AnM-QAMSignalModulationRecognitionAlgorithmin AWGNChannel

Research ArticleAn M-QAM Signal Modulation Recognition Algorithm inAWGN Channel

Ahmed K Ali and Ergun Erccedilelebi

Department of Electric and Electronic Engineering Gaziantep University Gaziantep 27310 Turkey

Correspondence should be addressed to Ahmed K Ali engineer28ahmedgmailcom

Received 10 November 2018 Revised 10 February 2019 Accepted 14 March 2019 Published 12 May 2019

Academic Editor Autilia Vitiello

Copyrightcopy 2019AhmedKAli andErgunErccedilelebi)is is an open access article distributed under theCreativeCommonsAttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Computing the distinct features from input data before the classification is a part of complexity to the methods of automaticmodulation classification (AMC) which deals with modulation classification and is a pattern recognition problem However thealgorithms that focus onmultilevel quadrature amplitudemodulation (M-QAM) which underneath different channel scenarios is welldetailed A search of the literature revealed that few studies were performed on the classification of high-order M-QAM modulationschemes such as 128-QAM 256-QAM 512-QAM and 1024-QAM)is work focuses on the investigation of the powerful capability ofthe natural logarithmic properties and the possibility of extracting higher order cumulantrsquos (HOC) features from input data receivedraw)e HOC signals were extracted under the additive white Gaussian noise (AWGN) channel with four effective parameters whichwere defined to distinguish the types of modulation from the set 4-QAMsim1024-QAM )is approach makes the classifier moreintelligent and improves the success rate of classification)e simulation results manifest that a very good classification rate is achievedat a low SNR of 5 dB which was performed under conditions of statistical noisy channel models )is shows the potential of thelogarithmic classifier model for the application ofM-QAM signal classification furthermore most results were promising and showedthat the logarithmic classifier works well under both AWGN and different fading channels as well as it can achieve a reliablerecognition rate even at a lower signal-to-noise ratio (less than zero) It can be considered as an integrated automatic modulationclassification (AMC) system in order to identify the higher order ofM-QAMsignals that has a unique logarithmic classifier to representhigher versatility Hence it has a superior performance in all previous works in automatic modulation identification systems

1 Introduction

Efficacious information transmission can be realized veryclearly in trendy communication systems and the trans-mitted signals are typically modulated by using variousmodulation ways Modulation recognition is an in-termediate way that must usually be achieved before signaldemodulation and information detection and it representsthe substantial feature in modern radio systems to giveknowledge on modulation signals rather than signal de-modulation and can be used in decoding both civilian andmilitary applications such as cognitive radio signal iden-tification menace assessment spectrum senses and man-agement which allows to more efficiently use the availablespectrum and increase the speed of data transfer Further-more the unknown signal classification is a decisive weaponin electronic warfare scenarios )e electronic supportmanagement system plays a paramount role as a source of

information is required to conduct electronic counter re-pression threat analysis warning and target acquisition

Particular recognition to modulation is the identificationof types of the transmitted signals that lie in noncooperativechannel environment groups which are significant for fol-lowing up the signal demodulation and data extraction andthis was considered as the major turn to automatic modu-lation classification (AMC) which became an attractivesubject for researchers yet there is a major challenging forengineers who deal with the design of software-defined radiosystems (SDRSs) and transmission deviation )e imple-mentation of sophisticated information services and systemsto military applications under a congested electromagneticspectrum is a major concern issue to communication engi-neers Friendly signals must be safely transmitted and re-ceived whilst enemy signals should be found and jammed [1]

)e first base of AMC theory is provided in [2] theessential ideas proposed at Stanford University in domestic

HindawiScientific ProgrammingVolume 2019 Article ID 6752694 17 pageshttpsdoiorg10115520196752694

project and was documented since 1969 and nowadays theAMC is extensively used and well known for communica-tion engineers as a significant part in the internal design ofintelligent radio systems [3 4]

