the computation sharply Moreover frequencyoffset is considered and an advanced method is proposedfor frequency offset estimation and correction First a nor-malization of the baseband signal is performed After thenonlinear operation of raising the signal to a power of 119876 theestimate of frequency offset is obtained via the weighted sum-mation of the differential phase of the signalrsquos autocorrelationThis method balances estimation accuracy and range underlow SNR conditions which sharply improves the estimationaccuracy without shrinking the maximum estimation rangeeven if the SNR is as low as minus15 dB Seven common PSKsignals are adopted for simulation experiments The classi-fication performance and the estimation and correlation forfrequency offset are displayed and demonstrated with severalsimulation result figures which illustrate their feasibility andpractice

Mobile Information Systems 9

Order classification by advanced phase clustering

0 5 10 15 20 25minus5SNR (dB)

0

2

4

6

8

10

12

14

16

18

20

Ord

er

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 3 Order classification by advanced phase clustering

Correct order recognition rate by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 4 Correct order recognition rate by advanced phase cluster-ing

Generally this classifier which is derived from datamining and image processing has a guiding value for signalprocessing in electronic surveillance and electronic counter-measure of communication networks Further work such asthe initial optimization of clustering centers 120579 and multipath

Estimation of frequency offset (Δf = 0001)

NDA WNALPPROPOSEDMCRLB

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

10minus2

Varia

nce o

f fre

quen

cy o

ffset

estim

atio

n

minus10 minus5 0 5 10 15 20minus15

SNR (dB)

Figure 5 Comparison of estimation variance of frequency offset

NDA WNALPPROPOSEDMCRLB

Estimation of frequency offset (SNR = 15 dB)

minus005 0 005 01 015minus01

Frequency offset (normalized)

minus01

minus005

0

005

01

015

Mea

n va

lues

of e

stim

ated

freq

uenc

y off

set

Figure 6 Estimated range comparison

and Rayleigh channel and other practical problems is con-sidered for applications

Competing Interests

The authors declare that they have no competing interests

10 Mobile Information Systems

BPSK

minus1

0

1

0 2

05

15

minus05

minus15minus2

QPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

8PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

16PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Without FOCWith FOC

Without FOCWith FOC

Without FOCWith FOC

UQPSK

0 1

0

05

1

minus05

minus1minus1

PI4DQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

OQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Figure 7 Comparison of frequency offset correction

Acknowledgments

The authors would like to thank the support of FundamentalResearch Funds for the Central Universities (designationNSFC61371184)

References

[1] F F Liedtke ldquoComputer simulation of an automatic classifica-tion procedure for digitally modulated communication signalswith unknown parametersrdquo Signal Processing vol 6 no 4 pp311ndash323 1984

[2] Q Shi and Y Karasawa ldquoAutomatic modulation identificationbased on the probability density function of signal phaserdquo IEEETransactions on Communications vol 60 no 4 pp 1033ndash10442012

[3] A K Nandi and E E Azzouz ldquoAlgorithms for automatic mod-ulation recognition of communication signalsrdquo IEEE Transac-tions on Communications vol 46 no 4 pp 431ndash436 1998

[4] K Kim andA Polydoros ldquoDigitalmodulation classification theBPSK versus QPSK caserdquo in Proceedings of the IEEE MilitaryCommunications Conference Conference Record 21st CenturyMilitary CommunicationsmdashWhatrsquos Possible (MILCOM rsquo88) pp431ndash436 San Diego Calif USA October 1988

[5] K Kim and A Polydoros ldquoOn the detection and classificationof quadrature digital modulations in broad-band noiserdquo IEEETransactions on Communications vol 38 no 8 pp 1199ndash12111990

[6] C S Long K M Chugg and A Polydoros ldquoFurther results inlikelihood classification of QAM signalsrdquo in Proceedings of theIEEE Military Communications Conference (MILCOM rsquo94) vol1 pp 57ndash61 IEEE Fort Monmouth NJ USA October 1994

[7] Y-C Lin and C-C J Kuo ldquoClassification of quadrature ampli-tude modulated (QAM) signals via sequential probability ratiotest (SPRT)rdquo Signal Processing vol 60 no 3 pp 263ndash280 1997

[8] W A Gardner and C M Spooner ldquoCyclic spectral analysis forsignal detection and modulation recognitionrdquo in Proceedings ofthe IEEEMilitary Communications Conference pp 419ndash424 SanDiego Calif USA October 1988

[9] L Hong and K C Ho ldquoIdentification of digital modulationtypes using the wavelet transformrdquo in Proceedings of the Mili-tary Communications Conference (MILCOM rsquo99) pp 427ndash431Atlantic City NJ USA November 1999

[10] K C Ho W Prokopiw and Y T Chan ldquoModulation iden-tification of digital signals by the wavelet transformrdquo IEEProceedingsmdashRadar Sonar and Navigation vol 147 no 4 pp169ndash176 2000

Mobile Information Systems 11

[11] C Cui H Li and J Yu ldquoMPSKmodulation classification basedon morlet transformrdquo Communication Technology vol 43 no3 pp 10ndash12 2010

[12] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009

[13] J-F Wang Y Yue and J Yao ldquoA MPSK recognition methodbased on high order cumulantsrdquo Communication Technologyvol 9 no 43 pp 4ndash6 2010

[14] J-X Wang and H Song ldquoDigital modulation recognitionbased on constellation diagramrdquo Journal of China Institute ofCommunications vol 25 no 6 pp 166ndash173 2004

[15] R Ghunhui W Ping and X Xianci ldquoClassification of MPSKsignals using the distribution of in-phase and quadraturesignalsrdquo Signal Processing vol 22 no 6 pp 787ndash790 2006

[16] T-J Lu S-B Guo and X-C Xiao ldquoFractal characteristicsresearch of modulated signalsrdquo Science in China Series ETechnological Sciences vol 31 no 6 pp 508ndash510 2001

[17] C Weber M Peter and T Felhauer ldquoAutomatic modulationclassification technique for radio monitoringrdquo Electronics Let-ters vol 51 no 10 pp 794ndash796 2015

[18] J-F Xu F-P Wang and Z-J Wang ldquoMPSK modulationrecognition method based on phase clusteringrdquo Journal ofCircuits and Systems vol 16 no 5 pp 55ndash58 2011

[19] X-Y Chen Y-F Min L-R Zheng and L Yang ldquoQuick moun-tain clustering algorithmrdquo Application Research of Computersvol 25 no 7 pp 2043ndash2045 2008

[20] N Ahmadi ldquoUsing fuzzy clustering and TTSAS algorithmfor modulation classification based on constellation diagramrdquoEngineering Applications of Artificial Intelligence vol 23 no 3pp 357ndash370 2010

[21] D C Rife and R R Boorstyn ldquoSingle-tone parameter esti-mation from discrete-time observationsrdquo IEEE Transactions onInformation Theory vol IT-20 no 5 pp 591ndash598 1974

[22] A B Awoseyila C Kasparis and B G Evans ldquoImproved singlefrequency estimation with wide acquisition rangerdquo ElectronicsLetters vol 44 no 3 pp 245ndash247 2008

Submit your manuscripts athttpwwwhindawicom

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International Journal of

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Distributed Sensor Networks

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Advances in

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Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

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Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

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International Journal of

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ArtificialNeural Systems

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RoboticsJournal of

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Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

2 Mobile Information Systems

orthogonal components of the carrier In recent years it hasbeen widely used in satellite digital communication networksor transmission and tracking systems between aircraft andgrounded processing systems

The present algorithms of PSK signalsrsquo modulation recog-nition are mostly based on decision theory and statisticpattern [1ndash3] The former [1] is usually analyzed via themaximum likelihood function A sufficient statistic for clas-sification is obtained and simplified and then a suitablethreshold is chosen for comparing with this statistical param-eter to achieve the modulation classification Based on thisgeneral principle some improved algorithms such as Quasi-Log Likelihood Ratio [4 5] (qLLR) Average Log LikelihoodFunction [6] (ALLF) Sequential Probability Ratio Test [7](SPRT) and other improvements were proposed by homeand abroad scholars However these methods require a lotof known parameters have a sensitive touch of symbolsrsquo syn-chrony andmodemismatch and lead to a huge computationwhich limit its own practical application heavily

According to different statistical classification charac-teristics the statistic pattern recognition methods can bedivided into a number of branches which are mainly basedon instant information in time domain or other transformingdomains spectral correlation [8] (eg high order cumulant)constellations chaos theory and fractal theory and otherproperties Extracted from the instant information of thereceived signal in time and frequency domains severalparameters are adopted in Traditional Digitally ModulatedSignal Recognition Algorithm [3] (DMRA) This methodhas a large correct recognition set which makes it suitablefor real-time data analysis However since each thresholdis heavily dependent on SNR DMRA cannot be effectivelyaccomplished in practice especially in the situations with lowSNR The algorithm derived from wavelet transform [9ndash11]can extract the signalsrsquo instant phase accurately Yet it is onlysuitable for pulse shaping signals and deteriorates seriouslyfor other kinds of signals Based on spectral correlationhigh order cumulant [12 13] has a great property of anti-noise However it is limited to its exponentially increasingcomputation as the signalsrsquo modulation order is bigger-than-equal eight and cannot achieve online real-time data analysiswhich limits its practical application heavily Besides themethods based on constellations [14 15] and fractal theory[16] and any other methods are restricted to various extentsto apply in practice

Inspired by data mining and image processing somenovel algorithms are proposed in the recent one or two yearsin noncooperative communication The approach based onclustering algorithms is a new trend inAutomaticModulationClassification (AMC) for digital modulations An advancedmethod derived from 119870-means algorithm is proposed byWeber et al [17] for Quadrature Amplitude Modulation(QAM) and PSK signals In this paper a novel utility functionwhich indicates the best fitting constellation diagram isdefined for the AMC decision Simulations and measure-ments in a real monitoring environment demonstrate itseffectiveness Xu et al [18] proposed a new method for phaseclustering Originated from mountain cluster algorithm [19]this technique can achieve multiple peaks in only one

Preprocessing Processing DemodulatorInputdata

Basebanddata

Outputdata

AMC

Algorithms Identifier

Figure 1 Receiver model

calculation process and avoid repeated peak cutting Onthe other hand it has about seven times computation timethan high order cumulant due to its principle of repeatedsearching Moreover the author did a fault analysis at thecondition of frequency offset existence Both the algorithmsabove are formulated in the following section as objects forperformance comparison

In view of these above problems this paper proposesan effective classifier The structure is as follows In thesecond part one traditional and two novel methods of recentworks on the PSK signal classification are formulated andtheir shortcomings are pointed out respectively In the thirdpart an improved method is proposed and elaborated forclassification Furthermore a robust estimator for frequencyoffset is presented and described in detail in the subsequentpart Necessary comparisons and simulations are performedand shown in the fifth part which demonstrate the feasibilityand effectiveness of proposed methods in this paper

2 Recent Works

AMC is a significant step after signal detection in a radiomonitoring environment and is fatal to the following processsuch as signalsrsquo demodulation and other stepsThe simplifiedblock diagram of the receiver is depicted in Figure 1 Afterseries of preprocessing the received signal in the receiveris transformed into a baseband signal It is identified forsignal modulation recognition which leads to a more effec-tive signal processing such as demodulation and decodingsubsequently

From the beginning of requirement in electronic mon-itoring and countermeasures lots of researches are studiedby home and aboard scholars Their proposed algorithmsand methods develop and improve the performance of NDAAMC of intercepted signals A traditional algorithm highorder cumulant and two novel methods advanced119870-meansalgorithm and phase clustering method are introduced andelaborated in this section They are adopted as the compari-son objections

21 High Order Cumulant Assume that the signal to beprocessed 119909(119899) is a 119896 order stationary random process withzero mean According to the basic theory of stochasticprocesses the 119896 order cumulant and 119896 order moment of 119909(119899)are both relative to time delay yet irrelevant to the 119899th timespot

Mobile Information Systems 3

For complex stationary random signal119883(119905) its high ordermoment can be unitedly expressed as

119872119901+119902119901

= 119864 [119883119901

(119883lowast

)119902

] (1)

where 119901 and 119902 are the index number of 119883 and 119883lowast respec-tively Several high order cumulants commonly used can berepresented by high order moment as follows

11986220

= 11987220

11986221

= 11987221

11986240

= 11987240

minus 31198722

20

11986241

= 11987241

minus 311987221

11987220

11986242

= 11987242

minus100381610038161003816100381611987220

10038161003816100381610038162

minus 21198722

21

11986260

= 11987240

minus 151198724

11987220

minus 301198723

20

(2)

In theory the algorithm of high order accumulation cancompletely eliminate the effect of Gaussian noise and bean ideal tool for signal processing under Gaussian noiseHowever this method is not suitable for online real-timesignal processing due to its amount of calculation Thehigher modulation order the intercepted signal has the morecomputation which increases exponentially it costs

22 Advanced K-Means Method The 119870-means algorithm isan optimal method for hard clustering when the number ofclusters 119870 in the input data 119909 is known Equation (3) is thecost formula where 119894 is the index and 119873 is the length of theinput data 119909

119869 =

119873

sum

119894=1

1003816100381610038161003816119909119894 minus 11991111989411989611987511987010038161003816100381610038162

(3)

The variable 119911119894119896

is the membership indicator which isequal to unity if the input data 119909

119894

belongs to the cluster 119896 andzero otherwise The membership indicator 119911

119894119896

is calculatedbased on the shortest distance of the input data 119909

119894

to theprototypes 119875

119870

as given in (4) where 119908119894

represents the index119896 of the winning prototype 119875

119896

for the input data 119909119894

120596119894

= argmin119875119870

(1003816100381610038161003816119909119894 minus 119875119870

1003816100381610038161003816) (4)

The 119870-means algorithm iteratively solves the clusteringproblem stated in (4) by alternating between a competitiveand a learning step In the competitive step the allocation ofthe input symbols 119909

119894

to the prototypes 119875119870

is carried out insuch a way that 119869 in (3) is minimised In the learning stepthe prototype positions are updated by calculating the meanvalue of the corresponding input symbols 119909

119894

A novel utility function 119865 is proposed byWeber that indi-cates the best fitting constellation diagram to the calculatedprototypes of the clustering algorithm

119865 = 1198652

1

(119862119878119870

) lowast 1198652

(119862119878119870

)

1198651

(119862119878119870

) =1

1 + 119869119862119878119870119870

1198652

(119862119878119870

) =1

1 + (1119870)sum119870

119896=1

1003816100381610038161003816119862119896 minus 1198751198961003816100381610038161003816

sum119870

119896=1

Φ(119875119896

)

119870

Φ (119875119896

) =

1 for119873

sum

119894=1

119911119894119896

gt 0

0 else

(5)

where 119869119862119878119870

is the result of the cost function in (3) for a specificconstellation pattern 119862

119878119870

of the considered modulation pool119872

119878119870

The variable119870 represents the number of prototypes orthemodulation order of119862

119878119870

and 119878 represents themodulationscheme 119862

119870

are the specific symbol positions of the constel-lation pattern 119862

119878119870

and 119875119870

are the calculated prototypesGenerally the first term of the utility function 119865

1

(119862119878119870

)

indicates the minimisation of cluster variances and thesecond factor119865

2

(119862119878119870

) evaluates the position of the calculatedprototypes 119875

119870

to the given constellation pattern 119862119878119870

andthe assignment of the input symbols 119909

119894

to the prototypesTo conclude the utility function 119865 = 1198652

1

(119862119878119870

) lowast 1198652

(119862119878119870

)

evaluates if all prototypes are covered by the input samplesand if the variance of the clusters and the EVM can beminimised For this reason this algorithm is named thehighest constellation pattern matching (HCPM) algorithm

A real monitoring environment is employed for field trialinWeberrsquos paper Eight signals including 4 kinds of QAM andMPSK signals respectively are introduced for identificationcapability demonstration Two-Threshold Sequential Algo-rithmic Scheme (TTSAS) [20] fuzzy algorithm [20] and the119870-centre algorithm are adopted for performance compari-son Simulations andmeasurements show the effectiveness ofthe proposed method than the other three counterparts

The idea gives a new direction for signal recognitionWhat is better it can be extended to the application of QAMsignal detection and identification However the simulationrunning time it needed is too long that is to say it isnot relatively suitable for real-time signal processing thansome other methods The simulation time of this method isdisplayed in the table in Simulation which shows that it hasa larger weakness as it compares to its counterparts

23 Phase ClusteringMethod Anothermethod based on datamining is phase clustering method proposed by Xu et al [18]Inspired by subtractive clustering method a novel clusteringfunction is derived for signalsrsquo classification Because themethod proposed in this paper is an improvement of thismethod the specific process is no longer described here

The carrier frequency offset is also considered in XursquospaperThe premise is that the received signal has been timingsynchronized When the carrier frequency offset Δ119891 satisfies

4 Mobile Information Systems

Δ119891119879119887

le 015 an approximate exact complex sequence can beobtained from [21] and the phase sequence can be expressedas

120593119903

(119896) = 120593119909

(119896) + 2120587119896Δ119891119879119887

+ 120593119899

(119896) (6)

where 119879119887

is the symbol period and 119896 = 1 119873 is the samplespot where 119873 is the sample number of each data package120593119899

(119896) is the noisersquos phase and the phase of received signal120593119909

(119896) is

120593119909

(119896) isin 2120587119898

119872+ 120579

0

119898 = 0 1 119872 minus 1 (7)

In order to eliminate the influence of frequency offset asmuch as possible a new sequence can be obtained by makingdifference to 120593

119909

(119896) that is

1205931015840

119903

(119896) = 120593119903

(119896 + 1) minus 120593119903

(119896)

= 120593119909

(119896 + 1) minus 120593119909

(119896) + 2120587Δ119891119879119887

+ 120593119899

(119896 + 1)

minus 120593119899

(119896) = 1205931015840

119909

(119896) + 1205931015840

119899

(119896)

(8)

where

1205931015840

119909

(119896) isin 2120587119898

119872+ 2120587Δ119891119879

119887

119898 = 0 1 119872 minus 1 (9)

The major idea of Xursquos method for reducing the influenceof frequency offset is to employ the difference of phase of thebaseband signal 1205931015840

119903

(119896) as the signal to be processed the sameas the condition without frequency offset to get the correctsignal modulation order A significant premise mentionedin his paper is that 1205931015840

119909

(119896) is a uniform distribution objectHowever in this case the effective part (9) is no longer subjectto uniform distribution which directly leads to the phaseclustering algorithm invalid

Four commonMPSK signals are introduced for classifica-tion performance in XUrsquos paper The correction classificationprobability is adopted as the measure index

In order to enhance the recognition efficiency this paperproposes an improved method for phase clustering whichcan effectively reduce the signal processing time withoutdegrading the classification performance In addition in viewof the carrier frequency offset this paper also gives a feasiblesolution for its estimation and correction

3 Proposed Method

In order to achieve a better NDA classification performancefor signals an improved phase clusteringmethod is proposedin this paper Then a robust estimation method is proposedfor frequency offset correction

31 Advanced Phase ClusteringMethod The received wave ofmodulated PSK signal can be generally expressed as

119903 (119905) = sum119899

119886119899

119892 (119905 minus 119899119879119904

) 119890119895(2120587119891119888119905+1205790) + 119899 (119905) (10)

where 119886119899

isin exp(minus119895(2120587119898119872)) 119898 = 0 1 119872 minus 1 is thesymbol sequence 119872 is the modulation order 119892(119905) is the

shaping pulse of shaping filter 119879119904

is the sample period 119891119888

isthe carrier frequency and 120579

0

is the carrier phase (Figure 3)119899(119905) is the white Gaussian noise with zero mean and 119873

0

varianceRoot Raised Cosine (RRC) filter is generally adopted for

signal shaping in wireless communication networks It is alsoconsidered in this paper Under the premise of carrier andtiming synchronization the output baseband signalrsquos phaseafter matching filter can be written as

120593119903

(119896) = 120593119909

(119896) + 1205790

+ 120593119899

(119896) 119896 = 1 2 119873 (11)

where 120593119909

(119896) denotes the phase sequence of transmittedsignal 120593

119899

(119896) denotes the phase sequence of noise and 119873 isthe sample number of each data package For PSK signalits phase 120593

119909

(119896) expressed as follows commonly obeys touniform distribution which means that there are 119872119873sample spots intensely around each constellation point if119872-order modulated signal is sampled at119873 points

120593119909

(119896) isin 2120587119898

119872 119898 = 0 1 119872 minus 1 (12)

In order tomeasure the radian distance between the phaseof sampled point and reference phase a distance function119863(120576) is defined with independent variable 120576 isin [0 2120587) here

119863 (120576) =

|120576| |120576| le 120587

2120587 minus |120576| |120576| gt 120587(13)

An advanced clustering function is proposed for phaseclustering and expressed as fractional form which has aremarkable reduction on computation as comparing to theindex form as

V119903

(120579) =

119873

sum

119896=1

1

1 + (119873120587)119863 (120593119903

(119896) minus 120579) (14)

where 120579 isin [0 2120587) denotes the phase variable as the referencephase

A division set of 120579 is installed as the reference phasefor phase clustering As is shown in formula (14) all thephase to be processed need to measure the distance to eachreference phase 120579 before clustering In fact the clusteringprocess is similar to a repeated search process Just because ofthis the computational quantity of phase clustering is totallydetermined by the division set of 120579 A suitable division cannot only reduce the calculation amount of this method butalso enhance the correction rate of clustering The uniformdistance from 0 to 2120587 is a commonmethod of reference phasesegmentation

For simplicity an approximation is used to reduce calcu-lation amount When119863(120593

119903

(119896) minus 120579) ge 9120587119873

1

1 + (119873120587)119863 (120593119903

(119896) minus 120579)le 01 (15)

And it can be regarded as

1

1 + (119873120587)119863 (120593119903

(119896) minus 120579)asymp 0 (16)

Mobile Information Systems 5

When a baseband PSK signal is to be processed the advancedphase clustering (APC) function can be expressed as

V119903

(120579) =

119873

sum

119896=1

1

1 + (119873120587)119863 (120593119909

(119896) + 1205790

+ 120593119899

(119896) minus 120579) (17)

Assume that 120593119909

(119896) is distributed independently and hasan equal occurrence probability Since 120593

119899

(119896) is a stationaryGaussian phase noise formula (17) can transform into

V119903

(120579)

asymp119873

119872

119872minus1

sum119898=0

1

1 + (119873120587)119863 (2120587119898119872 + 1205790

+ 1205931015840119899

(119898) minus 120579)

(18)

Note that the necessary condition of the upper equationis the uniform distribution of the transmitted signal phasewithout noise In the ideal constellation there are approxi-mate119873119872 sample points distributed on the location of eachconstellation if the sample number of the received signalwhich has119872 modulation order is 119873 Otherwise the aboveequation is not established anymore

Due to the particularity of the distance function 119863(120576)has a periodicity of 2120587 On the other hand the independentvariable 120579 in the clustering function (14) is only related to thedistance function which leads to the fact that the clusteringfunction also has the periodicity of 2120587

The character of periodicity of formula (14) is given indetail When 120579 + 2120587119872 lt 2120587 the periodicity of clusteringfunction is formulated and elaborated in formula (19) It alsocan be proved as the sameway that V

119903

(120579+2120587119872minus2120587) = V119903

(120579)if 120579 + 2120587119872 gt 2120587

V119903

(120579 +2120587

119872) =

119873

119872

sdot

119872minus1

sum119898=0

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus (120579 + 2120587119872))

=119873

119872(

1

1 + (119873120587)119863 (120601 minus (120579 + 2120587119872))

+

119872minus1

sum119898=2

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus (120579 + 2120587119872))

+1

1 + (119873120587)119863 (2120587119872 + 120601 minus (120579 + 2120587119872)))

=119873

119872(

1

1 + (119873120587)119863 (2120587 + 120601 minus (120579 + 2120587119872))

+

119872minus2

sum119898=1

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus 120579)

+1

1 + (119873120587)119863 (120601 minus 120579)) =

119873

119872

sdot

119872minus1

sum119898=0

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus 120579)= V

119903

(120579)

(19)

The expression of clustering function V119903

(120579) is a periodicalfunction with

119879V =2120587

119872 (20)

Since the periodic signal has special spectral propertiesin frequency domain the period of clustering functioncan be extracted easily through Fast Fourier Transform(FFT) 119881

120579

(120596) = FFT[V119903

(120579)] The certain frequency whichis corresponding to the place of maximum value of itsFourier transform result indicates 119879V Modulation order 119872can be calculated through the above equation then signalsrsquoclassification is achieved More favorably carrier phase 120579

0

is irrelevant to this method for 119879V which means that thisproposed method is also robust to signalrsquos constellationrotation

If deep recognition requirements are needed for PSKsignals with the same modulation order lots of statisticsparameters can be chosen and employed For examplethere are two sets of data 4PSK and OQPSK 8PSK and(1205874)DQPSK Envelope entropy of differential phase of thebaseband signals can be introduced to distinguish themrespectively The recognition performance is certainly deter-mined by the introduced statistics parameters yet regardlessof the APC method

The APC method has several advantages

(1) Since it is derived from the coding characters ratherthan statistical properties the direct influence of SNRis reduced

(2) As an optimization algorithm of multiple peakssearching it achieves all the peaks in one calculationprocess and avoids repeated peak cuttings

(3) Fraction is used instead of exponential function inthe clustering function so that the calculation processis simplified which leads to a much lower computa-tional quantity

32 Frequency Offset Correction In the digital communica-tion system the carrier frequency offset is often introducedby the difference between the receiver and the transmitteroscillator and also caused by the Doppler frequency shiftwhich is brought by the channel nonlinearity and phase noiseIn the wireless network especially the electronic monitor-ing and other noncooperative communication systems theaccuracy of frequency offset estimation directly affects theperformance of the receiver

6 Mobile Information Systems

In Xursquos method mentioned in last section phase cluster-ing algorithm is directly adopted with the difference phase ofreceived signal However the difference phase of the effectivepart of signal which carries messages is no longer uniformdistribution Only frequency offset estimation and correctioncan be considered in this case to eliminate the impact offrequency offset as much as possible

The frequency offset estimations of the Fitz and LampRalgorithms are directly achieved via the weighted summationof the autocorrelation of the signal This means that thesetwo algorithms and the improvedmethods based upon themare all heavily affected by the correlation interval on theestimated range unless the correlation interval achieves itsmaximum value of sampled number 119873 However in thiscase the calculation amount increases dramatically especiallywhen 119873 is large For this particular reason most of theimproved methods are derived from Kayrsquos algorithm Theautocorrelation function of the processing signal is used inthe MampM algorithm used in Kayrsquos and LampWrsquos algorithmsfor weakening the influence brought on by phase noiseHowever the addition operation of the autocorrelationrsquosphase introduces the phase folding problem An objectionphase of the baseband signal which has a real value near minus120587or120587may be changed to a completely different value under theinfluence of noise and this leads to an error in the frequencyoffset estimation result The WNALP algorithm is derivedfrom the MampM algorithm which solves the phase foldingproblem and broadens the estimation range remarkablyHowever the signal in real noncooperative environmentsis usually intercepted under a low SNR due to its specialcondition which causes great difficulties in subsequent signalprocessing

In order to reduce the thresholdsrsquo effect and improvethe unbalance between estimation accuracy and estimationrange of frequency offset under low SNR an advancedNDA estimator based on the weighted summation of thedifferential phase of the autocorrelation is proposed in thispaper

Assume that timing synchronization is accomplishedThe baseband signal sequence with frequency offset 119909(119896) isexpressed as

119909 (119896) = 119888119896

exp119895(2120587119891Δ119896119879119904+120579) + 119899 (119896) (21)

where 119888119896

(119896 = 1 2 119873) is the modulated symbol sequencefrom the transmitting end 119873 is the number of samplingpoints of the selected signal segment in the receiving end119891Δ

is the unknown frequency offset to be estimated 119879119904

isthe sample period and 120579 is a random initial carrier phasewhich follows the uniformdistribution in the range of [0 2120587)Usually the channel noise of the communication system119899(119896) is considered to be random complex additive Gaussiannoise with zeromean and bilateral spectral density119873

0

2 Wenormalize its amplitude as

(119896) =119909 (119896)

|119909 (119896)| 119896 = 1 2 119873 (22)

Then under the hypothesis of 119899(119896) ≫ 1 for a large enoughSNR

(119896) ≃ 119890119895(2120587119896119891Δ119879119904+120579+

120573(119896))

(23)

where (119896) is also a Gaussian process with zero meanThe autocorrelation is defined as

1198770

(119898) =

119873

sum

119896=119898+1

(119896) lowast

(119896 minus 119898) 119898 = 1 2 119871119903

(24)

where (119896) = 119876

(119896) is the normalized baseband signalraised to the power of 119876 and 119871

119903

is the set maximumcorrelation interval Using the same principle as above theautocorrelation function can be continuously transformed as

1198770

(119898) ≃ 119890119895(2120587119898119891Δ119879119904+(119898)) (25)

where (119898) is also a Gaussian process with zeromeanWe seethat

ang1198770

(119898) 119877lowast

0

(119898 minus 1) = 2120587119891Δ

119879119904

+ (119898) + (119898 minus 1)

2 le 119898 le 119871119903

(26)

We define Δ1205930119877(119898)

≜ ang1198770

(119898)119877lowast

0

(119898minus 1) According to theprinciple of Kayrsquos algorithm an objective function can be setas

J0

= (Δ1205930 minus 2120587119891Δ119879119904e)119879Cminus1 (Δ1205930 minus 2120587119891Δ119879119904e) (27)

where Δ1205930 = [Δ1205930119877(1) Δ1205930119877(2) Δ1205930119877(119871119903)]119879 The estimated

value of the frequency offset Δ

is obtained when theobjective function J

0

obtains its minimum value So thenormalized weighted correlation linear estimator proposedcan be expressed as

Δ

=1

2120587119876119879119904

sdot

119871119903

sum119898=2

1205960

(119898) sdot arg [1198770

(119898) 119877lowast

0

(119898 minus 1)] (28)

where 1205960

is the weight of the differential phase

1205960

(119898) =3 [(119873 minus 119898) (119873 minus 119898 + 1) minus 119871

119903

(119873 minus 119871119903

)]

119871119903

(41198712119903

minus 6119871119903

119873 + 31198732 minus 1) (29)

The normalized baseband signal is considered to bethe signal to be processed which effectively weakens theperformance loss resulting from the nonlinear operation ofraising to a power of 119876 The weighted summation of thedifferential phase of the autocorrelation also decreases theinfluence of noise effectively compared to the method ofargument operation after weighting the conjugate differenceof the autocorrelation Thus it provides a better estimationaccuracy and is described in Kayrsquos paper [5]The difference ofautocorrelation is a great improvement which can make theestimation range independent of the maximum correlationinterval 119871

119903

and solve the phase folding problem comparedto Fitzrsquos and the LampR algorithm and the improved methodsbased upon them Meanwhile the proposed method in this

Mobile Information Systems 7

Table 1 Simulation time for order classification

Simulation time (s)HOMmethod 00158AKMCmethod 04523PC method 00720APC method 00345

paper has the same estimation range as its counterpartWNALP algorithm Importantly the large estimation vari-ance of the WNALP algorithm under low SNR conditionsis improved which effectively balances the trade-off betweenestimation accuracy and estimation range under low SNR inthe process of frequency offset estimation

4 Simulation

Computer simulations are performed to test the performanceof the methods proposed in this paper Considering thebackground of electronic monitoring and countermeasurein satellite communication and wireless communication net-works the simulation set contains six common modulationtypes of PSK signals BPSK QPSK 8PSK 16PSK OQPSK(1205874)DQPSK and UQPSK Each simulation result is theaverage of 1000 independent runs Because of the specialenvironment we assumed no a priori knowledge of inter-cepted signal is assumed for all the experiments

Regular communication equipment and environment areadopted for these simulations The signals are shaped byraised root cosine filter with its roll-off factor 120572 = 022 Thereceived intercepted signal is sampled 119873 = 512 points fortest with Sample frequency 119891

119904

= 20MHz We suppose thatthe symbol rate119873

119904

has been estimated accurately by a certainalgorithm and the sample number in per symbol period is119873119887

= 119873119904

lowast 119873119891119904

= 32 Additive white Gaussian noise isconsidered in this situationMoreover channel effects such asfading andmultipath propagation are ignored andwe assumethat perfect time and frequency synchronization have beenachievedThe SNR in this paper is defined as119864

119904

1198730

where119864119904

is the energy per symbol and1198730

is the power spectral densityof the Gaussian noise

A common method based on four-order cumulant(HOC) and two new ways derived from data miningadvanced 119870-means clustering (AKMC) and phase clustering(PC) are adopted for performance comparison of signalclassification Classification capabilities and simulation timesin a single run of the subroutines are shown in Figure 2 andTable 1 respectively

The same set of signal data to be processed are introducedin four subroutines respectively for classification perfor-mance and simulation time comparison Except for four-order cumulant the other three methods present obviouscorrect classification rate trends and a large SNR tolerancefor all the involved signals The 16PSK signal can be correctlyclassified from approximate 2 dB and the other six signalshave larger SNR tolerances less than minus5 dB Even so they aredistinguished clearly via simulation time table It is shown inTable 1 that PC method and AKMCmethod both cost two or

more times simulation time than APC method proposed inthis paper If the modulation order of signal to be processedis 16 the order needs to be chosen as 16 for accumulation inHOC algorithm However the computation amount of thisalgorithm increases exponentially It is a predictable resultthat its simulation time could be bigger than or equal tothe time of APC method Due to the instability of the APCalgorithm at the low SNRs few wrong judgements of thesignalrsquos modulation order appear That is the reason why theorder of 16PSK signal gets 17 during 1sim2 dB

In summary APC method proposed in this paper hasa better classification capability than its counterparts andgives a new guidance for practical signal processing Orderclassification result and correct classification rate by APCmethod are separately displayed in Figures 4-5

Frequency offset directly impacts on the performance ofsignal classification In order to verify the effectiveness ofthe proposed NWALPmethod theWNALP algorithm fromwhich the proposed method in this paper is derived wasselected for comparison in this paper

Let us assume that the signal to be processed is a QPSKsignal with additive Gaussian noise The number of samplepoints is set as 119873 = 256 and the sampling frequency isnormalized to the unit as 119891

119904

= 1 The correlation intervalof autocorrelation is set as 119871

119903

= 1198732 Each simulation ofestimation accuracy and estimation range for the frequencyoffset was run at least 100 times The estimation varianceis adopted as the measure of estimation accuracy TheMCRLB [22] is also calculated as an absolute measure of thetheoretical optimal valuation

MCRLB = 3

21205872119873(1198732 minus 1)sdot1

119864119904

1198730

(30)

The performance of the proposed method compared tothe abovementioned methods is shown in Figure 5 under anormalized frequency offset 119891

Δ

= 0001 as the SNR changeswithin the range ofminus15sim20 dB by 1 dB steps It can be seen thateven when the frequency offset is set at a smaller value theWNALPalgorithm still shows a poor estimation performanceof about 10minus2 under low SNRs This means that when thefrequency offset is small the error of the algorithm may beof the same order of magnitude as the frequency offset itselfSuch a large estimation error leads to a complete failure ofthe algorithm However it can be obviously seen that theestimation accuracy of the proposed method remains steadyin the vicinity of 10minus4 under low SNR conditions and hasan improved estimation accuracy of at least two orders ofmagnitude compared to the original WNALP algorithm Onthe other hand the estimation error of the proposed methodrapidly decreases to a magnitude near the MCRLB Even asthe SNR increases it remains steady at approximately 10minus7due to the SNR threshold effect

The estimation range of the carrier frequency offset isusually observed under large SNRs in order to obtain widerand more accurate bounds When SNR = 15 dB the esti-mated ranges of the chosen algorithms were simulated asshown in Figure 6 As can be seen the proposed NWALPmethod can achieve the same frequency offset estimation

8 Mobile Information Systems

0 5 10 15 20 25minus5SNR (dB)

0

02

04

06

08

1

CORR

CORR by 4-order cumulants CORR by advanced K-means clustering

CORR by phase clustering

0 5 10 15 20 25minus5

SNR (dB)

0

02

04

06

08

1

CORR

CORR by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5

SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

minus5 5 10 15 20 250SNR (dB)

0

02

04

06

08

1

CORR

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 2 Comparison of correct order recognition rate

range asWNALP which has proved to be a better choice for alarge estimation range than other algorithmsThis estimationrange cannot be increased even if the SNR increases It canbe seen that the proposed method in this paper can achieve alarge frequency offset estimation range

Figure 7 vividly shows the difference of constellationchanges before and after frequency offset correction bytwo distinct colors Signal with frequency offset make itsconstellation is displayed as a blue ring which cannot catchany constellation point However the approximate originalappearance is displayed after frequency offset correction withred It can be seen that the proposedmethod in this paper hasa remarkable effectiveness under 0 dB

5 Conclusion

This paper presents a robust classifier for NDA recognition innoncooperative wireless environment Nonsupervised clus-tering of the signal phase is achieved bymeasuring the radian

distance between each signal phase and the reference phaseThis method proposed optimizes the clustering functionand reduces the computation sharply Moreover frequencyoffset is considered and an advanced method is proposedfor frequency offset estimation and correction First a nor-malization of the baseband signal is performed After thenonlinear operation of raising the signal to a power of 119876 theestimate of frequency offset is obtained via the weighted sum-mation of the differential phase of the signalrsquos autocorrelationThis method balances estimation accuracy and range underlow SNR conditions which sharply improves the estimationaccuracy without shrinking the maximum estimation rangeeven if the SNR is as low as minus15 dB Seven common PSKsignals are adopted for simulation experiments The classi-fication performance and the estimation and correlation forfrequency offset are displayed and demonstrated with severalsimulation result figures which illustrate their feasibility andpractice

Mobile Information Systems 9

Order classification by advanced phase clustering

0 5 10 15 20 25minus5SNR (dB)

0

2

4

6

8

10

12

14

16

18

20

Ord

er

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 3 Order classification by advanced phase clustering

Correct order recognition rate by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 4 Correct order recognition rate by advanced phase cluster-ing

Generally this classifier which is derived from datamining and image processing has a guiding value for signalprocessing in electronic surveillance and electronic counter-measure of communication networks Further work such asthe initial optimization of clustering centers 120579 and multipath

Estimation of frequency offset (Δf = 0001)

NDA WNALPPROPOSEDMCRLB

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

10minus2

Varia

nce o

f fre

quen

cy o

ffset

estim

atio

n

minus10 minus5 0 5 10 15 20minus15

SNR (dB)

Figure 5 Comparison of estimation variance of frequency offset

NDA WNALPPROPOSEDMCRLB

Estimation of frequency offset (SNR = 15 dB)

minus005 0 005 01 015minus01

Frequency offset (normalized)

minus01

minus005

0

005

01

015

Mea

n va

lues

of e

stim

ated

freq

uenc

y off

set

Figure 6 Estimated range comparison

and Rayleigh channel and other practical problems is con-sidered for applications

Competing Interests

The authors declare that they have no competing interests

10 Mobile Information Systems

BPSK

minus1

0

1

0 2

05

15

minus05

minus15minus2

QPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

8PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

16PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Without FOCWith FOC

Without FOCWith FOC

Without FOCWith FOC

UQPSK

0 1

0

05

1

minus05

minus1minus1

PI4DQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

OQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Figure 7 Comparison of frequency offset correction

Acknowledgments

The authors would like to thank the support of FundamentalResearch Funds for the Central Universities (designationNSFC61371184)

References

[1] F F Liedtke ldquoComputer simulation of an automatic classifica-tion procedure for digitally modulated communication signalswith unknown parametersrdquo Signal Processing vol 6 no 4 pp311ndash323 1984

[2] Q Shi and Y Karasawa ldquoAutomatic modulation identificationbased on the probability density function of signal phaserdquo IEEETransactions on Communications vol 60 no 4 pp 1033ndash10442012

[3] A K Nandi and E E Azzouz ldquoAlgorithms for automatic mod-ulation recognition of communication signalsrdquo IEEE Transac-tions on Communications vol 46 no 4 pp 431ndash436 1998

[4] K Kim andA Polydoros ldquoDigitalmodulation classification theBPSK versus QPSK caserdquo in Proceedings of the IEEE MilitaryCommunications Conference Conference Record 21st CenturyMilitary CommunicationsmdashWhatrsquos Possible (MILCOM rsquo88) pp431ndash436 San Diego Calif USA October 1988

[5] K Kim and A Polydoros ldquoOn the detection and classificationof quadrature digital modulations in broad-band noiserdquo IEEETransactions on Communications vol 38 no 8 pp 1199ndash12111990

[6] C S Long K M Chugg and A Polydoros ldquoFurther results inlikelihood classification of QAM signalsrdquo in Proceedings of theIEEE Military Communications Conference (MILCOM rsquo94) vol1 pp 57ndash61 IEEE Fort Monmouth NJ USA October 1994

[7] Y-C Lin and C-C J Kuo ldquoClassification of quadrature ampli-tude modulated (QAM) signals via sequential probability ratiotest (SPRT)rdquo Signal Processing vol 60 no 3 pp 263ndash280 1997

[8] W A Gardner and C M Spooner ldquoCyclic spectral analysis forsignal detection and modulation recognitionrdquo in Proceedings ofthe IEEEMilitary Communications Conference pp 419ndash424 SanDiego Calif USA October 1988

[9] L Hong and K C Ho ldquoIdentification of digital modulationtypes using the wavelet transformrdquo in Proceedings of the Mili-tary Communications Conference (MILCOM rsquo99) pp 427ndash431Atlantic City NJ USA November 1999

[10] K C Ho W Prokopiw and Y T Chan ldquoModulation iden-tification of digital signals by the wavelet transformrdquo IEEProceedingsmdashRadar Sonar and Navigation vol 147 no 4 pp169ndash176 2000

Mobile Information Systems 11

[11] C Cui H Li and J Yu ldquoMPSKmodulation classification basedon morlet transformrdquo Communication Technology vol 43 no3 pp 10ndash12 2010

[12] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009

[13] J-F Wang Y Yue and J Yao ldquoA MPSK recognition methodbased on high order cumulantsrdquo Communication Technologyvol 9 no 43 pp 4ndash6 2010

[14] J-X Wang and H Song ldquoDigital modulation recognitionbased on constellation diagramrdquo Journal of China Institute ofCommunications vol 25 no 6 pp 166ndash173 2004

[15] R Ghunhui W Ping and X Xianci ldquoClassification of MPSKsignals using the distribution of in-phase and quadraturesignalsrdquo Signal Processing vol 22 no 6 pp 787ndash790 2006

[16] T-J Lu S-B Guo and X-C Xiao ldquoFractal characteristicsresearch of modulated signalsrdquo Science in China Series ETechnological Sciences vol 31 no 6 pp 508ndash510 2001

[17] C Weber M Peter and T Felhauer ldquoAutomatic modulationclassification technique for radio monitoringrdquo Electronics Let-ters vol 51 no 10 pp 794ndash796 2015

[18] J-F Xu F-P Wang and Z-J Wang ldquoMPSK modulationrecognition method based on phase clusteringrdquo Journal ofCircuits and Systems vol 16 no 5 pp 55ndash58 2011

[19] X-Y Chen Y-F Min L-R Zheng and L Yang ldquoQuick moun-tain clustering algorithmrdquo Application Research of Computersvol 25 no 7 pp 2043ndash2045 2008

[20] N Ahmadi ldquoUsing fuzzy clustering and TTSAS algorithmfor modulation classification based on constellation diagramrdquoEngineering Applications of Artificial Intelligence vol 23 no 3pp 357ndash370 2010

[21] D C Rife and R R Boorstyn ldquoSingle-tone parameter esti-mation from discrete-time observationsrdquo IEEE Transactions onInformation Theory vol IT-20 no 5 pp 591ndash598 1974

[22] A B Awoseyila C Kasparis and B G Evans ldquoImproved singlefrequency estimation with wide acquisition rangerdquo ElectronicsLetters vol 44 no 3 pp 245ndash247 2008

Submit your manuscripts athttpwwwhindawicom

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Distributed Sensor Networks

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Applied Computational Intelligence and Soft Computing

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Electrical and Computer Engineering

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mobile Information Systems 3

For complex stationary random signal119883(119905) its high ordermoment can be unitedly expressed as

119872119901+119902119901

= 119864 [119883119901

(119883lowast

)119902

] (1)

where 119901 and 119902 are the index number of 119883 and 119883lowast respec-tively Several high order cumulants commonly used can berepresented by high order moment as follows

11986220

= 11987220

11986221

= 11987221

11986240

= 11987240

minus 31198722

20

11986241

= 11987241

minus 311987221

11987220

11986242

= 11987242

minus100381610038161003816100381611987220

10038161003816100381610038162

minus 21198722

21

11986260

= 11987240

minus 151198724

11987220

minus 301198723

20

(2)

In theory the algorithm of high order accumulation cancompletely eliminate the effect of Gaussian noise and bean ideal tool for signal processing under Gaussian noiseHowever this method is not suitable for online real-timesignal processing due to its amount of calculation Thehigher modulation order the intercepted signal has the morecomputation which increases exponentially it costs