Currently digital modulation identification algorithms canbe split into two techniques a maximum likelihood hypothesismethod which is based on decision theory [5] and statisticalpattern recognition which relies upon the feature extractionideas [6 7] in uncooperative channel environment )e al-gorithms of the pattern recognition technique are usually usedin practical application and that is due to the absence of priorknowledge from received modulation signals [8] )e dis-crimination method has particularly beneficial features forpattern recognition which are initially extracted from thevectors of data and the identification of the signal modulationmode that was completed upon the coverage between char-acteristic parameters and limits of the extracted features whichwas considered as the knownmode of the modulation type [9]

In the last five years a new modulation classificationtechnique has been proposed at the same time with the evo-lution of the automatic digital signal modulation recognitionalgorithms research and this new modulation offers a newtrend of complicated signal sets and higher order modulationsignals )e most commonly used features are high-ordercumulants (HOC) and high-order moment (HOM) [10] )eHOC-based techniques show superior performance to classifythe digital modulation signals at a low signal-to-noise ratio(SNR) these algorithms were documented in literature[11ndash13] Nevertheless they were not appropriate to classifyhigher-order M-QAM modulation formats Constellationshape varies from one modulation signal type to another inorder to be considered as a robust signature

)e constellation shape was used in the algorithms inreferences [14ndash16] to recognize various types of higher ordermodulation including 8-PSK and 16-QAM )e recognitionof success rate probabilities is around 95 but it still requiredmore SNR which may reach 4 dB However the constellationshape can be classified into M-PSK and M-QAM and at thesame time they are sensitive to several wireless channels thatcould seriously make confusions in work these comprisefrequency offset phase rotation and the application of raisedcosine roll-off filters Under this situation the symbol rate andfrequency offset setting must be more accurate during theperiods of presentment and at the same time the most widelyused features are a cyclic spectrum and cyclic frequency thatcould help multiple unwanted signals to be detected with eachof temporal and frequency-based overlaps [17ndash20]

In 2012 Dobber and his coworkers [21] suggested twonovel algorithms for the recognition of 4-QAM 16-QAM64-QAM and QAMV29 modulation schemes also other[22 23] authors suggested to use higher order cycliccumulants (CCs) which were obtained from received signalsas features for modulation classification Also this had beenput forward in [24] which presents a method to classifya number of mixed modulation schemes with an assort-ment of N-class problems and this technique alsoachieved a notable performance at low ranges of SNR Dueto the development of algorithms in machine learning the

researchers had started to design classification algorithmsbased on some aspects of machine learning which improvedthe classification ability and gives further pros to the clas-sifier in terms of distinguished types of modulation signals

Some investigations which were achieved on the behav-iors of hidden naive Bayes (HNB) [25] and on combination ofnaive Bayes (NB) and other types of classifiers to create a newclassifier named multiple classifier [26] certified that suchclassifier types were highly effective compared to conventionalclassifiers in terms of a small number of training iterations

Supervised learning technique was combined witha modified K-means algorithm that is based on four famousoptimization algorithms )is modification presented a newgeneration of the AMC technique Likewise artificial neuralnetworks (ANNs) with genetic algorithms were studied andconsidered by Norouz and his coworkers [27] and alsosupport vector machine (SVM) classifier in [28 29]

)e ways based on ANN and SVM show a superiorperformance although there is less prior information ofsignal features However multiple training samples anda long training period are necessary to accomplish sufficientlearning which increases the computational complexity andmakes the processing time longer

In the last five years researches widely explored the newtechniques in order to reduce the required SNR and make itmore efficient of recognition capability through focusing onrobust features and classifier designs One of the weak pointsof the previous algorithms is that the nature of the decision-tree is that it requires fixed threshold values due to thefeatures that had been proposed by the authors and thesefeatures are highly sensitive to any changes in SNR that canmake the threshold values be valid for small ranges of SNRabove to 10 dB However there had been no work until nowthat concentrates on the recognition of higher order QAMsignals in terms of the shape of feature distribution curves

In fact this assumption gives a good understanding of thebehavior of systems and reflects their major trends thereforeunder the circumstance of a channel corrupted by AWGNthis paper derived a relationship among of the higher ordercumulant as features and threshold levels in order to evaluatethe performance ofM-QAMmodulation recognition technique