22 Advanced K-Means Method The 119870-means algorithm isan optimal method for hard clustering when the number ofclusters 119870 in the input data 119909 is known Equation (3) is thecost formula where 119894 is the index and 119873 is the length of theinput data 119909

119869 =

119873

sum

119894=1

1003816100381610038161003816119909119894 minus 11991111989411989611987511987010038161003816100381610038162

(3)

The variable 119911119894119896

is the membership indicator which isequal to unity if the input data 119909

119894

belongs to the cluster 119896 andzero otherwise The membership indicator 119911

119894119896

is calculatedbased on the shortest distance of the input data 119909

119894

to theprototypes 119875

119870

as given in (4) where 119908119894

represents the index119896 of the winning prototype 119875

119896

for the input data 119909119894

120596119894

= argmin119875119870

(1003816100381610038161003816119909119894 minus 119875119870

1003816100381610038161003816) (4)

The 119870-means algorithm iteratively solves the clusteringproblem stated in (4) by alternating between a competitiveand a learning step In the competitive step the allocation ofthe input symbols 119909

119894

to the prototypes 119875119870

is carried out insuch a way that 119869 in (3) is minimised In the learning stepthe prototype positions are updated by calculating the meanvalue of the corresponding input symbols 119909

119894

A novel utility function 119865 is proposed byWeber that indi-cates the best fitting constellation diagram to the calculatedprototypes of the clustering algorithm

119865 = 1198652

1

(119862119878119870

) lowast 1198652

(119862119878119870

)

1198651

(119862119878119870

) =1

1 + 119869119862119878119870119870

1198652

(119862119878119870

) =1

1 + (1119870)sum119870

119896=1

1003816100381610038161003816119862119896 minus 1198751198961003816100381610038161003816

sum119870

119896=1

Φ(119875119896

)

119870

Φ (119875119896

) =

1 for119873

sum

119894=1

119911119894119896

gt 0

0 else

(5)

where 119869119862119878119870

is the result of the cost function in (3) for a specificconstellation pattern 119862

119878119870

of the considered modulation pool119872

119878119870

The variable119870 represents the number of prototypes orthemodulation order of119862

119878119870

and 119878 represents themodulationscheme 119862

119870

are the specific symbol positions of the constel-lation pattern 119862

119878119870

and 119875119870

are the calculated prototypesGenerally the first term of the utility function 119865

1

(119862119878119870

)

indicates the minimisation of cluster variances and thesecond factor119865

2

(119862119878119870

) evaluates the position of the calculatedprototypes 119875

119870

to the given constellation pattern 119862119878119870

andthe assignment of the input symbols 119909

119894

to the prototypesTo conclude the utility function 119865 = 1198652

1

(119862119878119870

) lowast 1198652

(119862119878119870

)

evaluates if all prototypes are covered by the input samplesand if the variance of the clusters and the EVM can beminimised For this reason this algorithm is named thehighest constellation pattern matching (HCPM) algorithm

A real monitoring environment is employed for field trialinWeberrsquos paper Eight signals including 4 kinds of QAM andMPSK signals respectively are introduced for identificationcapability demonstration Two-Threshold Sequential Algo-rithmic Scheme (TTSAS) [20] fuzzy algorithm [20] and the119870-centre algorithm are adopted for performance compari-son Simulations andmeasurements show the effectiveness ofthe proposed method than the other three counterparts

The idea gives a new direction for signal recognitionWhat is better it can be extended to the application of QAMsignal detection and identification However the simulationrunning time it needed is too long that is to say it isnot relatively suitable for real-time signal processing thansome other methods The simulation time of this method isdisplayed in the table in Simulation which shows that it hasa larger weakness as it compares to its counterparts

23 Phase ClusteringMethod Anothermethod based on datamining is phase clustering method proposed by Xu et al [18]Inspired by subtractive clustering method a novel clusteringfunction is derived for signalsrsquo classification Because themethod proposed in this paper is an improvement of thismethod the specific process is no longer described here

The carrier frequency offset is also considered in XursquospaperThe premise is that the received signal has been timingsynchronized When the carrier frequency offset Δ119891 satisfies

4 Mobile Information Systems

Δ119891119879119887

le 015 an approximate exact complex sequence can beobtained from [21] and the phase sequence can be expressedas

120593119903

(119896) = 120593119909

(119896) + 2120587119896Δ119891119879119887

+ 120593119899

(119896) (6)

where 119879119887

is the symbol period and 119896 = 1 119873 is the samplespot where 119873 is the sample number of each data package120593119899

(119896) is the noisersquos phase and the phase of received signal120593119909

(119896) is

120593119909

(119896) isin 2120587119898

119872+ 120579

0

119898 = 0 1 119872 minus 1 (7)

In order to eliminate the influence of frequency offset asmuch as possible a new sequence can be obtained by makingdifference to 120593

119909

(119896) that is

1205931015840

119903

(119896) = 120593119903

(119896 + 1) minus 120593119903

(119896)

= 120593119909

(119896 + 1) minus 120593119909

(119896) + 2120587Δ119891119879119887

+ 120593119899

(119896 + 1)

minus 120593119899

(119896) = 1205931015840

119909

(119896) + 1205931015840

119899

(119896)

(8)

where

1205931015840

119909

(119896) isin 2120587119898

119872+ 2120587Δ119891119879

119887

119898 = 0 1 119872 minus 1 (9)

The major idea of Xursquos method for reducing the influenceof frequency offset is to employ the difference of phase of thebaseband signal 1205931015840

119903

(119896) as the signal to be processed the sameas the condition without frequency offset to get the correctsignal modulation order A significant premise mentionedin his paper is that 1205931015840

119909

(119896) is a uniform distribution objectHowever in this case the effective part (9) is no longer subjectto uniform distribution which directly leads to the phaseclustering algorithm invalid

Four commonMPSK signals are introduced for classifica-tion performance in XUrsquos paper The correction classificationprobability is adopted as the measure index

In order to enhance the recognition efficiency this paperproposes an improved method for phase clustering whichcan effectively reduce the signal processing time withoutdegrading the classification performance In addition in viewof the carrier frequency offset this paper also gives a feasiblesolution for its estimation and correction

3 Proposed Method

In order to achieve a better NDA classification performancefor signals an improved phase clusteringmethod is proposedin this paper Then a robust estimation method is proposedfor frequency offset correction

31 Advanced Phase ClusteringMethod The received wave ofmodulated PSK signal can be generally expressed as

119903 (119905) = sum119899

119886119899

119892 (119905 minus 119899119879119904

) 119890119895(2120587119891119888119905+1205790) + 119899 (119905) (10)

where 119886119899

isin exp(minus119895(2120587119898119872)) 119898 = 0 1 119872 minus 1 is thesymbol sequence 119872 is the modulation order 119892(119905) is the

shaping pulse of shaping filter 119879119904

is the sample period 119891119888

isthe carrier frequency and 120579

0

is the carrier phase (Figure 3)119899(119905) is the white Gaussian noise with zero mean and 119873

0

varianceRoot Raised Cosine (RRC) filter is generally adopted for

signal shaping in wireless communication networks It is alsoconsidered in this paper Under the premise of carrier andtiming synchronization the output baseband signalrsquos phaseafter matching filter can be written as

120593119903

(119896) = 120593119909

(119896) + 1205790

+ 120593119899

(119896) 119896 = 1 2 119873 (11)

where 120593119909

(119896) denotes the phase sequence of transmittedsignal 120593

119899

(119896) denotes the phase sequence of noise and 119873 isthe sample number of each data package For PSK signalits phase 120593

119909

(119896) expressed as follows commonly obeys touniform distribution which means that there are 119872119873sample spots intensely around each constellation point if119872-order modulated signal is sampled at119873 points

120593119909

(119896) isin 2120587119898

119872 119898 = 0 1 119872 minus 1 (12)

In order tomeasure the radian distance between the phaseof sampled point and reference phase a distance function119863(120576) is defined with independent variable 120576 isin [0 2120587) here

119863 (120576) =

|120576| |120576| le 120587

2120587 minus |120576| |120576| gt 120587(13)

An advanced clustering function is proposed for phaseclustering and expressed as fractional form which has aremarkable reduction on computation as comparing to theindex form as

V119903

(120579) =

119873

sum

119896=1

1

1 + (119873120587)119863 (120593119903

(119896) minus 120579) (14)

where 120579 isin [0 2120587) denotes the phase variable as the referencephase

A division set of 120579 is installed as the reference phasefor phase clustering As is shown in formula (14) all thephase to be processed need to measure the distance to eachreference phase 120579 before clustering In fact the clusteringprocess is similar to a repeated search process Just because ofthis the computational quantity of phase clustering is totallydetermined by the division set of 120579 A suitable division cannot only reduce the calculation amount of this method butalso enhance the correction rate of clustering The uniformdistance from 0 to 2120587 is a commonmethod of reference phasesegmentation

For simplicity an approximation is used to reduce calcu-lation amount When119863(120593

119903

(119896) minus 120579) ge 9120587119873

1

1 + (119873120587)119863 (120593119903

(119896) minus 120579)le 01 (15)

And it can be regarded as

1

1 + (119873120587)119863 (120593119903

(119896) minus 120579)asymp 0 (16)

Mobile Information Systems 5

When a baseband PSK signal is to be processed the advancedphase clustering (APC) function can be expressed as

V119903

(120579) =

119873

sum

119896=1

1

1 + (119873120587)119863 (120593119909

(119896) + 1205790

+ 120593119899

(119896) minus 120579) (17)

Assume that 120593119909

(119896) is distributed independently and hasan equal occurrence probability Since 120593

119899

(119896) is a stationaryGaussian phase noise formula (17) can transform into

V119903

(120579)

asymp119873

119872

119872minus1

sum119898=0

1

1 + (119873120587)119863 (2120587119898119872 + 1205790

+ 1205931015840119899

(119898) minus 120579)

(18)

Note that the necessary condition of the upper equationis the uniform distribution of the transmitted signal phasewithout noise In the ideal constellation there are approxi-mate119873119872 sample points distributed on the location of eachconstellation if the sample number of the received signalwhich has119872 modulation order is 119873 Otherwise the aboveequation is not established anymore

Due to the particularity of the distance function 119863(120576)has a periodicity of 2120587 On the other hand the independentvariable 120579 in the clustering function (14) is only related to thedistance function which leads to the fact that the clusteringfunction also has the periodicity of 2120587

The character of periodicity of formula (14) is given indetail When 120579 + 2120587119872 lt 2120587 the periodicity of clusteringfunction is formulated and elaborated in formula (19) It alsocan be proved as the sameway that V

119903

(120579+2120587119872minus2120587) = V119903

(120579)if 120579 + 2120587119872 gt 2120587

V119903

(120579 +2120587

119872) =

119873

119872

sdot

119872minus1

sum119898=0

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus (120579 + 2120587119872))

=119873

119872(

1

1 + (119873120587)119863 (120601 minus (120579 + 2120587119872))

+

119872minus1

sum119898=2

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus (120579 + 2120587119872))

+1

1 + (119873120587)119863 (2120587119872 + 120601 minus (120579 + 2120587119872)))

=119873

119872(

1

1 + (119873120587)119863 (2120587 + 120601 minus (120579 + 2120587119872))

+

119872minus2

sum119898=1

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus 120579)

+1

1 + (119873120587)119863 (120601 minus 120579)) =

119873

119872

sdot

119872minus1

sum119898=0

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus 120579)= V

119903

(120579)

(19)

The expression of clustering function V119903

(120579) is a periodicalfunction with

119879V =2120587

119872 (20)

Since the periodic signal has special spectral propertiesin frequency domain the period of clustering functioncan be extracted easily through Fast Fourier Transform(FFT) 119881

120579

(120596) = FFT[V119903

(120579)] The certain frequency whichis corresponding to the place of maximum value of itsFourier transform result indicates 119879V Modulation order 119872can be calculated through the above equation then signalsrsquoclassification is achieved More favorably carrier phase 120579

0

is irrelevant to this method for 119879V which means that thisproposed method is also robust to signalrsquos constellationrotation

If deep recognition requirements are needed for PSKsignals with the same modulation order lots of statisticsparameters can be chosen and employed For examplethere are two sets of data 4PSK and OQPSK 8PSK and(1205874)DQPSK Envelope entropy of differential phase of thebaseband signals can be introduced to distinguish themrespectively The recognition performance is certainly deter-mined by the introduced statistics parameters yet regardlessof the APC method

The APC method has several advantages

(1) Since it is derived from the coding characters ratherthan statistical properties the direct influence of SNRis reduced

(2) As an optimization algorithm of multiple peakssearching it achieves all the peaks in one calculationprocess and avoids repeated peak cuttings

(3) Fraction is used instead of exponential function inthe clustering function so that the calculation processis simplified which leads to a much lower computa-tional quantity

32 Frequency Offset Correction In the digital communica-tion system the carrier frequency offset is often introducedby the difference between the receiver and the transmitteroscillator and also caused by the Doppler frequency shiftwhich is brought by the channel nonlinearity and phase noiseIn the wireless network especially the electronic monitor-ing and other noncooperative communication systems theaccuracy of frequency offset estimation directly affects theperformance of the receiver

6 Mobile Information Systems

In Xursquos method mentioned in last section phase cluster-ing algorithm is directly adopted with the difference phase ofreceived signal However the difference phase of the effectivepart of signal which carries messages is no longer uniformdistribution Only frequency offset estimation and correctioncan be considered in this case to eliminate the impact offrequency offset as much as possible

The frequency offset estimations of the Fitz and LampRalgorithms are directly achieved via the weighted summationof the autocorrelation of the signal This means that thesetwo algorithms and the improvedmethods based upon themare all heavily affected by the correlation interval on theestimated range unless the correlation interval achieves itsmaximum value of sampled number 119873 However in thiscase the calculation amount increases dramatically especiallywhen 119873 is large For this particular reason most of theimproved methods are derived from Kayrsquos algorithm Theautocorrelation function of the processing signal is used inthe MampM algorithm used in Kayrsquos and LampWrsquos algorithmsfor weakening the influence brought on by phase noiseHowever the addition operation of the autocorrelationrsquosphase introduces the phase folding problem An objectionphase of the baseband signal which has a real value near minus120587or120587may be changed to a completely different value under theinfluence of noise and this leads to an error in the frequencyoffset estimation result The WNALP algorithm is derivedfrom the MampM algorithm which solves the phase foldingproblem and broadens the estimation range remarkablyHowever the signal in real noncooperative environmentsis usually intercepted under a low SNR due to its specialcondition which causes great difficulties in subsequent signalprocessing

In order to reduce the thresholdsrsquo effect and improvethe unbalance between estimation accuracy and estimationrange of frequency offset under low SNR an advancedNDA estimator based on the weighted summation of thedifferential phase of the autocorrelation is proposed in thispaper

Assume that timing synchronization is accomplishedThe baseband signal sequence with frequency offset 119909(119896) isexpressed as

119909 (119896) = 119888119896

exp119895(2120587119891Δ119896119879119904+120579) + 119899 (119896) (21)

where 119888119896

(119896 = 1 2 119873) is the modulated symbol sequencefrom the transmitting end 119873 is the number of samplingpoints of the selected signal segment in the receiving end119891Δ

is the unknown frequency offset to be estimated 119879119904

isthe sample period and 120579 is a random initial carrier phasewhich follows the uniformdistribution in the range of [0 2120587)Usually the channel noise of the communication system119899(119896) is considered to be random complex additive Gaussiannoise with zeromean and bilateral spectral density119873

0

2 Wenormalize its amplitude as

(119896) =119909 (119896)

|119909 (119896)| 119896 = 1 2 119873 (22)

Then under the hypothesis of 119899(119896) ≫ 1 for a large enoughSNR

(119896) ≃ 119890119895(2120587119896119891Δ119879119904+120579+

120573(119896))

(23)

where (119896) is also a Gaussian process with zero meanThe autocorrelation is defined as

1198770

(119898) =

119873

sum

119896=119898+1

(119896) lowast

(119896 minus 119898) 119898 = 1 2 119871119903

(24)

where (119896) = 119876

(119896) is the normalized baseband signalraised to the power of 119876 and 119871

119903

is the set maximumcorrelation interval Using the same principle as above theautocorrelation function can be continuously transformed as

1198770

(119898) ≃ 119890119895(2120587119898119891Δ119879119904+(119898)) (25)

where (119898) is also a Gaussian process with zeromeanWe seethat

ang1198770

(119898) 119877lowast

0

(119898 minus 1) = 2120587119891Δ

119879119904

+ (119898) + (119898 minus 1)

2 le 119898 le 119871119903

(26)

We define Δ1205930119877(119898)

≜ ang1198770

(119898)119877lowast

0

(119898minus 1) According to theprinciple of Kayrsquos algorithm an objective function can be setas

J0

= (Δ1205930 minus 2120587119891Δ119879119904e)119879Cminus1 (Δ1205930 minus 2120587119891Δ119879119904e) (27)

where Δ1205930 = [Δ1205930119877(1) Δ1205930119877(2) Δ1205930119877(119871119903)]119879 The estimated

value of the frequency offset Δ

is obtained when theobjective function J

0

obtains its minimum value So thenormalized weighted correlation linear estimator proposedcan be expressed as

Δ

=1

2120587119876119879119904

sdot

119871119903

sum119898=2

1205960

(119898) sdot arg [1198770

(119898) 119877lowast

0

(119898 minus 1)] (28)

where 1205960

is the weight of the differential phase

1205960

(119898) =3 [(119873 minus 119898) (119873 minus 119898 + 1) minus 119871

119903

(119873 minus 119871119903

)]

119871119903

(41198712119903

minus 6119871119903

119873 + 31198732 minus 1) (29)

The normalized baseband signal is considered to bethe signal to be processed which effectively weakens theperformance loss resulting from the nonlinear operation ofraising to a power of 119876 The weighted summation of thedifferential phase of the autocorrelation also decreases theinfluence of noise effectively compared to the method ofargument operation after weighting the conjugate differenceof the autocorrelation Thus it provides a better estimationaccuracy and is described in Kayrsquos paper [5]The difference ofautocorrelation is a great improvement which can make theestimation range independent of the maximum correlationinterval 119871

119903

and solve the phase folding problem comparedto Fitzrsquos and the LampR algorithm and the improved methodsbased upon them Meanwhile the proposed method in this

Mobile Information Systems 7

Table 1 Simulation time for order classification

Simulation time (s)HOMmethod 00158AKMCmethod 04523PC method 00720APC method 00345

paper has the same estimation range as its counterpartWNALP algorithm Importantly the large estimation vari-ance of the WNALP algorithm under low SNR conditionsis improved which effectively balances the trade-off betweenestimation accuracy and estimation range under low SNR inthe process of frequency offset estimation

4 Simulation

Computer simulations are performed to test the performanceof the methods proposed in this paper Considering thebackground of electronic monitoring and countermeasurein satellite communication and wireless communication net-works the simulation set contains six common modulationtypes of PSK signals BPSK QPSK 8PSK 16PSK OQPSK(1205874)DQPSK and UQPSK Each simulation result is theaverage of 1000 independent runs Because of the specialenvironment we assumed no a priori knowledge of inter-cepted signal is assumed for all the experiments

Regular communication equipment and environment areadopted for these simulations The signals are shaped byraised root cosine filter with its roll-off factor 120572 = 022 Thereceived intercepted signal is sampled 119873 = 512 points fortest with Sample frequency 119891

119904

= 20MHz We suppose thatthe symbol rate119873

119904

has been estimated accurately by a certainalgorithm and the sample number in per symbol period is119873119887

= 119873119904

lowast 119873119891119904

= 32 Additive white Gaussian noise isconsidered in this situationMoreover channel effects such asfading andmultipath propagation are ignored andwe assumethat perfect time and frequency synchronization have beenachievedThe SNR in this paper is defined as119864

119904

1198730

where119864119904

is the energy per symbol and1198730

is the power spectral densityof the Gaussian noise

A common method based on four-order cumulant(HOC) and two new ways derived from data miningadvanced 119870-means clustering (AKMC) and phase clustering(PC) are adopted for performance comparison of signalclassification Classification capabilities and simulation timesin a single run of the subroutines are shown in Figure 2 andTable 1 respectively

The same set of signal data to be processed are introducedin four subroutines respectively for classification perfor-mance and simulation time comparison Except for four-order cumulant the other three methods present obviouscorrect classification rate trends and a large SNR tolerancefor all the involved signals The 16PSK signal can be correctlyclassified from approximate 2 dB and the other six signalshave larger SNR tolerances less than minus5 dB Even so they aredistinguished clearly via simulation time table It is shown inTable 1 that PC method and AKMCmethod both cost two or

more times simulation time than APC method proposed inthis paper If the modulation order of signal to be processedis 16 the order needs to be chosen as 16 for accumulation inHOC algorithm However the computation amount of thisalgorithm increases exponentially It is a predictable resultthat its simulation time could be bigger than or equal tothe time of APC method Due to the instability of the APCalgorithm at the low SNRs few wrong judgements of thesignalrsquos modulation order appear That is the reason why theorder of 16PSK signal gets 17 during 1sim2 dB

In summary APC method proposed in this paper hasa better classification capability than its counterparts andgives a new guidance for practical signal processing Orderclassification result and correct classification rate by APCmethod are separately displayed in Figures 4-5

Frequency offset directly impacts on the performance ofsignal classification In order to verify the effectiveness ofthe proposed NWALPmethod theWNALP algorithm fromwhich the proposed method in this paper is derived wasselected for comparison in this paper

Let us assume that the signal to be processed is a QPSKsignal with additive Gaussian noise The number of samplepoints is set as 119873 = 256 and the sampling frequency isnormalized to the unit as 119891

119904

= 1 The correlation intervalof autocorrelation is set as 119871

119903

= 1198732 Each simulation ofestimation accuracy and estimation range for the frequencyoffset was run at least 100 times The estimation varianceis adopted as the measure of estimation accuracy TheMCRLB [22] is also calculated as an absolute measure of thetheoretical optimal valuation

MCRLB = 3

21205872119873(1198732 minus 1)sdot1

119864119904

1198730

(30)

The performance of the proposed method compared tothe abovementioned methods is shown in Figure 5 under anormalized frequency offset 119891

Δ

= 0001 as the SNR changeswithin the range ofminus15sim20 dB by 1 dB steps It can be seen thateven when the frequency offset is set at a smaller value theWNALPalgorithm still shows a poor estimation performanceof about 10minus2 under low SNRs This means that when thefrequency offset is small the error of the algorithm may beof the same order of magnitude as the frequency offset itselfSuch a large estimation error leads to a complete failure ofthe algorithm However it can be obviously seen that theestimation accuracy of the proposed method remains steadyin the vicinity of 10minus4 under low SNR conditions and hasan improved estimation accuracy of at least two orders ofmagnitude compared to the original WNALP algorithm Onthe other hand the estimation error of the proposed methodrapidly decreases to a magnitude near the MCRLB Even asthe SNR increases it remains steady at approximately 10minus7due to the SNR threshold effect

The estimation range of the carrier frequency offset isusually observed under large SNRs in order to obtain widerand more accurate bounds When SNR = 15 dB the esti-mated ranges of the chosen algorithms were simulated asshown in Figure 6 As can be seen the proposed NWALPmethod can achieve the same frequency offset estimation

8 Mobile Information Systems

0 5 10 15 20 25minus5SNR (dB)

0

02

04

06

08

1

CORR

CORR by 4-order cumulants CORR by advanced K-means clustering

CORR by phase clustering

0 5 10 15 20 25minus5

SNR (dB)

0

02

04

06

08

1

CORR

CORR by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5

SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

minus5 5 10 15 20 250SNR (dB)

0

02

04

06

08

1

CORR

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 2 Comparison of correct order recognition rate

range asWNALP which has proved to be a better choice for alarge estimation range than other algorithmsThis estimationrange cannot be increased even if the SNR increases It canbe seen that the proposed method in this paper can achieve alarge frequency offset estimation range

Figure 7 vividly shows the difference of constellationchanges before and after frequency offset correction bytwo distinct colors Signal with frequency offset make itsconstellation is displayed as a blue ring which cannot catchany constellation point However the approximate originalappearance is displayed after frequency offset correction withred It can be seen that the proposedmethod in this paper hasa remarkable effectiveness under 0 dB

5 Conclusion

This paper presents a robust classifier for NDA recognition innoncooperative wireless environment Nonsupervised clus-tering of the signal phase is achieved bymeasuring the radian

distance between each signal phase and the reference phaseThis method proposed optimizes the clustering functionand reduces the computation sharply Moreover frequencyoffset is considered and an advanced method is proposedfor frequency offset estimation and correction First a nor-malization of the baseband signal is performed After thenonlinear operation of raising the signal to a power of 119876 theestimate of frequency offset is obtained via the weighted sum-mation of the differential phase of the signalrsquos autocorrelationThis method balances estimation accuracy and range underlow SNR conditions which sharply improves the estimationaccuracy without shrinking the maximum estimation rangeeven if the SNR is as low as minus15 dB Seven common PSKsignals are adopted for simulation experiments The classi-fication performance and the estimation and correlation forfrequency offset are displayed and demonstrated with severalsimulation result figures which illustrate their feasibility andpractice

Mobile Information Systems 9

Order classification by advanced phase clustering

0 5 10 15 20 25minus5SNR (dB)

0

2

4

6

8

10

12

14

16

18

20

Ord

er

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 3 Order classification by advanced phase clustering

Correct order recognition rate by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 4 Correct order recognition rate by advanced phase cluster-ing

Generally this classifier which is derived from datamining and image processing has a guiding value for signalprocessing in electronic surveillance and electronic counter-measure of communication networks Further work such asthe initial optimization of clustering centers 120579 and multipath

Estimation of frequency offset (Δf = 0001)

NDA WNALPPROPOSEDMCRLB

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

10minus2

Varia

nce o

f fre

quen

cy o

ffset

estim

atio

n

minus10 minus5 0 5 10 15 20minus15

SNR (dB)

Figure 5 Comparison of estimation variance of frequency offset

NDA WNALPPROPOSEDMCRLB

Estimation of frequency offset (SNR = 15 dB)

minus005 0 005 01 015minus01

Frequency offset (normalized)

minus01

minus005

0

005

01

015

Mea

n va

lues

of e

stim

ated

freq

uenc

y off

set

Figure 6 Estimated range comparison

and Rayleigh channel and other practical problems is con-sidered for applications

Competing Interests

The authors declare that they have no competing interests

10 Mobile Information Systems

BPSK

minus1

0

1

0 2

05

15

minus05

minus15minus2

QPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

8PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

16PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Without FOCWith FOC

Without FOCWith FOC

Without FOCWith FOC

UQPSK

0 1

0

05

1

minus05

minus1minus1

PI4DQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

OQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Figure 7 Comparison of frequency offset correction

Acknowledgments

The authors would like to thank the support of FundamentalResearch Funds for the Central Universities (designationNSFC61371184)

References

[1] F F Liedtke ldquoComputer simulation of an automatic classifica-tion procedure for digitally modulated communication signalswith unknown parametersrdquo Signal Processing vol 6 no 4 pp311ndash323 1984

[2] Q Shi and Y Karasawa ldquoAutomatic modulation identificationbased on the probability density function of signal phaserdquo IEEETransactions on Communications vol 60 no 4 pp 1033ndash10442012

[3] A K Nandi and E E Azzouz ldquoAlgorithms for automatic mod-ulation recognition of communication signalsrdquo IEEE Transac-tions on Communications vol 46 no 4 pp 431ndash436 1998

[4] K Kim andA Polydoros ldquoDigitalmodulation classification theBPSK versus QPSK caserdquo in Proceedings of the IEEE MilitaryCommunications Conference Conference Record 21st CenturyMilitary CommunicationsmdashWhatrsquos Possible (MILCOM rsquo88) pp431ndash436 San Diego Calif USA October 1988

[5] K Kim and A Polydoros ldquoOn the detection and classificationof quadrature digital modulations in broad-band noiserdquo IEEETransactions on Communications vol 38 no 8 pp 1199ndash12111990

[6] C S Long K M Chugg and A Polydoros ldquoFurther results inlikelihood classification of QAM signalsrdquo in Proceedings of theIEEE Military Communications Conference (MILCOM rsquo94) vol1 pp 57ndash61 IEEE Fort Monmouth NJ USA October 1994

[7] Y-C Lin and C-C J Kuo ldquoClassification of quadrature ampli-tude modulated (QAM) signals via sequential probability ratiotest (SPRT)rdquo Signal Processing vol 60 no 3 pp 263ndash280 1997

[8] W A Gardner and C M Spooner ldquoCyclic spectral analysis forsignal detection and modulation recognitionrdquo in Proceedings ofthe IEEEMilitary Communications Conference pp 419ndash424 SanDiego Calif USA October 1988

[9] L Hong and K C Ho ldquoIdentification of digital modulationtypes using the wavelet transformrdquo in Proceedings of the Mili-tary Communications Conference (MILCOM rsquo99) pp 427ndash431Atlantic City NJ USA November 1999

[10] K C Ho W Prokopiw and Y T Chan ldquoModulation iden-tification of digital signals by the wavelet transformrdquo IEEProceedingsmdashRadar Sonar and Navigation vol 147 no 4 pp169ndash176 2000

Mobile Information Systems 11

[11] C Cui H Li and J Yu ldquoMPSKmodulation classification basedon morlet transformrdquo Communication Technology vol 43 no3 pp 10ndash12 2010

[12] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009

[13] J-F Wang Y Yue and J Yao ldquoA MPSK recognition methodbased on high order cumulantsrdquo Communication Technologyvol 9 no 43 pp 4ndash6 2010

[14] J-X Wang and H Song ldquoDigital modulation recognitionbased on constellation diagramrdquo Journal of China Institute ofCommunications vol 25 no 6 pp 166ndash173 2004

[15] R Ghunhui W Ping and X Xianci ldquoClassification of MPSKsignals using the distribution of in-phase and quadraturesignalsrdquo Signal Processing vol 22 no 6 pp 787ndash790 2006

[16] T-J Lu S-B Guo and X-C Xiao ldquoFractal characteristicsresearch of modulated signalsrdquo Science in China Series ETechnological Sciences vol 31 no 6 pp 508ndash510 2001

[17] C Weber M Peter and T Felhauer ldquoAutomatic modulationclassification technique for radio monitoringrdquo Electronics Let-ters vol 51 no 10 pp 794ndash796 2015

[18] J-F Xu F-P Wang and Z-J Wang ldquoMPSK modulationrecognition method based on phase clusteringrdquo Journal ofCircuits and Systems vol 16 no 5 pp 55ndash58 2011

[19] X-Y Chen Y-F Min L-R Zheng and L Yang ldquoQuick moun-tain clustering algorithmrdquo Application Research of Computersvol 25 no 7 pp 2043ndash2045 2008

[20] N Ahmadi ldquoUsing fuzzy clustering and TTSAS algorithmfor modulation classification based on constellation diagramrdquoEngineering Applications of Artificial Intelligence vol 23 no 3pp 357ndash370 2010

[21] D C Rife and R R Boorstyn ldquoSingle-tone parameter esti-mation from discrete-time observationsrdquo IEEE Transactions onInformation Theory vol IT-20 no 5 pp 591ndash598 1974

[22] A B Awoseyila C Kasparis and B G Evans ldquoImproved singlefrequency estimation with wide acquisition rangerdquo ElectronicsLetters vol 44 no 3 pp 245ndash247 2008

Submit your manuscripts athttpwwwhindawicom

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

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4 Mobile Information Systems

Δ119891119879119887

le 015 an approximate exact complex sequence can beobtained from [21] and the phase sequence can be expressedas

120593119903

(119896) = 120593119909

(119896) + 2120587119896Δ119891119879119887

+ 120593119899

(119896) (6)

where 119879119887

is the symbol period and 119896 = 1 119873 is the samplespot where 119873 is the sample number of each data package120593119899

(119896) is the noisersquos phase and the phase of received signal120593119909

(119896) is

120593119909

(119896) isin 2120587119898

119872+ 120579

0

119898 = 0 1 119872 minus 1 (7)

In order to eliminate the influence of frequency offset asmuch as possible a new sequence can be obtained by makingdifference to 120593

119909

(119896) that is

1205931015840

119903

(119896) = 120593119903

(119896 + 1) minus 120593119903

(119896)

= 120593119909

(119896 + 1) minus 120593119909

(119896) + 2120587Δ119891119879119887

+ 120593119899

(119896 + 1)

minus 120593119899

(119896) = 1205931015840

119909

(119896) + 1205931015840

119899

(119896)

(8)

where

1205931015840

119909

(119896) isin 2120587119898

119872+ 2120587Δ119891119879

119887

119898 = 0 1 119872 minus 1 (9)

The major idea of Xursquos method for reducing the influenceof frequency offset is to employ the difference of phase of thebaseband signal 1205931015840

119903

(119896) as the signal to be processed the sameas the condition without frequency offset to get the correctsignal modulation order A significant premise mentionedin his paper is that 1205931015840

119909

(119896) is a uniform distribution objectHowever in this case the effective part (9) is no longer subjectto uniform distribution which directly leads to the phaseclustering algorithm invalid

Four commonMPSK signals are introduced for classifica-tion performance in XUrsquos paper The correction classificationprobability is adopted as the measure index

In order to enhance the recognition efficiency this paperproposes an improved method for phase clustering whichcan effectively reduce the signal processing time withoutdegrading the classification performance In addition in viewof the carrier frequency offset this paper also gives a feasiblesolution for its estimation and correction

3 Proposed Method

In order to achieve a better NDA classification performancefor signals an improved phase clusteringmethod is proposedin this paper Then a robust estimation method is proposedfor frequency offset correction

31 Advanced Phase ClusteringMethod The received wave ofmodulated PSK signal can be generally expressed as

119903 (119905) = sum119899

119886119899

119892 (119905 minus 119899119879119904

) 119890119895(2120587119891119888119905+1205790) + 119899 (119905) (10)

where 119886119899

isin exp(minus119895(2120587119898119872)) 119898 = 0 1 119872 minus 1 is thesymbol sequence 119872 is the modulation order 119892(119905) is the

shaping pulse of shaping filter 119879119904

is the sample period 119891119888

isthe carrier frequency and 120579

0

is the carrier phase (Figure 3)119899(119905) is the white Gaussian noise with zero mean and 119873

0

varianceRoot Raised Cosine (RRC) filter is generally adopted for

signal shaping in wireless communication networks It is alsoconsidered in this paper Under the premise of carrier andtiming synchronization the output baseband signalrsquos phaseafter matching filter can be written as

120593119903

(119896) = 120593119909

(119896) + 1205790

+ 120593119899

(119896) 119896 = 1 2 119873 (11)

where 120593119909

(119896) denotes the phase sequence of transmittedsignal 120593

119899

(119896) denotes the phase sequence of noise and 119873 isthe sample number of each data package For PSK signalits phase 120593

119909

(119896) expressed as follows commonly obeys touniform distribution which means that there are 119872119873sample spots intensely around each constellation point if119872-order modulated signal is sampled at119873 points

120593119909

(119896) isin 2120587119898

119872 119898 = 0 1 119872 minus 1 (12)

In order tomeasure the radian distance between the phaseof sampled point and reference phase a distance function119863(120576) is defined with independent variable 120576 isin [0 2120587) here

119863 (120576) =

|120576| |120576| le 120587

2120587 minus |120576| |120576| gt 120587(13)

An advanced clustering function is proposed for phaseclustering and expressed as fractional form which has aremarkable reduction on computation as comparing to theindex form as

V119903

(120579) =

119873

sum

119896=1

1

1 + (119873120587)119863 (120593119903

(119896) minus 120579) (14)

where 120579 isin [0 2120587) denotes the phase variable as the referencephase

A division set of 120579 is installed as the reference phasefor phase clustering As is shown in formula (14) all thephase to be processed need to measure the distance to eachreference phase 120579 before clustering In fact the clusteringprocess is similar to a repeated search process Just because ofthis the computational quantity of phase clustering is totallydetermined by the division set of 120579 A suitable division cannot only reduce the calculation amount of this method butalso enhance the correction rate of clustering The uniformdistance from 0 to 2120587 is a commonmethod of reference phasesegmentation

For simplicity an approximation is used to reduce calcu-lation amount When119863(120593

119903

(119896) minus 120579) ge 9120587119873

1

1 + (119873120587)119863 (120593119903

(119896) minus 120579)le 01 (15)

And it can be regarded as

1

1 + (119873120587)119863 (120593119903

(119896) minus 120579)asymp 0 (16)

Mobile Information Systems 5

When a baseband PSK signal is to be processed the advancedphase clustering (APC) function can be expressed as

V119903

(120579) =

119873

sum

119896=1

1

1 + (119873120587)119863 (120593119909

(119896) + 1205790

+ 120593119899

(119896) minus 120579) (17)

Assume that 120593119909

(119896) is distributed independently and hasan equal occurrence probability Since 120593

119899

(119896) is a stationaryGaussian phase noise formula (17) can transform into

V119903

(120579)

asymp119873

119872

119872minus1

sum119898=0

1

1 + (119873120587)119863 (2120587119898119872 + 1205790

+ 1205931015840119899

(119898) minus 120579)

(18)

Note that the necessary condition of the upper equationis the uniform distribution of the transmitted signal phasewithout noise In the ideal constellation there are approxi-mate119873119872 sample points distributed on the location of eachconstellation if the sample number of the received signalwhich has119872 modulation order is 119873 Otherwise the aboveequation is not established anymore

Due to the particularity of the distance function 119863(120576)has a periodicity of 2120587 On the other hand the independentvariable 120579 in the clustering function (14) is only related to thedistance function which leads to the fact that the clusteringfunction also has the periodicity of 2120587

The character of periodicity of formula (14) is given indetail When 120579 + 2120587119872 lt 2120587 the periodicity of clusteringfunction is formulated and elaborated in formula (19) It alsocan be proved as the sameway that V

119903

(120579+2120587119872minus2120587) = V119903

(120579)if 120579 + 2120587119872 gt 2120587

V119903

(120579 +2120587

119872) =

119873

119872

sdot

119872minus1

sum119898=0

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus (120579 + 2120587119872))

=119873

119872(

1

1 + (119873120587)119863 (120601 minus (120579 + 2120587119872))

+

119872minus1

sum119898=2

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus (120579 + 2120587119872))

+1

1 + (119873120587)119863 (2120587119872 + 120601 minus (120579 + 2120587119872)))

=119873

119872(

1

1 + (119873120587)119863 (2120587 + 120601 minus (120579 + 2120587119872))

+

119872minus2

sum119898=1

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus 120579)

+1

1 + (119873120587)119863 (120601 minus 120579)) =

119873

119872

sdot

119872minus1

sum119898=0

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus 120579)= V

119903

(120579)

(19)

The expression of clustering function V119903

(120579) is a periodicalfunction with

119879V =2120587

119872 (20)

Since the periodic signal has special spectral propertiesin frequency domain the period of clustering functioncan be extracted easily through Fast Fourier Transform(FFT) 119881

120579

(120596) = FFT[V119903

(120579)] The certain frequency whichis corresponding to the place of maximum value of itsFourier transform result indicates 119879V Modulation order 119872can be calculated through the above equation then signalsrsquoclassification is achieved More favorably carrier phase 120579

0

is irrelevant to this method for 119879V which means that thisproposed method is also robust to signalrsquos constellationrotation

If deep recognition requirements are needed for PSKsignals with the same modulation order lots of statisticsparameters can be chosen and employed For examplethere are two sets of data 4PSK and OQPSK 8PSK and(1205874)DQPSK Envelope entropy of differential phase of thebaseband signals can be introduced to distinguish themrespectively The recognition performance is certainly deter-mined by the introduced statistics parameters yet regardlessof the APC method

The APC method has several advantages

(1) Since it is derived from the coding characters ratherthan statistical properties the direct influence of SNRis reduced

(2) As an optimization algorithm of multiple peakssearching it achieves all the peaks in one calculationprocess and avoids repeated peak cuttings

(3) Fraction is used instead of exponential function inthe clustering function so that the calculation processis simplified which leads to a much lower computa-tional quantity

32 Frequency Offset Correction In the digital communica-tion system the carrier frequency offset is often introducedby the difference between the receiver and the transmitteroscillator and also caused by the Doppler frequency shiftwhich is brought by the channel nonlinearity and phase noiseIn the wireless network especially the electronic monitor-ing and other noncooperative communication systems theaccuracy of frequency offset estimation directly affects theperformance of the receiver

6 Mobile Information Systems

In Xursquos method mentioned in last section phase cluster-ing algorithm is directly adopted with the difference phase ofreceived signal However the difference phase of the effectivepart of signal which carries messages is no longer uniformdistribution Only frequency offset estimation and correctioncan be considered in this case to eliminate the impact offrequency offset as much as possible

The frequency offset estimations of the Fitz and LampRalgorithms are directly achieved via the weighted summationof the autocorrelation of the signal This means that thesetwo algorithms and the improvedmethods based upon themare all heavily affected by the correlation interval on theestimated range unless the correlation interval achieves itsmaximum value of sampled number 119873 However in thiscase the calculation amount increases dramatically especiallywhen 119873 is large For this particular reason most of theimproved methods are derived from Kayrsquos algorithm Theautocorrelation function of the processing signal is used inthe MampM algorithm used in Kayrsquos and LampWrsquos algorithmsfor weakening the influence brought on by phase noiseHowever the addition operation of the autocorrelationrsquosphase introduces the phase folding problem An objectionphase of the baseband signal which has a real value near minus120587or120587may be changed to a completely different value under theinfluence of noise and this leads to an error in the frequencyoffset estimation result The WNALP algorithm is derivedfrom the MampM algorithm which solves the phase foldingproblem and broadens the estimation range remarkablyHowever the signal in real noncooperative environmentsis usually intercepted under a low SNR due to its specialcondition which causes great difficulties in subsequent signalprocessing

In order to reduce the thresholdsrsquo effect and improvethe unbalance between estimation accuracy and estimationrange of frequency offset under low SNR an advancedNDA estimator based on the weighted summation of thedifferential phase of the autocorrelation is proposed in thispaper

Assume that timing synchronization is accomplishedThe baseband signal sequence with frequency offset 119909(119896) isexpressed as

119909 (119896) = 119888119896

exp119895(2120587119891Δ119896119879119904+120579) + 119899 (119896) (21)

where 119888119896

(119896 = 1 2 119873) is the modulated symbol sequencefrom the transmitting end 119873 is the number of samplingpoints of the selected signal segment in the receiving end119891Δ

is the unknown frequency offset to be estimated 119879119904

isthe sample period and 120579 is a random initial carrier phasewhich follows the uniformdistribution in the range of [0 2120587)Usually the channel noise of the communication system119899(119896) is considered to be random complex additive Gaussiannoise with zeromean and bilateral spectral density119873

0

2 Wenormalize its amplitude as

(119896) =119909 (119896)

|119909 (119896)| 119896 = 1 2 119873 (22)

Then under the hypothesis of 119899(119896) ≫ 1 for a large enoughSNR

(119896) ≃ 119890119895(2120587119896119891Δ119879119904+120579+

120573(119896))

(23)

where (119896) is also a Gaussian process with zero meanThe autocorrelation is defined as

1198770

(119898) =

119873

sum

119896=119898+1

(119896) lowast

(119896 minus 119898) 119898 = 1 2 119871119903

(24)

where (119896) = 119876

(119896) is the normalized baseband signalraised to the power of 119876 and 119871

119903

is the set maximumcorrelation interval Using the same principle as above theautocorrelation function can be continuously transformed as

1198770

(119898) ≃ 119890119895(2120587119898119891Δ119879119904+(119898)) (25)

where (119898) is also a Gaussian process with zeromeanWe seethat

ang1198770

(119898) 119877lowast

0

(119898 minus 1) = 2120587119891Δ

119879119904

+ (119898) + (119898 minus 1)

2 le 119898 le 119871119903

(26)

We define Δ1205930119877(119898)

≜ ang1198770

(119898)119877lowast

0

(119898minus 1) According to theprinciple of Kayrsquos algorithm an objective function can be setas

J0

= (Δ1205930 minus 2120587119891Δ119879119904e)119879Cminus1 (Δ1205930 minus 2120587119891Δ119879119904e) (27)

where Δ1205930 = [Δ1205930119877(1) Δ1205930119877(2) Δ1205930119877(119871119903)]119879 The estimated

value of the frequency offset Δ

is obtained when theobjective function J

0

obtains its minimum value So thenormalized weighted correlation linear estimator proposedcan be expressed as

Δ

=1

2120587119876119879119904

sdot

119871119903

sum119898=2

1205960

(119898) sdot arg [1198770

(119898) 119877lowast

0

(119898 minus 1)] (28)

where 1205960

is the weight of the differential phase

1205960

(119898) =3 [(119873 minus 119898) (119873 minus 119898 + 1) minus 119871

119903

(119873 minus 119871119903

)]

119871119903

(41198712119903

minus 6119871119903

119873 + 31198732 minus 1) (29)

The normalized baseband signal is considered to bethe signal to be processed which effectively weakens theperformance loss resulting from the nonlinear operation ofraising to a power of 119876 The weighted summation of thedifferential phase of the autocorrelation also decreases theinfluence of noise effectively compared to the method ofargument operation after weighting the conjugate differenceof the autocorrelation Thus it provides a better estimationaccuracy and is described in Kayrsquos paper [5]The difference ofautocorrelation is a great improvement which can make theestimation range independent of the maximum correlationinterval 119871

119903

and solve the phase folding problem comparedto Fitzrsquos and the LampR algorithm and the improved methodsbased upon them Meanwhile the proposed method in this

Mobile Information Systems 7

Table 1 Simulation time for order classification

Simulation time (s)HOMmethod 00158AKMCmethod 04523PC method 00720APC method 00345

paper has the same estimation range as its counterpartWNALP algorithm Importantly the large estimation vari-ance of the WNALP algorithm under low SNR conditionsis improved which effectively balances the trade-off betweenestimation accuracy and estimation range under low SNR inthe process of frequency offset estimation

4 Simulation

Computer simulations are performed to test the performanceof the methods proposed in this paper Considering thebackground of electronic monitoring and countermeasurein satellite communication and wireless communication net-works the simulation set contains six common modulationtypes of PSK signals BPSK QPSK 8PSK 16PSK OQPSK(1205874)DQPSK and UQPSK Each simulation result is theaverage of 1000 independent runs Because of the specialenvironment we assumed no a priori knowledge of inter-cepted signal is assumed for all the experiments

Regular communication equipment and environment areadopted for these simulations The signals are shaped byraised root cosine filter with its roll-off factor 120572 = 022 Thereceived intercepted signal is sampled 119873 = 512 points fortest with Sample frequency 119891

119904

= 20MHz We suppose thatthe symbol rate119873

119904

has been estimated accurately by a certainalgorithm and the sample number in per symbol period is119873119887

= 119873119904

lowast 119873119891119904

= 32 Additive white Gaussian noise isconsidered in this situationMoreover channel effects such asfading andmultipath propagation are ignored andwe assumethat perfect time and frequency synchronization have beenachievedThe SNR in this paper is defined as119864

119904

1198730

where119864119904

is the energy per symbol and1198730

is the power spectral densityof the Gaussian noise

A common method based on four-order cumulant(HOC) and two new ways derived from data miningadvanced 119870-means clustering (AKMC) and phase clustering(PC) are adopted for performance comparison of signalclassification Classification capabilities and simulation timesin a single run of the subroutines are shown in Figure 2 andTable 1 respectively

The same set of signal data to be processed are introducedin four subroutines respectively for classification perfor-mance and simulation time comparison Except for four-order cumulant the other three methods present obviouscorrect classification rate trends and a large SNR tolerancefor all the involved signals The 16PSK signal can be correctlyclassified from approximate 2 dB and the other six signalshave larger SNR tolerances less than minus5 dB Even so they aredistinguished clearly via simulation time table It is shown inTable 1 that PC method and AKMCmethod both cost two or

more times simulation time than APC method proposed inthis paper If the modulation order of signal to be processedis 16 the order needs to be chosen as 16 for accumulation inHOC algorithm However the computation amount of thisalgorithm increases exponentially It is a predictable resultthat its simulation time could be bigger than or equal tothe time of APC method Due to the instability of the APCalgorithm at the low SNRs few wrong judgements of thesignalrsquos modulation order appear That is the reason why theorder of 16PSK signal gets 17 during 1sim2 dB

In summary APC method proposed in this paper hasa better classification capability than its counterparts andgives a new guidance for practical signal processing Orderclassification result and correct classification rate by APCmethod are separately displayed in Figures 4-5

Frequency offset directly impacts on the performance ofsignal classification In order to verify the effectiveness ofthe proposed NWALPmethod theWNALP algorithm fromwhich the proposed method in this paper is derived wasselected for comparison in this paper

Let us assume that the signal to be processed is a QPSKsignal with additive Gaussian noise The number of samplepoints is set as 119873 = 256 and the sampling frequency isnormalized to the unit as 119891

119904

= 1 The correlation intervalof autocorrelation is set as 119871

119903

= 1198732 Each simulation ofestimation accuracy and estimation range for the frequencyoffset was run at least 100 times The estimation varianceis adopted as the measure of estimation accuracy TheMCRLB [22] is also calculated as an absolute measure of thetheoretical optimal valuation

MCRLB = 3

21205872119873(1198732 minus 1)sdot1

119864119904

1198730

(30)

The performance of the proposed method compared tothe abovementioned methods is shown in Figure 5 under anormalized frequency offset 119891

Δ

= 0001 as the SNR changeswithin the range ofminus15sim20 dB by 1 dB steps It can be seen thateven when the frequency offset is set at a smaller value theWNALPalgorithm still shows a poor estimation performanceof about 10minus2 under low SNRs This means that when thefrequency offset is small the error of the algorithm may beof the same order of magnitude as the frequency offset itselfSuch a large estimation error leads to a complete failure ofthe algorithm However it can be obviously seen that theestimation accuracy of the proposed method remains steadyin the vicinity of 10minus4 under low SNR conditions and hasan improved estimation accuracy of at least two orders ofmagnitude compared to the original WNALP algorithm Onthe other hand the estimation error of the proposed methodrapidly decreases to a magnitude near the MCRLB Even asthe SNR increases it remains steady at approximately 10minus7due to the SNR threshold effect

The estimation range of the carrier frequency offset isusually observed under large SNRs in order to obtain widerand more accurate bounds When SNR = 15 dB the esti-mated ranges of the chosen algorithms were simulated asshown in Figure 6 As can be seen the proposed NWALPmethod can achieve the same frequency offset estimation

8 Mobile Information Systems

0 5 10 15 20 25minus5SNR (dB)

0

02

04

06

08

1

CORR

CORR by 4-order cumulants CORR by advanced K-means clustering

CORR by phase clustering

0 5 10 15 20 25minus5

SNR (dB)

0

02

04

06

08

1

CORR

CORR by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5

SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

minus5 5 10 15 20 250SNR (dB)

0

02

04

06

08

1

CORR

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 2 Comparison of correct order recognition rate

range asWNALP which has proved to be a better choice for alarge estimation range than other algorithmsThis estimationrange cannot be increased even if the SNR increases It canbe seen that the proposed method in this paper can achieve alarge frequency offset estimation range

Figure 7 vividly shows the difference of constellationchanges before and after frequency offset correction bytwo distinct colors Signal with frequency offset make itsconstellation is displayed as a blue ring which cannot catchany constellation point However the approximate originalappearance is displayed after frequency offset correction withred It can be seen that the proposedmethod in this paper hasa remarkable effectiveness under 0 dB

5 Conclusion

This paper presents a robust classifier for NDA recognition innoncooperative wireless environment Nonsupervised clus-tering of the signal phase is achieved bymeasuring the radian

distance between each signal phase and the reference phaseThis method proposed optimizes the clustering functionand reduces the computation sharply Moreover frequencyoffset is considered and an advanced method is proposedfor frequency offset estimation and correction First a nor-malization of the baseband signal is performed After thenonlinear operation of raising the signal to a power of 119876 theestimate of frequency offset is obtained via the weighted sum-mation of the differential phase of the signalrsquos autocorrelationThis method balances estimation accuracy and range underlow SNR conditions which sharply improves the estimationaccuracy without shrinking the maximum estimation rangeeven if the SNR is as low as minus15 dB Seven common PSKsignals are adopted for simulation experiments The classi-fication performance and the estimation and correlation forfrequency offset are displayed and demonstrated with severalsimulation result figures which illustrate their feasibility andpractice

Mobile Information Systems 9

Order classification by advanced phase clustering

0 5 10 15 20 25minus5SNR (dB)

0

2

4

6

8

10

12

14

16

18

20

Ord

er

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 3 Order classification by advanced phase clustering

Correct order recognition rate by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 4 Correct order recognition rate by advanced phase cluster-ing

Generally this classifier which is derived from datamining and image processing has a guiding value for signalprocessing in electronic surveillance and electronic counter-measure of communication networks Further work such asthe initial optimization of clustering centers 120579 and multipath

Estimation of frequency offset (Δf = 0001)

NDA WNALPPROPOSEDMCRLB

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

10minus2

Varia

nce o

f fre

quen

cy o

ffset

estim

atio

n

minus10 minus5 0 5 10 15 20minus15

SNR (dB)

Figure 5 Comparison of estimation variance of frequency offset

NDA WNALPPROPOSEDMCRLB

Estimation of frequency offset (SNR = 15 dB)

minus005 0 005 01 015minus01

Frequency offset (normalized)

minus01

minus005

0

005

01

015

Mea

n va

lues

of e

stim

ated

freq

uenc

y off

set

Figure 6 Estimated range comparison

and Rayleigh channel and other practical problems is con-sidered for applications

Competing Interests

The authors declare that they have no competing interests

10 Mobile Information Systems

BPSK

minus1

0

1

0 2

05

15

minus05

minus15minus2

QPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

8PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

16PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Without FOCWith FOC

Without FOCWith FOC

Without FOCWith FOC

UQPSK

0 1

0

05

1

minus05

minus1minus1

PI4DQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

OQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Figure 7 Comparison of frequency offset correction

Acknowledgments

The authors would like to thank the support of FundamentalResearch Funds for the Central Universities (designationNSFC61371184)

References

[1] F F Liedtke ldquoComputer simulation of an automatic classifica-tion procedure for digitally modulated communication signalswith unknown parametersrdquo Signal Processing vol 6 no 4 pp311ndash323 1984

[2] Q Shi and Y Karasawa ldquoAutomatic modulation identificationbased on the probability density function of signal phaserdquo IEEETransactions on Communications vol 60 no 4 pp 1033ndash10442012

[3] A K Nandi and E E Azzouz ldquoAlgorithms for automatic mod-ulation recognition of communication signalsrdquo IEEE Transac-tions on Communications vol 46 no 4 pp 431ndash436 1998

[4] K Kim andA Polydoros ldquoDigitalmodulation classification theBPSK versus QPSK caserdquo in Proceedings of the IEEE MilitaryCommunications Conference Conference Record 21st CenturyMilitary CommunicationsmdashWhatrsquos Possible (MILCOM rsquo88) pp431ndash436 San Diego Calif USA October 1988

[5] K Kim and A Polydoros ldquoOn the detection and classificationof quadrature digital modulations in broad-band noiserdquo IEEETransactions on Communications vol 38 no 8 pp 1199ndash12111990

[6] C S Long K M Chugg and A Polydoros ldquoFurther results inlikelihood classification of QAM signalsrdquo in Proceedings of theIEEE Military Communications Conference (MILCOM rsquo94) vol1 pp 57ndash61 IEEE Fort Monmouth NJ USA October 1994

[7] Y-C Lin and C-C J Kuo ldquoClassification of quadrature ampli-tude modulated (QAM) signals via sequential probability ratiotest (SPRT)rdquo Signal Processing vol 60 no 3 pp 263ndash280 1997

[8] W A Gardner and C M Spooner ldquoCyclic spectral analysis forsignal detection and modulation recognitionrdquo in Proceedings ofthe IEEEMilitary Communications Conference pp 419ndash424 SanDiego Calif USA October 1988

[9] L Hong and K C Ho ldquoIdentification of digital modulationtypes using the wavelet transformrdquo in Proceedings of the Mili-tary Communications Conference (MILCOM rsquo99) pp 427ndash431Atlantic City NJ USA November 1999

[10] K C Ho W Prokopiw and Y T Chan ldquoModulation iden-tification of digital signals by the wavelet transformrdquo IEEProceedingsmdashRadar Sonar and Navigation vol 147 no 4 pp169ndash176 2000

Mobile Information Systems 11

[11] C Cui H Li and J Yu ldquoMPSKmodulation classification basedon morlet transformrdquo Communication Technology vol 43 no3 pp 10ndash12 2010

[12] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009

[13] J-F Wang Y Yue and J Yao ldquoA MPSK recognition methodbased on high order cumulantsrdquo Communication Technologyvol 9 no 43 pp 4ndash6 2010

[14] J-X Wang and H Song ldquoDigital modulation recognitionbased on constellation diagramrdquo Journal of China Institute ofCommunications vol 25 no 6 pp 166ndash173 2004

[15] R Ghunhui W Ping and X Xianci ldquoClassification of MPSKsignals using the distribution of in-phase and quadraturesignalsrdquo Signal Processing vol 22 no 6 pp 787ndash790 2006

[16] T-J Lu S-B Guo and X-C Xiao ldquoFractal characteristicsresearch of modulated signalsrdquo Science in China Series ETechnological Sciences vol 31 no 6 pp 508ndash510 2001

[17] C Weber M Peter and T Felhauer ldquoAutomatic modulationclassification technique for radio monitoringrdquo Electronics Let-ters vol 51 no 10 pp 794ndash796 2015

[18] J-F Xu F-P Wang and Z-J Wang ldquoMPSK modulationrecognition method based on phase clusteringrdquo Journal ofCircuits and Systems vol 16 no 5 pp 55ndash58 2011

[19] X-Y Chen Y-F Min L-R Zheng and L Yang ldquoQuick moun-tain clustering algorithmrdquo Application Research of Computersvol 25 no 7 pp 2043ndash2045 2008

[20] N Ahmadi ldquoUsing fuzzy clustering and TTSAS algorithmfor modulation classification based on constellation diagramrdquoEngineering Applications of Artificial Intelligence vol 23 no 3pp 357ndash370 2010

[21] D C Rife and R R Boorstyn ldquoSingle-tone parameter esti-mation from discrete-time observationsrdquo IEEE Transactions onInformation Theory vol IT-20 no 5 pp 591ndash598 1974

[22] A B Awoseyila C Kasparis and B G Evans ldquoImproved singlefrequency estimation with wide acquisition rangerdquo ElectronicsLetters vol 44 no 3 pp 245ndash247 2008

Submit your manuscripts athttpwwwhindawicom

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Distributed Sensor Networks

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Electrical and Computer Engineering

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mobile Information Systems 5

When a baseband PSK signal is to be processed the advancedphase clustering (APC) function can be expressed as

V119903

(120579) =

119873

sum

119896=1

1

1 + (119873120587)119863 (120593119909

(119896) + 1205790

+ 120593119899

(119896) minus 120579) (17)

Assume that 120593119909

(119896) is distributed independently and hasan equal occurrence probability Since 120593

119899

(119896) is a stationaryGaussian phase noise formula (17) can transform into

V119903

(120579)

asymp119873

119872

119872minus1

sum119898=0

1

1 + (119873120587)119863 (2120587119898119872 + 1205790

+ 1205931015840119899

(119898) minus 120579)

(18)

Note that the necessary condition of the upper equationis the uniform distribution of the transmitted signal phasewithout noise In the ideal constellation there are approxi-mate119873119872 sample points distributed on the location of eachconstellation if the sample number of the received signalwhich has119872 modulation order is 119873 Otherwise the aboveequation is not established anymore

Due to the particularity of the distance function 119863(120576)has a periodicity of 2120587 On the other hand the independentvariable 120579 in the clustering function (14) is only related to thedistance function which leads to the fact that the clusteringfunction also has the periodicity of 2120587

The character of periodicity of formula (14) is given indetail When 120579 + 2120587119872 lt 2120587 the periodicity of clusteringfunction is formulated and elaborated in formula (19) It alsocan be proved as the sameway that V

119903

(120579+2120587119872minus2120587) = V119903

(120579)if 120579 + 2120587119872 gt 2120587

V119903

(120579 +2120587

119872) =

119873

119872

sdot

119872minus1

sum119898=0

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus (120579 + 2120587119872))

=119873

119872(

1

1 + (119873120587)119863 (120601 minus (120579 + 2120587119872))

+

119872minus1

sum119898=2

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus (120579 + 2120587119872))

+1

1 + (119873120587)119863 (2120587119872 + 120601 minus (120579 + 2120587119872)))

=119873

119872(

1

1 + (119873120587)119863 (2120587 + 120601 minus (120579 + 2120587119872))

+

119872minus2

sum119898=1

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus 120579)

+1

1 + (119873120587)119863 (120601 minus 120579)) =

119873

119872

sdot

119872minus1

sum119898=0

1

1 + (119873120587)119863 (2120587119898119872 + 120601 minus 120579)= V

119903

(120579)

(19)

The expression of clustering function V119903

(120579) is a periodicalfunction with

119879V =2120587

119872 (20)

Since the periodic signal has special spectral propertiesin frequency domain the period of clustering functioncan be extracted easily through Fast Fourier Transform(FFT) 119881

120579

(120596) = FFT[V119903

(120579)] The certain frequency whichis corresponding to the place of maximum value of itsFourier transform result indicates 119879V Modulation order 119872can be calculated through the above equation then signalsrsquoclassification is achieved More favorably carrier phase 120579

0

is irrelevant to this method for 119879V which means that thisproposed method is also robust to signalrsquos constellationrotation

If deep recognition requirements are needed for PSKsignals with the same modulation order lots of statisticsparameters can be chosen and employed For examplethere are two sets of data 4PSK and OQPSK 8PSK and(1205874)DQPSK Envelope entropy of differential phase of thebaseband signals can be introduced to distinguish themrespectively The recognition performance is certainly deter-mined by the introduced statistics parameters yet regardlessof the APC method

The APC method has several advantages

(1) Since it is derived from the coding characters ratherthan statistical properties the direct influence of SNRis reduced

(2) As an optimization algorithm of multiple peakssearching it achieves all the peaks in one calculationprocess and avoids repeated peak cuttings

(3) Fraction is used instead of exponential function inthe clustering function so that the calculation processis simplified which leads to a much lower computa-tional quantity

32 Frequency Offset Correction In the digital communica-tion system the carrier frequency offset is often introducedby the difference between the receiver and the transmitteroscillator and also caused by the Doppler frequency shiftwhich is brought by the channel nonlinearity and phase noiseIn the wireless network especially the electronic monitor-ing and other noncooperative communication systems theaccuracy of frequency offset estimation directly affects theperformance of the receiver

6 Mobile Information Systems

In Xursquos method mentioned in last section phase cluster-ing algorithm is directly adopted with the difference phase ofreceived signal However the difference phase of the effectivepart of signal which carries messages is no longer uniformdistribution Only frequency offset estimation and correctioncan be considered in this case to eliminate the impact offrequency offset as much as possible

The frequency offset estimations of the Fitz and LampRalgorithms are directly achieved via the weighted summationof the autocorrelation of the signal This means that thesetwo algorithms and the improvedmethods based upon themare all heavily affected by the correlation interval on theestimated range unless the correlation interval achieves itsmaximum value of sampled number 119873 However in thiscase the calculation amount increases dramatically especiallywhen 119873 is large For this particular reason most of theimproved methods are derived from Kayrsquos algorithm Theautocorrelation function of the processing signal is used inthe MampM algorithm used in Kayrsquos and LampWrsquos algorithmsfor weakening the influence brought on by phase noiseHowever the addition operation of the autocorrelationrsquosphase introduces the phase folding problem An objectionphase of the baseband signal which has a real value near minus120587or120587may be changed to a completely different value under theinfluence of noise and this leads to an error in the frequencyoffset estimation result The WNALP algorithm is derivedfrom the MampM algorithm which solves the phase foldingproblem and broadens the estimation range remarkablyHowever the signal in real noncooperative environmentsis usually intercepted under a low SNR due to its specialcondition which causes great difficulties in subsequent signalprocessing

In order to reduce the thresholdsrsquo effect and improvethe unbalance between estimation accuracy and estimationrange of frequency offset under low SNR an advancedNDA estimator based on the weighted summation of thedifferential phase of the autocorrelation is proposed in thispaper

Assume that timing synchronization is accomplishedThe baseband signal sequence with frequency offset 119909(119896) isexpressed as

119909 (119896) = 119888119896

exp119895(2120587119891Δ119896119879119904+120579) + 119899 (119896) (21)

where 119888119896

(119896 = 1 2 119873) is the modulated symbol sequencefrom the transmitting end 119873 is the number of samplingpoints of the selected signal segment in the receiving end119891Δ

is the unknown frequency offset to be estimated 119879119904

isthe sample period and 120579 is a random initial carrier phasewhich follows the uniformdistribution in the range of [0 2120587)Usually the channel noise of the communication system119899(119896) is considered to be random complex additive Gaussiannoise with zeromean and bilateral spectral density119873

0

2 Wenormalize its amplitude as

(119896) =119909 (119896)

|119909 (119896)| 119896 = 1 2 119873 (22)

Then under the hypothesis of 119899(119896) ≫ 1 for a large enoughSNR

(119896) ≃ 119890119895(2120587119896119891Δ119879119904+120579+

120573(119896))

(23)

where (119896) is also a Gaussian process with zero meanThe autocorrelation is defined as

1198770

(119898) =

119873

sum

119896=119898+1

(119896) lowast

(119896 minus 119898) 119898 = 1 2 119871119903

(24)

where (119896) = 119876

(119896) is the normalized baseband signalraised to the power of 119876 and 119871

119903

is the set maximumcorrelation interval Using the same principle as above theautocorrelation function can be continuously transformed as

1198770

(119898) ≃ 119890119895(2120587119898119891Δ119879119904+(119898)) (25)

where (119898) is also a Gaussian process with zeromeanWe seethat

ang1198770

(119898) 119877lowast

0

(119898 minus 1) = 2120587119891Δ

119879119904

+ (119898) + (119898 minus 1)

2 le 119898 le 119871119903

(26)

We define Δ1205930119877(119898)

≜ ang1198770

(119898)119877lowast

0

(119898minus 1) According to theprinciple of Kayrsquos algorithm an objective function can be setas

J0

= (Δ1205930 minus 2120587119891Δ119879119904e)119879Cminus1 (Δ1205930 minus 2120587119891Δ119879119904e) (27)

where Δ1205930 = [Δ1205930119877(1) Δ1205930119877(2) Δ1205930119877(119871119903)]119879 The estimated

value of the frequency offset Δ

is obtained when theobjective function J

0

obtains its minimum value So thenormalized weighted correlation linear estimator proposedcan be expressed as

Δ

=1

2120587119876119879119904

sdot

119871119903

sum119898=2

1205960

(119898) sdot arg [1198770

(119898) 119877lowast

0

(119898 minus 1)] (28)

where 1205960

is the weight of the differential phase

1205960

(119898) =3 [(119873 minus 119898) (119873 minus 119898 + 1) minus 119871

119903

(119873 minus 119871119903

)]

119871119903

(41198712119903

minus 6119871119903

119873 + 31198732 minus 1) (29)

The normalized baseband signal is considered to bethe signal to be processed which effectively weakens theperformance loss resulting from the nonlinear operation ofraising to a power of 119876 The weighted summation of thedifferential phase of the autocorrelation also decreases theinfluence of noise effectively compared to the method ofargument operation after weighting the conjugate differenceof the autocorrelation Thus it provides a better estimationaccuracy and is described in Kayrsquos paper [5]The difference ofautocorrelation is a great improvement which can make theestimation range independent of the maximum correlationinterval 119871

119903

and solve the phase folding problem comparedto Fitzrsquos and the LampR algorithm and the improved methodsbased upon them Meanwhile the proposed method in this

Mobile Information Systems 7

Table 1 Simulation time for order classification

Simulation time (s)HOMmethod 00158AKMCmethod 04523PC method 00720APC method 00345

paper has the same estimation range as its counterpartWNALP algorithm Importantly the large estimation vari-ance of the WNALP algorithm under low SNR conditionsis improved which effectively balances the trade-off betweenestimation accuracy and estimation range under low SNR inthe process of frequency offset estimation

4 Simulation

Computer simulations are performed to test the performanceof the methods proposed in this paper Considering thebackground of electronic monitoring and countermeasurein satellite communication and wireless communication net-works the simulation set contains six common modulationtypes of PSK signals BPSK QPSK 8PSK 16PSK OQPSK(1205874)DQPSK and UQPSK Each simulation result is theaverage of 1000 independent runs Because of the specialenvironment we assumed no a priori knowledge of inter-cepted signal is assumed for all the experiments

Regular communication equipment and environment areadopted for these simulations The signals are shaped byraised root cosine filter with its roll-off factor 120572 = 022 Thereceived intercepted signal is sampled 119873 = 512 points fortest with Sample frequency 119891

119904

= 20MHz We suppose thatthe symbol rate119873

119904

has been estimated accurately by a certainalgorithm and the sample number in per symbol period is119873119887

= 119873119904

lowast 119873119891119904

= 32 Additive white Gaussian noise isconsidered in this situationMoreover channel effects such asfading andmultipath propagation are ignored andwe assumethat perfect time and frequency synchronization have beenachievedThe SNR in this paper is defined as119864

119904

1198730

where119864119904

is the energy per symbol and1198730

is the power spectral densityof the Gaussian noise

A common method based on four-order cumulant(HOC) and two new ways derived from data miningadvanced 119870-means clustering (AKMC) and phase clustering(PC) are adopted for performance comparison of signalclassification Classification capabilities and simulation timesin a single run of the subroutines are shown in Figure 2 andTable 1 respectively

The same set of signal data to be processed are introducedin four subroutines respectively for classification perfor-mance and simulation time comparison Except for four-order cumulant the other three methods present obviouscorrect classification rate trends and a large SNR tolerancefor all the involved signals The 16PSK signal can be correctlyclassified from approximate 2 dB and the other six signalshave larger SNR tolerances less than minus5 dB Even so they aredistinguished clearly via simulation time table It is shown inTable 1 that PC method and AKMCmethod both cost two or

more times simulation time than APC method proposed inthis paper If the modulation order of signal to be processedis 16 the order needs to be chosen as 16 for accumulation inHOC algorithm However the computation amount of thisalgorithm increases exponentially It is a predictable resultthat its simulation time could be bigger than or equal tothe time of APC method Due to the instability of the APCalgorithm at the low SNRs few wrong judgements of thesignalrsquos modulation order appear That is the reason why theorder of 16PSK signal gets 17 during 1sim2 dB

In summary APC method proposed in this paper hasa better classification capability than its counterparts andgives a new guidance for practical signal processing Orderclassification result and correct classification rate by APCmethod are separately displayed in Figures 4-5

Frequency offset directly impacts on the performance ofsignal classification In order to verify the effectiveness ofthe proposed NWALPmethod theWNALP algorithm fromwhich the proposed method in this paper is derived wasselected for comparison in this paper

Let us assume that the signal to be processed is a QPSKsignal with additive Gaussian noise The number of samplepoints is set as 119873 = 256 and the sampling frequency isnormalized to the unit as 119891

119904

= 1 The correlation intervalof autocorrelation is set as 119871

119903

= 1198732 Each simulation ofestimation accuracy and estimation range for the frequencyoffset was run at least 100 times The estimation varianceis adopted as the measure of estimation accuracy TheMCRLB [22] is also calculated as an absolute measure of thetheoretical optimal valuation

MCRLB = 3

21205872119873(1198732 minus 1)sdot1

119864119904

1198730

(30)

The performance of the proposed method compared tothe abovementioned methods is shown in Figure 5 under anormalized frequency offset 119891

Δ

= 0001 as the SNR changeswithin the range ofminus15sim20 dB by 1 dB steps It can be seen thateven when the frequency offset is set at a smaller value theWNALPalgorithm still shows a poor estimation performanceof about 10minus2 under low SNRs This means that when thefrequency offset is small the error of the algorithm may beof the same order of magnitude as the frequency offset itselfSuch a large estimation error leads to a complete failure ofthe algorithm However it can be obviously seen that theestimation accuracy of the proposed method remains steadyin the vicinity of 10minus4 under low SNR conditions and hasan improved estimation accuracy of at least two orders ofmagnitude compared to the original WNALP algorithm Onthe other hand the estimation error of the proposed methodrapidly decreases to a magnitude near the MCRLB Even asthe SNR increases it remains steady at approximately 10minus7due to the SNR threshold effect

The estimation range of the carrier frequency offset isusually observed under large SNRs in order to obtain widerand more accurate bounds When SNR = 15 dB the esti-mated ranges of the chosen algorithms were simulated asshown in Figure 6 As can be seen the proposed NWALPmethod can achieve the same frequency offset estimation

8 Mobile Information Systems

0 5 10 15 20 25minus5SNR (dB)

0

02

04

06

08

1

CORR

CORR by 4-order cumulants CORR by advanced K-means clustering

CORR by phase clustering

0 5 10 15 20 25minus5

SNR (dB)

0

02

04

06

08

1

CORR

CORR by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5

SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

minus5 5 10 15 20 250SNR (dB)

0

02

04

06

08

1

CORR

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 2 Comparison of correct order recognition rate

range asWNALP which has proved to be a better choice for alarge estimation range than other algorithmsThis estimationrange cannot be increased even if the SNR increases It canbe seen that the proposed method in this paper can achieve alarge frequency offset estimation range

Figure 7 vividly shows the difference of constellationchanges before and after frequency offset correction bytwo distinct colors Signal with frequency offset make itsconstellation is displayed as a blue ring which cannot catchany constellation point However the approximate originalappearance is displayed after frequency offset correction withred It can be seen that the proposedmethod in this paper hasa remarkable effectiveness under 0 dB

5 Conclusion

This paper presents a robust classifier for NDA recognition innoncooperative wireless environment Nonsupervised clus-tering of the signal phase is achieved bymeasuring the radian

distance between each signal phase and the reference phaseThis method proposed optimizes the clustering functionand reduces the computation sharply Moreover frequencyoffset is considered and an advanced method is proposedfor frequency offset estimation and correction First a nor-malization of the baseband signal is performed After thenonlinear operation of raising the signal to a power of 119876 theestimate of frequency offset is obtained via the weighted sum-mation of the differential phase of the signalrsquos autocorrelationThis method balances estimation accuracy and range underlow SNR conditions which sharply improves the estimationaccuracy without shrinking the maximum estimation rangeeven if the SNR is as low as minus15 dB Seven common PSKsignals are adopted for simulation experiments The classi-fication performance and the estimation and correlation forfrequency offset are displayed and demonstrated with severalsimulation result figures which illustrate their feasibility andpractice

Mobile Information Systems 9

Order classification by advanced phase clustering

0 5 10 15 20 25minus5SNR (dB)

0

2

4

6

8

10

12

14

16

18

20

Ord

er

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 3 Order classification by advanced phase clustering

Correct order recognition rate by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 4 Correct order recognition rate by advanced phase cluster-ing

Generally this classifier which is derived from datamining and image processing has a guiding value for signalprocessing in electronic surveillance and electronic counter-measure of communication networks Further work such asthe initial optimization of clustering centers 120579 and multipath

Estimation of frequency offset (Δf = 0001)

NDA WNALPPROPOSEDMCRLB

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

10minus2

Varia

nce o

f fre

quen

cy o

ffset

estim

atio

n

minus10 minus5 0 5 10 15 20minus15

SNR (dB)

Figure 5 Comparison of estimation variance of frequency offset

NDA WNALPPROPOSEDMCRLB

Estimation of frequency offset (SNR = 15 dB)

minus005 0 005 01 015minus01

Frequency offset (normalized)

minus01

minus005

0

005

01

015

Mea

n va

lues

of e

stim

ated

freq

uenc

y off

set

Figure 6 Estimated range comparison

and Rayleigh channel and other practical problems is con-sidered for applications

Competing Interests

The authors declare that they have no competing interests

10 Mobile Information Systems

BPSK

minus1

0

1

0 2

05

15

minus05

minus15minus2

QPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

8PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

16PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Without FOCWith FOC

Without FOCWith FOC

Without FOCWith FOC

UQPSK

0 1

0

05

1

minus05

minus1minus1

PI4DQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

OQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Figure 7 Comparison of frequency offset correction

Acknowledgments

The authors would like to thank the support of FundamentalResearch Funds for the Central Universities (designationNSFC61371184)

References

[1] F F Liedtke ldquoComputer simulation of an automatic classifica-tion procedure for digitally modulated communication signalswith unknown parametersrdquo Signal Processing vol 6 no 4 pp311ndash323 1984

[2] Q Shi and Y Karasawa ldquoAutomatic modulation identificationbased on the probability density function of signal phaserdquo IEEETransactions on Communications vol 60 no 4 pp 1033ndash10442012

[3] A K Nandi and E E Azzouz ldquoAlgorithms for automatic mod-ulation recognition of communication signalsrdquo IEEE Transac-tions on Communications vol 46 no 4 pp 431ndash436 1998

[4] K Kim andA Polydoros ldquoDigitalmodulation classification theBPSK versus QPSK caserdquo in Proceedings of the IEEE MilitaryCommunications Conference Conference Record 21st CenturyMilitary CommunicationsmdashWhatrsquos Possible (MILCOM rsquo88) pp431ndash436 San Diego Calif USA October 1988

[5] K Kim and A Polydoros ldquoOn the detection and classificationof quadrature digital modulations in broad-band noiserdquo IEEETransactions on Communications vol 38 no 8 pp 1199ndash12111990

[6] C S Long K M Chugg and A Polydoros ldquoFurther results inlikelihood classification of QAM signalsrdquo in Proceedings of theIEEE Military Communications Conference (MILCOM rsquo94) vol1 pp 57ndash61 IEEE Fort Monmouth NJ USA October 1994

[7] Y-C Lin and C-C J Kuo ldquoClassification of quadrature ampli-tude modulated (QAM) signals via sequential probability ratiotest (SPRT)rdquo Signal Processing vol 60 no 3 pp 263ndash280 1997

[8] W A Gardner and C M Spooner ldquoCyclic spectral analysis forsignal detection and modulation recognitionrdquo in Proceedings ofthe IEEEMilitary Communications Conference pp 419ndash424 SanDiego Calif USA October 1988

[9] L Hong and K C Ho ldquoIdentification of digital modulationtypes using the wavelet transformrdquo in Proceedings of the Mili-tary Communications Conference (MILCOM rsquo99) pp 427ndash431Atlantic City NJ USA November 1999

[10] K C Ho W Prokopiw and Y T Chan ldquoModulation iden-tification of digital signals by the wavelet transformrdquo IEEProceedingsmdashRadar Sonar and Navigation vol 147 no 4 pp169ndash176 2000

Mobile Information Systems 11

[11] C Cui H Li and J Yu ldquoMPSKmodulation classification basedon morlet transformrdquo Communication Technology vol 43 no3 pp 10ndash12 2010

[12] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009

[13] J-F Wang Y Yue and J Yao ldquoA MPSK recognition methodbased on high order cumulantsrdquo Communication Technologyvol 9 no 43 pp 4ndash6 2010

[14] J-X Wang and H Song ldquoDigital modulation recognitionbased on constellation diagramrdquo Journal of China Institute ofCommunications vol 25 no 6 pp 166ndash173 2004

[15] R Ghunhui W Ping and X Xianci ldquoClassification of MPSKsignals using the distribution of in-phase and quadraturesignalsrdquo Signal Processing vol 22 no 6 pp 787ndash790 2006

[16] T-J Lu S-B Guo and X-C Xiao ldquoFractal characteristicsresearch of modulated signalsrdquo Science in China Series ETechnological Sciences vol 31 no 6 pp 508ndash510 2001

[17] C Weber M Peter and T Felhauer ldquoAutomatic modulationclassification technique for radio monitoringrdquo Electronics Let-ters vol 51 no 10 pp 794ndash796 2015

[18] J-F Xu F-P Wang and Z-J Wang ldquoMPSK modulationrecognition method based on phase clusteringrdquo Journal ofCircuits and Systems vol 16 no 5 pp 55ndash58 2011

[19] X-Y Chen Y-F Min L-R Zheng and L Yang ldquoQuick moun-tain clustering algorithmrdquo Application Research of Computersvol 25 no 7 pp 2043ndash2045 2008

[20] N Ahmadi ldquoUsing fuzzy clustering and TTSAS algorithmfor modulation classification based on constellation diagramrdquoEngineering Applications of Artificial Intelligence vol 23 no 3pp 357ndash370 2010

[21] D C Rife and R R Boorstyn ldquoSingle-tone parameter esti-mation from discrete-time observationsrdquo IEEE Transactions onInformation Theory vol IT-20 no 5 pp 591ndash598 1974

[22] A B Awoseyila C Kasparis and B G Evans ldquoImproved singlefrequency estimation with wide acquisition rangerdquo ElectronicsLetters vol 44 no 3 pp 245ndash247 2008

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

6 Mobile Information Systems

In Xursquos method mentioned in last section phase cluster-ing algorithm is directly adopted with the difference phase ofreceived signal However the difference phase of the effectivepart of signal which carries messages is no longer uniformdistribution Only frequency offset estimation and correctioncan be considered in this case to eliminate the impact offrequency offset as much as possible

The frequency offset estimations of the Fitz and LampRalgorithms are directly achieved via the weighted summationof the autocorrelation of the signal This means that thesetwo algorithms and the improvedmethods based upon themare all heavily affected by the correlation interval on theestimated range unless the correlation interval achieves itsmaximum value of sampled number 119873 However in thiscase the calculation amount increases dramatically especiallywhen 119873 is large For this particular reason most of theimproved methods are derived from Kayrsquos algorithm Theautocorrelation function of the processing signal is used inthe MampM algorithm used in Kayrsquos and LampWrsquos algorithmsfor weakening the influence brought on by phase noiseHowever the addition operation of the autocorrelationrsquosphase introduces the phase folding problem An objectionphase of the baseband signal which has a real value near minus120587or120587may be changed to a completely different value under theinfluence of noise and this leads to an error in the frequencyoffset estimation result The WNALP algorithm is derivedfrom the MampM algorithm which solves the phase foldingproblem and broadens the estimation range remarkablyHowever the signal in real noncooperative environmentsis usually intercepted under a low SNR due to its specialcondition which causes great difficulties in subsequent signalprocessing

In order to reduce the thresholdsrsquo effect and improvethe unbalance between estimation accuracy and estimationrange of frequency offset under low SNR an advancedNDA estimator based on the weighted summation of thedifferential phase of the autocorrelation is proposed in thispaper

Assume that timing synchronization is accomplishedThe baseband signal sequence with frequency offset 119909(119896) isexpressed as

119909 (119896) = 119888119896

exp119895(2120587119891Δ119896119879119904+120579) + 119899 (119896) (21)

where 119888119896

(119896 = 1 2 119873) is the modulated symbol sequencefrom the transmitting end 119873 is the number of samplingpoints of the selected signal segment in the receiving end119891Δ

is the unknown frequency offset to be estimated 119879119904

isthe sample period and 120579 is a random initial carrier phasewhich follows the uniformdistribution in the range of [0 2120587)Usually the channel noise of the communication system119899(119896) is considered to be random complex additive Gaussiannoise with zeromean and bilateral spectral density119873

0

2 Wenormalize its amplitude as

(119896) =119909 (119896)

|119909 (119896)| 119896 = 1 2 119873 (22)

Then under the hypothesis of 119899(119896) ≫ 1 for a large enoughSNR

(119896) ≃ 119890119895(2120587119896119891Δ119879119904+120579+

120573(119896))

(23)

where (119896) is also a Gaussian process with zero meanThe autocorrelation is defined as

1198770

(119898) =

119873

sum

119896=119898+1

(119896) lowast

(119896 minus 119898) 119898 = 1 2 119871119903

(24)

where (119896) = 119876

(119896) is the normalized baseband signalraised to the power of 119876 and 119871

119903

is the set maximumcorrelation interval Using the same principle as above theautocorrelation function can be continuously transformed as

1198770

(119898) ≃ 119890119895(2120587119898119891Δ119879119904+(119898)) (25)

where (119898) is also a Gaussian process with zeromeanWe seethat

ang1198770

(119898) 119877lowast

0

(119898 minus 1) = 2120587119891Δ

119879119904

+ (119898) + (119898 minus 1)

2 le 119898 le 119871119903

(26)

We define Δ1205930119877(119898)

≜ ang1198770

(119898)119877lowast

0

(119898minus 1) According to theprinciple of Kayrsquos algorithm an objective function can be setas

J0

= (Δ1205930 minus 2120587119891Δ119879119904e)119879Cminus1 (Δ1205930 minus 2120587119891Δ119879119904e) (27)

where Δ1205930 = [Δ1205930119877(1) Δ1205930119877(2) Δ1205930119877(119871119903)]119879 The estimated

value of the frequency offset Δ

is obtained when theobjective function J

0

obtains its minimum value So thenormalized weighted correlation linear estimator proposedcan be expressed as

Δ

=1

2120587119876119879119904

sdot

119871119903

sum119898=2

1205960

(119898) sdot arg [1198770

(119898) 119877lowast

0

(119898 minus 1)] (28)

where 1205960

is the weight of the differential phase

1205960

(119898) =3 [(119873 minus 119898) (119873 minus 119898 + 1) minus 119871

119903

(119873 minus 119871119903

)]

119871119903

(41198712119903

minus 6119871119903

119873 + 31198732 minus 1) (29)

The normalized baseband signal is considered to bethe signal to be processed which effectively weakens theperformance loss resulting from the nonlinear operation ofraising to a power of 119876 The weighted summation of thedifferential phase of the autocorrelation also decreases theinfluence of noise effectively compared to the method ofargument operation after weighting the conjugate differenceof the autocorrelation Thus it provides a better estimationaccuracy and is described in Kayrsquos paper [5]The difference ofautocorrelation is a great improvement which can make theestimation range independent of the maximum correlationinterval 119871

119903

and solve the phase folding problem comparedto Fitzrsquos and the LampR algorithm and the improved methodsbased upon them Meanwhile the proposed method in this

Mobile Information Systems 7

Table 1 Simulation time for order classification

Simulation time (s)HOMmethod 00158AKMCmethod 04523PC method 00720APC method 00345

paper has the same estimation range as its counterpartWNALP algorithm Importantly the large estimation vari-ance of the WNALP algorithm under low SNR conditionsis improved which effectively balances the trade-off betweenestimation accuracy and estimation range under low SNR inthe process of frequency offset estimation

4 Simulation

Computer simulations are performed to test the performanceof the methods proposed in this paper Considering thebackground of electronic monitoring and countermeasurein satellite communication and wireless communication net-works the simulation set contains six common modulationtypes of PSK signals BPSK QPSK 8PSK 16PSK OQPSK(1205874)DQPSK and UQPSK Each simulation result is theaverage of 1000 independent runs Because of the specialenvironment we assumed no a priori knowledge of inter-cepted signal is assumed for all the experiments

Regular communication equipment and environment areadopted for these simulations The signals are shaped byraised root cosine filter with its roll-off factor 120572 = 022 Thereceived intercepted signal is sampled 119873 = 512 points fortest with Sample frequency 119891

119904

= 20MHz We suppose thatthe symbol rate119873

119904

has been estimated accurately by a certainalgorithm and the sample number in per symbol period is119873119887

= 119873119904

lowast 119873119891119904

= 32 Additive white Gaussian noise isconsidered in this situationMoreover channel effects such asfading andmultipath propagation are ignored andwe assumethat perfect time and frequency synchronization have beenachievedThe SNR in this paper is defined as119864

119904

1198730

where119864119904

is the energy per symbol and1198730

is the power spectral densityof the Gaussian noise

A common method based on four-order cumulant(HOC) and two new ways derived from data miningadvanced 119870-means clustering (AKMC) and phase clustering(PC) are adopted for performance comparison of signalclassification Classification capabilities and simulation timesin a single run of the subroutines are shown in Figure 2 andTable 1 respectively

The same set of signal data to be processed are introducedin four subroutines respectively for classification perfor-mance and simulation time comparison Except for four-order cumulant the other three methods present obviouscorrect classification rate trends and a large SNR tolerancefor all the involved signals The 16PSK signal can be correctlyclassified from approximate 2 dB and the other six signalshave larger SNR tolerances less than minus5 dB Even so they aredistinguished clearly via simulation time table It is shown inTable 1 that PC method and AKMCmethod both cost two or

more times simulation time than APC method proposed inthis paper If the modulation order of signal to be processedis 16 the order needs to be chosen as 16 for accumulation inHOC algorithm However the computation amount of thisalgorithm increases exponentially It is a predictable resultthat its simulation time could be bigger than or equal tothe time of APC method Due to the instability of the APCalgorithm at the low SNRs few wrong judgements of thesignalrsquos modulation order appear That is the reason why theorder of 16PSK signal gets 17 during 1sim2 dB

In summary APC method proposed in this paper hasa better classification capability than its counterparts andgives a new guidance for practical signal processing Orderclassification result and correct classification rate by APCmethod are separately displayed in Figures 4-5

Frequency offset directly impacts on the performance ofsignal classification In order to verify the effectiveness ofthe proposed NWALPmethod theWNALP algorithm fromwhich the proposed method in this paper is derived wasselected for comparison in this paper

Let us assume that the signal to be processed is a QPSKsignal with additive Gaussian noise The number of samplepoints is set as 119873 = 256 and the sampling frequency isnormalized to the unit as 119891

119904

= 1 The correlation intervalof autocorrelation is set as 119871

119903

= 1198732 Each simulation ofestimation accuracy and estimation range for the frequencyoffset was run at least 100 times The estimation varianceis adopted as the measure of estimation accuracy TheMCRLB [22] is also calculated as an absolute measure of thetheoretical optimal valuation

MCRLB = 3

21205872119873(1198732 minus 1)sdot1

119864119904

1198730

(30)

The performance of the proposed method compared tothe abovementioned methods is shown in Figure 5 under anormalized frequency offset 119891

Δ

= 0001 as the SNR changeswithin the range ofminus15sim20 dB by 1 dB steps It can be seen thateven when the frequency offset is set at a smaller value theWNALPalgorithm still shows a poor estimation performanceof about 10minus2 under low SNRs This means that when thefrequency offset is small the error of the algorithm may beof the same order of magnitude as the frequency offset itselfSuch a large estimation error leads to a complete failure ofthe algorithm However it can be obviously seen that theestimation accuracy of the proposed method remains steadyin the vicinity of 10minus4 under low SNR conditions and hasan improved estimation accuracy of at least two orders ofmagnitude compared to the original WNALP algorithm Onthe other hand the estimation error of the proposed methodrapidly decreases to a magnitude near the MCRLB Even asthe SNR increases it remains steady at approximately 10minus7due to the SNR threshold effect

The estimation range of the carrier frequency offset isusually observed under large SNRs in order to obtain widerand more accurate bounds When SNR = 15 dB the esti-mated ranges of the chosen algorithms were simulated asshown in Figure 6 As can be seen the proposed NWALPmethod can achieve the same frequency offset estimation

8 Mobile Information Systems

0 5 10 15 20 25minus5SNR (dB)

0

02

04

06

08

1

CORR

CORR by 4-order cumulants CORR by advanced K-means clustering

CORR by phase clustering

0 5 10 15 20 25minus5

SNR (dB)

0

02

04

06

08

1

CORR

CORR by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5

SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

minus5 5 10 15 20 250SNR (dB)

0

02

04

06

08

1

CORR

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 2 Comparison of correct order recognition rate

range asWNALP which has proved to be a better choice for alarge estimation range than other algorithmsThis estimationrange cannot be increased even if the SNR increases It canbe seen that the proposed method in this paper can achieve alarge frequency offset estimation range

Figure 7 vividly shows the difference of constellationchanges before and after frequency offset correction bytwo distinct colors Signal with frequency offset make itsconstellation is displayed as a blue ring which cannot catchany constellation point However the approximate originalappearance is displayed after frequency offset correction withred It can be seen that the proposedmethod in this paper hasa remarkable effectiveness under 0 dB

5 Conclusion

This paper presents a robust classifier for NDA recognition innoncooperative wireless environment Nonsupervised clus-tering of the signal phase is achieved bymeasuring the radian

distance between each signal phase and the reference phaseThis method proposed optimizes the clustering functionand reduces the computation sharply Moreover frequencyoffset is considered and an advanced method is proposedfor frequency offset estimation and correction First a nor-malization of the baseband signal is performed After thenonlinear operation of raising the signal to a power of 119876 theestimate of frequency offset is obtained via the weighted sum-mation of the differential phase of the signalrsquos autocorrelationThis method balances estimation accuracy and range underlow SNR conditions which sharply improves the estimationaccuracy without shrinking the maximum estimation rangeeven if the SNR is as low as minus15 dB Seven common PSKsignals are adopted for simulation experiments The classi-fication performance and the estimation and correlation forfrequency offset are displayed and demonstrated with severalsimulation result figures which illustrate their feasibility andpractice

Mobile Information Systems 9

Order classification by advanced phase clustering

0 5 10 15 20 25minus5SNR (dB)

0

2

4

6

8

10

12

14

16

18

20

Ord

er

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 3 Order classification by advanced phase clustering

Correct order recognition rate by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 4 Correct order recognition rate by advanced phase cluster-ing

Generally this classifier which is derived from datamining and image processing has a guiding value for signalprocessing in electronic surveillance and electronic counter-measure of communication networks Further work such asthe initial optimization of clustering centers 120579 and multipath

Estimation of frequency offset (Δf = 0001)

NDA WNALPPROPOSEDMCRLB

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

10minus2

Varia

nce o

f fre

quen

cy o

ffset

estim

atio

n

minus10 minus5 0 5 10 15 20minus15

SNR (dB)

Figure 5 Comparison of estimation variance of frequency offset

NDA WNALPPROPOSEDMCRLB

Estimation of frequency offset (SNR = 15 dB)

minus005 0 005 01 015minus01

Frequency offset (normalized)

minus01

minus005

0

005

01

015

Mea

n va

lues

of e

stim

ated

freq

uenc

y off

set

Figure 6 Estimated range comparison

and Rayleigh channel and other practical problems is con-sidered for applications

Competing Interests

The authors declare that they have no competing interests

10 Mobile Information Systems

BPSK

minus1

0

1

0 2

05

15

minus05

minus15minus2

QPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

8PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

16PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Without FOCWith FOC

Without FOCWith FOC

Without FOCWith FOC

UQPSK

0 1

0

05

1

minus05

minus1minus1

PI4DQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

OQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Figure 7 Comparison of frequency offset correction

Acknowledgments

The authors would like to thank the support of FundamentalResearch Funds for the Central Universities (designationNSFC61371184)

References

[1] F F Liedtke ldquoComputer simulation of an automatic classifica-tion procedure for digitally modulated communication signalswith unknown parametersrdquo Signal Processing vol 6 no 4 pp311ndash323 1984

[2] Q Shi and Y Karasawa ldquoAutomatic modulation identificationbased on the probability density function of signal phaserdquo IEEETransactions on Communications vol 60 no 4 pp 1033ndash10442012

[3] A K Nandi and E E Azzouz ldquoAlgorithms for automatic mod-ulation recognition of communication signalsrdquo IEEE Transac-tions on Communications vol 46 no 4 pp 431ndash436 1998

[4] K Kim andA Polydoros ldquoDigitalmodulation classification theBPSK versus QPSK caserdquo in Proceedings of the IEEE MilitaryCommunications Conference Conference Record 21st CenturyMilitary CommunicationsmdashWhatrsquos Possible (MILCOM rsquo88) pp431ndash436 San Diego Calif USA October 1988

[5] K Kim and A Polydoros ldquoOn the detection and classificationof quadrature digital modulations in broad-band noiserdquo IEEETransactions on Communications vol 38 no 8 pp 1199ndash12111990

[6] C S Long K M Chugg and A Polydoros ldquoFurther results inlikelihood classification of QAM signalsrdquo in Proceedings of theIEEE Military Communications Conference (MILCOM rsquo94) vol1 pp 57ndash61 IEEE Fort Monmouth NJ USA October 1994

[7] Y-C Lin and C-C J Kuo ldquoClassification of quadrature ampli-tude modulated (QAM) signals via sequential probability ratiotest (SPRT)rdquo Signal Processing vol 60 no 3 pp 263ndash280 1997

[8] W A Gardner and C M Spooner ldquoCyclic spectral analysis forsignal detection and modulation recognitionrdquo in Proceedings ofthe IEEEMilitary Communications Conference pp 419ndash424 SanDiego Calif USA October 1988

[9] L Hong and K C Ho ldquoIdentification of digital modulationtypes using the wavelet transformrdquo in Proceedings of the Mili-tary Communications Conference (MILCOM rsquo99) pp 427ndash431Atlantic City NJ USA November 1999

[10] K C Ho W Prokopiw and Y T Chan ldquoModulation iden-tification of digital signals by the wavelet transformrdquo IEEProceedingsmdashRadar Sonar and Navigation vol 147 no 4 pp169ndash176 2000

Mobile Information Systems 11

[11] C Cui H Li and J Yu ldquoMPSKmodulation classification basedon morlet transformrdquo Communication Technology vol 43 no3 pp 10ndash12 2010

[12] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009

[13] J-F Wang Y Yue and J Yao ldquoA MPSK recognition methodbased on high order cumulantsrdquo Communication Technologyvol 9 no 43 pp 4ndash6 2010

[14] J-X Wang and H Song ldquoDigital modulation recognitionbased on constellation diagramrdquo Journal of China Institute ofCommunications vol 25 no 6 pp 166ndash173 2004

[15] R Ghunhui W Ping and X Xianci ldquoClassification of MPSKsignals using the distribution of in-phase and quadraturesignalsrdquo Signal Processing vol 22 no 6 pp 787ndash790 2006

[16] T-J Lu S-B Guo and X-C Xiao ldquoFractal characteristicsresearch of modulated signalsrdquo Science in China Series ETechnological Sciences vol 31 no 6 pp 508ndash510 2001

[17] C Weber M Peter and T Felhauer ldquoAutomatic modulationclassification technique for radio monitoringrdquo Electronics Let-ters vol 51 no 10 pp 794ndash796 2015

[18] J-F Xu F-P Wang and Z-J Wang ldquoMPSK modulationrecognition method based on phase clusteringrdquo Journal ofCircuits and Systems vol 16 no 5 pp 55ndash58 2011

[19] X-Y Chen Y-F Min L-R Zheng and L Yang ldquoQuick moun-tain clustering algorithmrdquo Application Research of Computersvol 25 no 7 pp 2043ndash2045 2008

[20] N Ahmadi ldquoUsing fuzzy clustering and TTSAS algorithmfor modulation classification based on constellation diagramrdquoEngineering Applications of Artificial Intelligence vol 23 no 3pp 357ndash370 2010

[21] D C Rife and R R Boorstyn ldquoSingle-tone parameter esti-mation from discrete-time observationsrdquo IEEE Transactions onInformation Theory vol IT-20 no 5 pp 591ndash598 1974

[22] A B Awoseyila C Kasparis and B G Evans ldquoImproved singlefrequency estimation with wide acquisition rangerdquo ElectronicsLetters vol 44 no 3 pp 245ndash247 2008

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mobile Information Systems 7

Table 1 Simulation time for order classification

Simulation time (s)HOMmethod 00158AKMCmethod 04523PC method 00720APC method 00345

paper has the same estimation range as its counterpartWNALP algorithm Importantly the large estimation vari-ance of the WNALP algorithm under low SNR conditionsis improved which effectively balances the trade-off betweenestimation accuracy and estimation range under low SNR inthe process of frequency offset estimation

4 Simulation

Computer simulations are performed to test the performanceof the methods proposed in this paper Considering thebackground of electronic monitoring and countermeasurein satellite communication and wireless communication net-works the simulation set contains six common modulationtypes of PSK signals BPSK QPSK 8PSK 16PSK OQPSK(1205874)DQPSK and UQPSK Each simulation result is theaverage of 1000 independent runs Because of the specialenvironment we assumed no a priori knowledge of inter-cepted signal is assumed for all the experiments

Regular communication equipment and environment areadopted for these simulations The signals are shaped byraised root cosine filter with its roll-off factor 120572 = 022 Thereceived intercepted signal is sampled 119873 = 512 points fortest with Sample frequency 119891

119904

= 20MHz We suppose thatthe symbol rate119873

119904

has been estimated accurately by a certainalgorithm and the sample number in per symbol period is119873119887

= 119873119904

lowast 119873119891119904

= 32 Additive white Gaussian noise isconsidered in this situationMoreover channel effects such asfading andmultipath propagation are ignored andwe assumethat perfect time and frequency synchronization have beenachievedThe SNR in this paper is defined as119864

119904

1198730

where119864119904

is the energy per symbol and1198730

is the power spectral densityof the Gaussian noise

A common method based on four-order cumulant(HOC) and two new ways derived from data miningadvanced 119870-means clustering (AKMC) and phase clustering(PC) are adopted for performance comparison of signalclassification Classification capabilities and simulation timesin a single run of the subroutines are shown in Figure 2 andTable 1 respectively

The same set of signal data to be processed are introducedin four subroutines respectively for classification perfor-mance and simulation time comparison Except for four-order cumulant the other three methods present obviouscorrect classification rate trends and a large SNR tolerancefor all the involved signals The 16PSK signal can be correctlyclassified from approximate 2 dB and the other six signalshave larger SNR tolerances less than minus5 dB Even so they aredistinguished clearly via simulation time table It is shown inTable 1 that PC method and AKMCmethod both cost two or

more times simulation time than APC method proposed inthis paper If the modulation order of signal to be processedis 16 the order needs to be chosen as 16 for accumulation inHOC algorithm However the computation amount of thisalgorithm increases exponentially It is a predictable resultthat its simulation time could be bigger than or equal tothe time of APC method Due to the instability of the APCalgorithm at the low SNRs few wrong judgements of thesignalrsquos modulation order appear That is the reason why theorder of 16PSK signal gets 17 during 1sim2 dB

In summary APC method proposed in this paper hasa better classification capability than its counterparts andgives a new guidance for practical signal processing Orderclassification result and correct classification rate by APCmethod are separately displayed in Figures 4-5

Frequency offset directly impacts on the performance ofsignal classification In order to verify the effectiveness ofthe proposed NWALPmethod theWNALP algorithm fromwhich the proposed method in this paper is derived wasselected for comparison in this paper

Let us assume that the signal to be processed is a QPSKsignal with additive Gaussian noise The number of samplepoints is set as 119873 = 256 and the sampling frequency isnormalized to the unit as 119891

119904

= 1 The correlation intervalof autocorrelation is set as 119871

119903

= 1198732 Each simulation ofestimation accuracy and estimation range for the frequencyoffset was run at least 100 times The estimation varianceis adopted as the measure of estimation accuracy TheMCRLB [22] is also calculated as an absolute measure of thetheoretical optimal valuation

MCRLB = 3

21205872119873(1198732 minus 1)sdot1

119864119904

1198730

(30)

The performance of the proposed method compared tothe abovementioned methods is shown in Figure 5 under anormalized frequency offset 119891

Δ

= 0001 as the SNR changeswithin the range ofminus15sim20 dB by 1 dB steps It can be seen thateven when the frequency offset is set at a smaller value theWNALPalgorithm still shows a poor estimation performanceof about 10minus2 under low SNRs This means that when thefrequency offset is small the error of the algorithm may beof the same order of magnitude as the frequency offset itselfSuch a large estimation error leads to a complete failure ofthe algorithm However it can be obviously seen that theestimation accuracy of the proposed method remains steadyin the vicinity of 10minus4 under low SNR conditions and hasan improved estimation accuracy of at least two orders ofmagnitude compared to the original WNALP algorithm Onthe other hand the estimation error of the proposed methodrapidly decreases to a magnitude near the MCRLB Even asthe SNR increases it remains steady at approximately 10minus7due to the SNR threshold effect

The estimation range of the carrier frequency offset isusually observed under large SNRs in order to obtain widerand more accurate bounds When SNR = 15 dB the esti-mated ranges of the chosen algorithms were simulated asshown in Figure 6 As can be seen the proposed NWALPmethod can achieve the same frequency offset estimation

8 Mobile Information Systems

0 5 10 15 20 25minus5SNR (dB)

0

02

04

06

08

1

CORR

CORR by 4-order cumulants CORR by advanced K-means clustering

CORR by phase clustering

0 5 10 15 20 25minus5

SNR (dB)

0

02

04

06

08

1

CORR

CORR by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5

SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

minus5 5 10 15 20 250SNR (dB)

0

02

04

06

08

1

CORR

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 2 Comparison of correct order recognition rate

range asWNALP which has proved to be a better choice for alarge estimation range than other algorithmsThis estimationrange cannot be increased even if the SNR increases It canbe seen that the proposed method in this paper can achieve alarge frequency offset estimation range

Figure 7 vividly shows the difference of constellationchanges before and after frequency offset correction bytwo distinct colors Signal with frequency offset make itsconstellation is displayed as a blue ring which cannot catchany constellation point However the approximate originalappearance is displayed after frequency offset correction withred It can be seen that the proposedmethod in this paper hasa remarkable effectiveness under 0 dB

5 Conclusion

This paper presents a robust classifier for NDA recognition innoncooperative wireless environment Nonsupervised clus-tering of the signal phase is achieved bymeasuring the radian

distance between each signal phase and the reference phaseThis method proposed optimizes the clustering functionand reduces the computation sharply Moreover frequencyoffset is considered and an advanced method is proposedfor frequency offset estimation and correction First a nor-malization of the baseband signal is performed After thenonlinear operation of raising the signal to a power of 119876 theestimate of frequency offset is obtained via the weighted sum-mation of the differential phase of the signalrsquos autocorrelationThis method balances estimation accuracy and range underlow SNR conditions which sharply improves the estimationaccuracy without shrinking the maximum estimation rangeeven if the SNR is as low as minus15 dB Seven common PSKsignals are adopted for simulation experiments The classi-fication performance and the estimation and correlation forfrequency offset are displayed and demonstrated with severalsimulation result figures which illustrate their feasibility andpractice

Mobile Information Systems 9

Order classification by advanced phase clustering

0 5 10 15 20 25minus5SNR (dB)

0

2

4

6

8

10

12

14

16

18

20

Ord

er

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 3 Order classification by advanced phase clustering

Correct order recognition rate by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 4 Correct order recognition rate by advanced phase cluster-ing

Generally this classifier which is derived from datamining and image processing has a guiding value for signalprocessing in electronic surveillance and electronic counter-measure of communication networks Further work such asthe initial optimization of clustering centers 120579 and multipath

Estimation of frequency offset (Δf = 0001)

NDA WNALPPROPOSEDMCRLB

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

10minus2

Varia

nce o

f fre

quen

cy o

ffset

estim

atio

n

minus10 minus5 0 5 10 15 20minus15

SNR (dB)

Figure 5 Comparison of estimation variance of frequency offset

NDA WNALPPROPOSEDMCRLB

Estimation of frequency offset (SNR = 15 dB)

minus005 0 005 01 015minus01

Frequency offset (normalized)

minus01

minus005

0

005

01

015

Mea

n va

lues

of e

stim

ated

freq

uenc

y off

set

Figure 6 Estimated range comparison

and Rayleigh channel and other practical problems is con-sidered for applications

Competing Interests

The authors declare that they have no competing interests

10 Mobile Information Systems

BPSK

minus1

0

1

0 2

05

15

minus05

minus15minus2

QPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

8PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

16PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Without FOCWith FOC

Without FOCWith FOC

Without FOCWith FOC

UQPSK

0 1

0

05

1

minus05

minus1minus1

PI4DQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

OQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Figure 7 Comparison of frequency offset correction

Acknowledgments

The authors would like to thank the support of FundamentalResearch Funds for the Central Universities (designationNSFC61371184)

References

[1] F F Liedtke ldquoComputer simulation of an automatic classifica-tion procedure for digitally modulated communication signalswith unknown parametersrdquo Signal Processing vol 6 no 4 pp311ndash323 1984

[2] Q Shi and Y Karasawa ldquoAutomatic modulation identificationbased on the probability density function of signal phaserdquo IEEETransactions on Communications vol 60 no 4 pp 1033ndash10442012

[3] A K Nandi and E E Azzouz ldquoAlgorithms for automatic mod-ulation recognition of communication signalsrdquo IEEE Transac-tions on Communications vol 46 no 4 pp 431ndash436 1998

[4] K Kim andA Polydoros ldquoDigitalmodulation classification theBPSK versus QPSK caserdquo in Proceedings of the IEEE MilitaryCommunications Conference Conference Record 21st CenturyMilitary CommunicationsmdashWhatrsquos Possible (MILCOM rsquo88) pp431ndash436 San Diego Calif USA October 1988

[5] K Kim and A Polydoros ldquoOn the detection and classificationof quadrature digital modulations in broad-band noiserdquo IEEETransactions on Communications vol 38 no 8 pp 1199ndash12111990

[6] C S Long K M Chugg and A Polydoros ldquoFurther results inlikelihood classification of QAM signalsrdquo in Proceedings of theIEEE Military Communications Conference (MILCOM rsquo94) vol1 pp 57ndash61 IEEE Fort Monmouth NJ USA October 1994

[7] Y-C Lin and C-C J Kuo ldquoClassification of quadrature ampli-tude modulated (QAM) signals via sequential probability ratiotest (SPRT)rdquo Signal Processing vol 60 no 3 pp 263ndash280 1997

[8] W A Gardner and C M Spooner ldquoCyclic spectral analysis forsignal detection and modulation recognitionrdquo in Proceedings ofthe IEEEMilitary Communications Conference pp 419ndash424 SanDiego Calif USA October 1988

[9] L Hong and K C Ho ldquoIdentification of digital modulationtypes using the wavelet transformrdquo in Proceedings of the Mili-tary Communications Conference (MILCOM rsquo99) pp 427ndash431Atlantic City NJ USA November 1999

[10] K C Ho W Prokopiw and Y T Chan ldquoModulation iden-tification of digital signals by the wavelet transformrdquo IEEProceedingsmdashRadar Sonar and Navigation vol 147 no 4 pp169ndash176 2000

Mobile Information Systems 11

[11] C Cui H Li and J Yu ldquoMPSKmodulation classification basedon morlet transformrdquo Communication Technology vol 43 no3 pp 10ndash12 2010

[12] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009

[13] J-F Wang Y Yue and J Yao ldquoA MPSK recognition methodbased on high order cumulantsrdquo Communication Technologyvol 9 no 43 pp 4ndash6 2010

[14] J-X Wang and H Song ldquoDigital modulation recognitionbased on constellation diagramrdquo Journal of China Institute ofCommunications vol 25 no 6 pp 166ndash173 2004

[15] R Ghunhui W Ping and X Xianci ldquoClassification of MPSKsignals using the distribution of in-phase and quadraturesignalsrdquo Signal Processing vol 22 no 6 pp 787ndash790 2006

[16] T-J Lu S-B Guo and X-C Xiao ldquoFractal characteristicsresearch of modulated signalsrdquo Science in China Series ETechnological Sciences vol 31 no 6 pp 508ndash510 2001

[17] C Weber M Peter and T Felhauer ldquoAutomatic modulationclassification technique for radio monitoringrdquo Electronics Let-ters vol 51 no 10 pp 794ndash796 2015

[18] J-F Xu F-P Wang and Z-J Wang ldquoMPSK modulationrecognition method based on phase clusteringrdquo Journal ofCircuits and Systems vol 16 no 5 pp 55ndash58 2011

[19] X-Y Chen Y-F Min L-R Zheng and L Yang ldquoQuick moun-tain clustering algorithmrdquo Application Research of Computersvol 25 no 7 pp 2043ndash2045 2008

[20] N Ahmadi ldquoUsing fuzzy clustering and TTSAS algorithmfor modulation classification based on constellation diagramrdquoEngineering Applications of Artificial Intelligence vol 23 no 3pp 357ndash370 2010

[21] D C Rife and R R Boorstyn ldquoSingle-tone parameter esti-mation from discrete-time observationsrdquo IEEE Transactions onInformation Theory vol IT-20 no 5 pp 591ndash598 1974

[22] A B Awoseyila C Kasparis and B G Evans ldquoImproved singlefrequency estimation with wide acquisition rangerdquo ElectronicsLetters vol 44 no 3 pp 245ndash247 2008

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

8 Mobile Information Systems

0 5 10 15 20 25minus5SNR (dB)

0

02

04

06

08

1

CORR

CORR by 4-order cumulants CORR by advanced K-means clustering

CORR by phase clustering

0 5 10 15 20 25minus5

SNR (dB)

0

02

04

06

08

1

CORR

CORR by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5

SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

minus5 5 10 15 20 250SNR (dB)

0

02

04

06

08

1

CORR

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 2 Comparison of correct order recognition rate

range asWNALP which has proved to be a better choice for alarge estimation range than other algorithmsThis estimationrange cannot be increased even if the SNR increases It canbe seen that the proposed method in this paper can achieve alarge frequency offset estimation range

Figure 7 vividly shows the difference of constellationchanges before and after frequency offset correction bytwo distinct colors Signal with frequency offset make itsconstellation is displayed as a blue ring which cannot catchany constellation point However the approximate originalappearance is displayed after frequency offset correction withred It can be seen that the proposedmethod in this paper hasa remarkable effectiveness under 0 dB

5 Conclusion

This paper presents a robust classifier for NDA recognition innoncooperative wireless environment Nonsupervised clus-tering of the signal phase is achieved bymeasuring the radian

distance between each signal phase and the reference phaseThis method proposed optimizes the clustering functionand reduces the computation sharply Moreover frequencyoffset is considered and an advanced method is proposedfor frequency offset estimation and correction First a nor-malization of the baseband signal is performed After thenonlinear operation of raising the signal to a power of 119876 theestimate of frequency offset is obtained via the weighted sum-mation of the differential phase of the signalrsquos autocorrelationThis method balances estimation accuracy and range underlow SNR conditions which sharply improves the estimationaccuracy without shrinking the maximum estimation rangeeven if the SNR is as low as minus15 dB Seven common PSKsignals are adopted for simulation experiments The classi-fication performance and the estimation and correlation forfrequency offset are displayed and demonstrated with severalsimulation result figures which illustrate their feasibility andpractice

Mobile Information Systems 9

Order classification by advanced phase clustering

0 5 10 15 20 25minus5SNR (dB)

0

2

4

6

8

10

12

14

16

18

20

Ord

er

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 3 Order classification by advanced phase clustering

Correct order recognition rate by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 4 Correct order recognition rate by advanced phase cluster-ing

Generally this classifier which is derived from datamining and image processing has a guiding value for signalprocessing in electronic surveillance and electronic counter-measure of communication networks Further work such asthe initial optimization of clustering centers 120579 and multipath

Estimation of frequency offset (Δf = 0001)

NDA WNALPPROPOSEDMCRLB

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

10minus2

Varia

nce o

f fre

quen

cy o

ffset

estim

atio

n

minus10 minus5 0 5 10 15 20minus15

SNR (dB)

Figure 5 Comparison of estimation variance of frequency offset

NDA WNALPPROPOSEDMCRLB

Estimation of frequency offset (SNR = 15 dB)

minus005 0 005 01 015minus01

Frequency offset (normalized)

minus01

minus005

0

005

01

015

Mea

n va

lues

of e

stim

ated

freq

uenc

y off

set

Figure 6 Estimated range comparison

and Rayleigh channel and other practical problems is con-sidered for applications

Competing Interests

The authors declare that they have no competing interests

10 Mobile Information Systems

BPSK

minus1

0

1

0 2

05

15

minus05

minus15minus2

QPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

8PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

16PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Without FOCWith FOC

Without FOCWith FOC

Without FOCWith FOC

UQPSK

0 1

0

05

1

minus05

minus1minus1

PI4DQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

OQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Figure 7 Comparison of frequency offset correction

Acknowledgments

The authors would like to thank the support of FundamentalResearch Funds for the Central Universities (designationNSFC61371184)

References

[1] F F Liedtke ldquoComputer simulation of an automatic classifica-tion procedure for digitally modulated communication signalswith unknown parametersrdquo Signal Processing vol 6 no 4 pp311ndash323 1984

[2] Q Shi and Y Karasawa ldquoAutomatic modulation identificationbased on the probability density function of signal phaserdquo IEEETransactions on Communications vol 60 no 4 pp 1033ndash10442012

[3] A K Nandi and E E Azzouz ldquoAlgorithms for automatic mod-ulation recognition of communication signalsrdquo IEEE Transac-tions on Communications vol 46 no 4 pp 431ndash436 1998

[4] K Kim andA Polydoros ldquoDigitalmodulation classification theBPSK versus QPSK caserdquo in Proceedings of the IEEE MilitaryCommunications Conference Conference Record 21st CenturyMilitary CommunicationsmdashWhatrsquos Possible (MILCOM rsquo88) pp431ndash436 San Diego Calif USA October 1988

[5] K Kim and A Polydoros ldquoOn the detection and classificationof quadrature digital modulations in broad-band noiserdquo IEEETransactions on Communications vol 38 no 8 pp 1199ndash12111990

[6] C S Long K M Chugg and A Polydoros ldquoFurther results inlikelihood classification of QAM signalsrdquo in Proceedings of theIEEE Military Communications Conference (MILCOM rsquo94) vol1 pp 57ndash61 IEEE Fort Monmouth NJ USA October 1994

[7] Y-C Lin and C-C J Kuo ldquoClassification of quadrature ampli-tude modulated (QAM) signals via sequential probability ratiotest (SPRT)rdquo Signal Processing vol 60 no 3 pp 263ndash280 1997

[8] W A Gardner and C M Spooner ldquoCyclic spectral analysis forsignal detection and modulation recognitionrdquo in Proceedings ofthe IEEEMilitary Communications Conference pp 419ndash424 SanDiego Calif USA October 1988

[9] L Hong and K C Ho ldquoIdentification of digital modulationtypes using the wavelet transformrdquo in Proceedings of the Mili-tary Communications Conference (MILCOM rsquo99) pp 427ndash431Atlantic City NJ USA November 1999

[10] K C Ho W Prokopiw and Y T Chan ldquoModulation iden-tification of digital signals by the wavelet transformrdquo IEEProceedingsmdashRadar Sonar and Navigation vol 147 no 4 pp169ndash176 2000

Mobile Information Systems 11

[11] C Cui H Li and J Yu ldquoMPSKmodulation classification basedon morlet transformrdquo Communication Technology vol 43 no3 pp 10ndash12 2010

[12] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009

[13] J-F Wang Y Yue and J Yao ldquoA MPSK recognition methodbased on high order cumulantsrdquo Communication Technologyvol 9 no 43 pp 4ndash6 2010

[14] J-X Wang and H Song ldquoDigital modulation recognitionbased on constellation diagramrdquo Journal of China Institute ofCommunications vol 25 no 6 pp 166ndash173 2004

[15] R Ghunhui W Ping and X Xianci ldquoClassification of MPSKsignals using the distribution of in-phase and quadraturesignalsrdquo Signal Processing vol 22 no 6 pp 787ndash790 2006

[16] T-J Lu S-B Guo and X-C Xiao ldquoFractal characteristicsresearch of modulated signalsrdquo Science in China Series ETechnological Sciences vol 31 no 6 pp 508ndash510 2001

[17] C Weber M Peter and T Felhauer ldquoAutomatic modulationclassification technique for radio monitoringrdquo Electronics Let-ters vol 51 no 10 pp 794ndash796 2015

[18] J-F Xu F-P Wang and Z-J Wang ldquoMPSK modulationrecognition method based on phase clusteringrdquo Journal ofCircuits and Systems vol 16 no 5 pp 55ndash58 2011

[19] X-Y Chen Y-F Min L-R Zheng and L Yang ldquoQuick moun-tain clustering algorithmrdquo Application Research of Computersvol 25 no 7 pp 2043ndash2045 2008

[20] N Ahmadi ldquoUsing fuzzy clustering and TTSAS algorithmfor modulation classification based on constellation diagramrdquoEngineering Applications of Artificial Intelligence vol 23 no 3pp 357ndash370 2010

[21] D C Rife and R R Boorstyn ldquoSingle-tone parameter esti-mation from discrete-time observationsrdquo IEEE Transactions onInformation Theory vol IT-20 no 5 pp 591ndash598 1974

[22] A B Awoseyila C Kasparis and B G Evans ldquoImproved singlefrequency estimation with wide acquisition rangerdquo ElectronicsLetters vol 44 no 3 pp 245ndash247 2008

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mobile Information Systems 9

Order classification by advanced phase clustering

0 5 10 15 20 25minus5SNR (dB)

0

2

4

6

8

10

12

14

16

18

20

Ord

er

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 3 Order classification by advanced phase clustering

Correct order recognition rate by advanced phase clustering

0

02

04

06

08

1

CORR

0 5 10 15 20 25minus5SNR (dB)

BPSKQPSK8PSK16PSK

PI4DQPSKOQPSKUQPSK

Figure 4 Correct order recognition rate by advanced phase cluster-ing

Generally this classifier which is derived from datamining and image processing has a guiding value for signalprocessing in electronic surveillance and electronic counter-measure of communication networks Further work such asthe initial optimization of clustering centers 120579 and multipath

Estimation of frequency offset (Δf = 0001)

NDA WNALPPROPOSEDMCRLB

10minus10

10minus9

10minus8

10minus7

10minus6

10minus5

10minus4

10minus3

10minus2

Varia

nce o

f fre

quen

cy o

ffset

estim

atio

n

minus10 minus5 0 5 10 15 20minus15

SNR (dB)

Figure 5 Comparison of estimation variance of frequency offset

NDA WNALPPROPOSEDMCRLB

Estimation of frequency offset (SNR = 15 dB)

minus005 0 005 01 015minus01

Frequency offset (normalized)

minus01

minus005

0

005

01

015

Mea

n va

lues

of e

stim

ated

freq

uenc

y off

set

Figure 6 Estimated range comparison

and Rayleigh channel and other practical problems is con-sidered for applications

Competing Interests

The authors declare that they have no competing interests

10 Mobile Information Systems

BPSK

minus1

0

1

0 2

05

15

minus05

minus15minus2

QPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

8PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

16PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Without FOCWith FOC

Without FOCWith FOC

Without FOCWith FOC

UQPSK

0 1

0

05

1

minus05

minus1minus1

PI4DQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

OQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Figure 7 Comparison of frequency offset correction

Acknowledgments

The authors would like to thank the support of FundamentalResearch Funds for the Central Universities (designationNSFC61371184)

References

[1] F F Liedtke ldquoComputer simulation of an automatic classifica-tion procedure for digitally modulated communication signalswith unknown parametersrdquo Signal Processing vol 6 no 4 pp311ndash323 1984

[2] Q Shi and Y Karasawa ldquoAutomatic modulation identificationbased on the probability density function of signal phaserdquo IEEETransactions on Communications vol 60 no 4 pp 1033ndash10442012

[3] A K Nandi and E E Azzouz ldquoAlgorithms for automatic mod-ulation recognition of communication signalsrdquo IEEE Transac-tions on Communications vol 46 no 4 pp 431ndash436 1998

[4] K Kim andA Polydoros ldquoDigitalmodulation classification theBPSK versus QPSK caserdquo in Proceedings of the IEEE MilitaryCommunications Conference Conference Record 21st CenturyMilitary CommunicationsmdashWhatrsquos Possible (MILCOM rsquo88) pp431ndash436 San Diego Calif USA October 1988

[5] K Kim and A Polydoros ldquoOn the detection and classificationof quadrature digital modulations in broad-band noiserdquo IEEETransactions on Communications vol 38 no 8 pp 1199ndash12111990

[6] C S Long K M Chugg and A Polydoros ldquoFurther results inlikelihood classification of QAM signalsrdquo in Proceedings of theIEEE Military Communications Conference (MILCOM rsquo94) vol1 pp 57ndash61 IEEE Fort Monmouth NJ USA October 1994

[7] Y-C Lin and C-C J Kuo ldquoClassification of quadrature ampli-tude modulated (QAM) signals via sequential probability ratiotest (SPRT)rdquo Signal Processing vol 60 no 3 pp 263ndash280 1997

[8] W A Gardner and C M Spooner ldquoCyclic spectral analysis forsignal detection and modulation recognitionrdquo in Proceedings ofthe IEEEMilitary Communications Conference pp 419ndash424 SanDiego Calif USA October 1988

[9] L Hong and K C Ho ldquoIdentification of digital modulationtypes using the wavelet transformrdquo in Proceedings of the Mili-tary Communications Conference (MILCOM rsquo99) pp 427ndash431Atlantic City NJ USA November 1999

[10] K C Ho W Prokopiw and Y T Chan ldquoModulation iden-tification of digital signals by the wavelet transformrdquo IEEProceedingsmdashRadar Sonar and Navigation vol 147 no 4 pp169ndash176 2000

Mobile Information Systems 11

[11] C Cui H Li and J Yu ldquoMPSKmodulation classification basedon morlet transformrdquo Communication Technology vol 43 no3 pp 10ndash12 2010

[12] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009

[13] J-F Wang Y Yue and J Yao ldquoA MPSK recognition methodbased on high order cumulantsrdquo Communication Technologyvol 9 no 43 pp 4ndash6 2010

[14] J-X Wang and H Song ldquoDigital modulation recognitionbased on constellation diagramrdquo Journal of China Institute ofCommunications vol 25 no 6 pp 166ndash173 2004

[15] R Ghunhui W Ping and X Xianci ldquoClassification of MPSKsignals using the distribution of in-phase and quadraturesignalsrdquo Signal Processing vol 22 no 6 pp 787ndash790 2006

[16] T-J Lu S-B Guo and X-C Xiao ldquoFractal characteristicsresearch of modulated signalsrdquo Science in China Series ETechnological Sciences vol 31 no 6 pp 508ndash510 2001

[17] C Weber M Peter and T Felhauer ldquoAutomatic modulationclassification technique for radio monitoringrdquo Electronics Let-ters vol 51 no 10 pp 794ndash796 2015

[18] J-F Xu F-P Wang and Z-J Wang ldquoMPSK modulationrecognition method based on phase clusteringrdquo Journal ofCircuits and Systems vol 16 no 5 pp 55ndash58 2011

[19] X-Y Chen Y-F Min L-R Zheng and L Yang ldquoQuick moun-tain clustering algorithmrdquo Application Research of Computersvol 25 no 7 pp 2043ndash2045 2008

[20] N Ahmadi ldquoUsing fuzzy clustering and TTSAS algorithmfor modulation classification based on constellation diagramrdquoEngineering Applications of Artificial Intelligence vol 23 no 3pp 357ndash370 2010

[21] D C Rife and R R Boorstyn ldquoSingle-tone parameter esti-mation from discrete-time observationsrdquo IEEE Transactions onInformation Theory vol IT-20 no 5 pp 591ndash598 1974

[22] A B Awoseyila C Kasparis and B G Evans ldquoImproved singlefrequency estimation with wide acquisition rangerdquo ElectronicsLetters vol 44 no 3 pp 245ndash247 2008

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

10 Mobile Information Systems

BPSK

minus1

0

1

0 2

05

15

minus05

minus15minus2

QPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

8PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

16PSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Without FOCWith FOC

Without FOCWith FOC

Without FOCWith FOC

UQPSK

0 1

0

05

1

minus05

minus1minus1

PI4DQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

OQPSK

0

1

0 2

05

15

minus05

minus1

minus15minus2

Figure 7 Comparison of frequency offset correction

Acknowledgments

The authors would like to thank the support of FundamentalResearch Funds for the Central Universities (designationNSFC61371184)

References

[1] F F Liedtke ldquoComputer simulation of an automatic classifica-tion procedure for digitally modulated communication signalswith unknown parametersrdquo Signal Processing vol 6 no 4 pp311ndash323 1984

[2] Q Shi and Y Karasawa ldquoAutomatic modulation identificationbased on the probability density function of signal phaserdquo IEEETransactions on Communications vol 60 no 4 pp 1033ndash10442012

[3] A K Nandi and E E Azzouz ldquoAlgorithms for automatic mod-ulation recognition of communication signalsrdquo IEEE Transac-tions on Communications vol 46 no 4 pp 431ndash436 1998

[4] K Kim andA Polydoros ldquoDigitalmodulation classification theBPSK versus QPSK caserdquo in Proceedings of the IEEE MilitaryCommunications Conference Conference Record 21st CenturyMilitary CommunicationsmdashWhatrsquos Possible (MILCOM rsquo88) pp431ndash436 San Diego Calif USA October 1988

[5] K Kim and A Polydoros ldquoOn the detection and classificationof quadrature digital modulations in broad-band noiserdquo IEEETransactions on Communications vol 38 no 8 pp 1199ndash12111990

[6] C S Long K M Chugg and A Polydoros ldquoFurther results inlikelihood classification of QAM signalsrdquo in Proceedings of theIEEE Military Communications Conference (MILCOM rsquo94) vol1 pp 57ndash61 IEEE Fort Monmouth NJ USA October 1994

[7] Y-C Lin and C-C J Kuo ldquoClassification of quadrature ampli-tude modulated (QAM) signals via sequential probability ratiotest (SPRT)rdquo Signal Processing vol 60 no 3 pp 263ndash280 1997

[8] W A Gardner and C M Spooner ldquoCyclic spectral analysis forsignal detection and modulation recognitionrdquo in Proceedings ofthe IEEEMilitary Communications Conference pp 419ndash424 SanDiego Calif USA October 1988

[9] L Hong and K C Ho ldquoIdentification of digital modulationtypes using the wavelet transformrdquo in Proceedings of the Mili-tary Communications Conference (MILCOM rsquo99) pp 427ndash431Atlantic City NJ USA November 1999

[10] K C Ho W Prokopiw and Y T Chan ldquoModulation iden-tification of digital signals by the wavelet transformrdquo IEEProceedingsmdashRadar Sonar and Navigation vol 147 no 4 pp169ndash176 2000

Mobile Information Systems 11

[11] C Cui H Li and J Yu ldquoMPSKmodulation classification basedon morlet transformrdquo Communication Technology vol 43 no3 pp 10ndash12 2010

[12] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009

[13] J-F Wang Y Yue and J Yao ldquoA MPSK recognition methodbased on high order cumulantsrdquo Communication Technologyvol 9 no 43 pp 4ndash6 2010

[14] J-X Wang and H Song ldquoDigital modulation recognitionbased on constellation diagramrdquo Journal of China Institute ofCommunications vol 25 no 6 pp 166ndash173 2004

[15] R Ghunhui W Ping and X Xianci ldquoClassification of MPSKsignals using the distribution of in-phase and quadraturesignalsrdquo Signal Processing vol 22 no 6 pp 787ndash790 2006

[16] T-J Lu S-B Guo and X-C Xiao ldquoFractal characteristicsresearch of modulated signalsrdquo Science in China Series ETechnological Sciences vol 31 no 6 pp 508ndash510 2001

[17] C Weber M Peter and T Felhauer ldquoAutomatic modulationclassification technique for radio monitoringrdquo Electronics Let-ters vol 51 no 10 pp 794ndash796 2015

[18] J-F Xu F-P Wang and Z-J Wang ldquoMPSK modulationrecognition method based on phase clusteringrdquo Journal ofCircuits and Systems vol 16 no 5 pp 55ndash58 2011

[19] X-Y Chen Y-F Min L-R Zheng and L Yang ldquoQuick moun-tain clustering algorithmrdquo Application Research of Computersvol 25 no 7 pp 2043ndash2045 2008

[20] N Ahmadi ldquoUsing fuzzy clustering and TTSAS algorithmfor modulation classification based on constellation diagramrdquoEngineering Applications of Artificial Intelligence vol 23 no 3pp 357ndash370 2010

[21] D C Rife and R R Boorstyn ldquoSingle-tone parameter esti-mation from discrete-time observationsrdquo IEEE Transactions onInformation Theory vol IT-20 no 5 pp 591ndash598 1974

[22] A B Awoseyila C Kasparis and B G Evans ldquoImproved singlefrequency estimation with wide acquisition rangerdquo ElectronicsLetters vol 44 no 3 pp 245ndash247 2008

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mobile Information Systems 11

[11] C Cui H Li and J Yu ldquoMPSKmodulation classification basedon morlet transformrdquo Communication Technology vol 43 no3 pp 10ndash12 2010

[12] V D Orlic and M L Dukic ldquoAutomatic modulation classifica-tion algorithm using higher-order cumulants under real-worldchannel conditionsrdquo IEEE Communications Letters vol 13 no12 pp 917ndash919 2009

[13] J-F Wang Y Yue and J Yao ldquoA MPSK recognition methodbased on high order cumulantsrdquo Communication Technologyvol 9 no 43 pp 4ndash6 2010

[14] J-X Wang and H Song ldquoDigital modulation recognitionbased on constellation diagramrdquo Journal of China Institute ofCommunications vol 25 no 6 pp 166ndash173 2004

[15] R Ghunhui W Ping and X Xianci ldquoClassification of MPSKsignals using the distribution of in-phase and quadraturesignalsrdquo Signal Processing vol 22 no 6 pp 787ndash790 2006

[16] T-J Lu S-B Guo and X-C Xiao ldquoFractal characteristicsresearch of modulated signalsrdquo Science in China Series ETechnological Sciences vol 31 no 6 pp 508ndash510 2001

[17] C Weber M Peter and T Felhauer ldquoAutomatic modulationclassification technique for radio monitoringrdquo Electronics Let-ters vol 51 no 10 pp 794ndash796 2015

[18] J-F Xu F-P Wang and Z-J Wang ldquoMPSK modulationrecognition method based on phase clusteringrdquo Journal ofCircuits and Systems vol 16 no 5 pp 55ndash58 2011

[19] X-Y Chen Y-F Min L-R Zheng and L Yang ldquoQuick moun-tain clustering algorithmrdquo Application Research of Computersvol 25 no 7 pp 2043ndash2045 2008

[20] N Ahmadi ldquoUsing fuzzy clustering and TTSAS algorithmfor modulation classification based on constellation diagramrdquoEngineering Applications of Artificial Intelligence vol 23 no 3pp 357ndash370 2010

[21] D C Rife and R R Boorstyn ldquoSingle-tone parameter esti-mation from discrete-time observationsrdquo IEEE Transactions onInformation Theory vol IT-20 no 5 pp 591ndash598 1974

[22] A B Awoseyila C Kasparis and B G Evans ldquoImproved singlefrequency estimation with wide acquisition rangerdquo ElectronicsLetters vol 44 no 3 pp 245ndash247 2008

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014