2 Mathematical Analyses

21 Logarithmic Calculation Below are some theoreticalanalyses that assumes two logarithmic functions denotedf1(x1) and f2(x2) carrying different variable ldquox1 x2rdquo buthave the same base value ldquonrdquo which can be written as follows

f1 x1( 1113857 logn x11113858 1113859

f1 x2( 1113857 logn x21113858 1113859(1)

where the range of variables x1 ne x2 and the base value isconsidered to be the same )e ratio between f1(x1)andf2(x2) can be expressed as

W x1 x2( 1113857 logn x11113858 1113859

logn x21113858 1113859ln x11113858 1113859ln(n)

ln x21113858 1113859ln(n) (2)

2 Scientific Programming

In general the logarithmic equations can be expressedinto another equivalent form written as

logn x11113858 1113859 ln x11113858 1113859

ln(n) (3)

Since ln[x] is a log function it can also be expressed aslogr[x] where ldquorrdquo indicates the base value of natural log-arithms )erefore also equation (2) can be calculated as

W x1 x2( 1113857 ln x11113858 1113859ln(n)

ln x21113858 1113859ln(n) (4)

Due to the equality between numerator and de-nominator the ln(n) part has been eliminated)is gives theresult expressed as below

W x1 x2( 1113857 ln x11113858 1113859

ln x21113858 1113859 (5)

where x2 is the constant value ldquo10rdquo that makes w(x1 x2)

a constant as well )e logarithmic functions are definedbased on the higher order cumulant In Section 3 the featuredistribution curves with logarithmic properties are obtainedand the plot depicts that the modulation scheme is lesssensitive to the variation of SNR

3 Parameter Extraction Based onLogarithmic Properties

31 Parameter Extraction Based on HOC It is well notablethat a random variable y(t) under complex-stationaryprocess always has a zero mean value )erefore the fol-lowing transformation formula which is based on higherorder moments can be accomplished

C11 cum y(n)lowast y(n)

lowast( 1113857 M11


lowast( 1113857 M22 minusM

220 minus 2M

211


lowast y(n)

lowast( 1113857 M33 minus 6M20M31

minus 9M22M11 + 18 M20( 11138572M11 + 12M

311


lowast y(n)

lowast y(n)


240

minus 18M222 minus 54M

420 minus 144M

411 minus 432M

220M

211

+ 12M40M220 + 192M31M11M20 + 144M22M

211

+ 72M22M220

(6)

where the sign cum() represents the cumulant operationwhile the superscript ldquolowastrdquo represents the operation ofcomplex conjugate [30]

32 Improved Higher Order Cumulant Feature )e loga-rithmic expression formulas in (7)ndash(10) below show themodified higher order cumulant in terms of logarithm )epros of modification not only make these features insensitiveto noise but also help classifiers to recognize the increase inthe higher order modulation signals )e simulation con-dition tests of 10000 signal realizations from 4sim1024-

QAM each consisting signal length N 4096 with a phaseoffset of ldquoπ6rdquo with the statistical average value are shown inFigures 1ndash4 the distribution curve of each feature withvarying values of the SNR)rough the simulation results itis clear that the feature distribution curve is not significantlyaffected by variation of noise However this modificationprovides a better improvement in the achieved classificationactivity

fa log10 C111113868111386811138681113868

11138681113868111386811138681113960 1113961 (7)

fb log10 C221113868111386811138681113868

11138681113868111386811138681113960 1113961 (8)

fc log10 C331113868111386811138681113868

11138681113868111386811138681113960 1113961 (9)

fd log10 C441113868111386811138681113868

11138681113868111386811138681113960 1113961 (10)

4 Details on Algorithm andSimulation Performance

)e above four HOC parameters have been derived andmodified by using the logarithmic function to get optimumquality to recognize the M-QAM signals in the AWGNchannel However the basic procedure of the automaticmodulation classification system is shown in Figure 5 [31]while the actual decision procedure of the algorithm thathas been proposed is demonstrated in Figure 6 yet thelogarithmic modulation recognition method is effectivewith nine sets of M-QAM signals )e feature distributioncurves in Figures 1ndash4 show the extracted features ofmodulation formats Feature extraction is a primary stepin the pattern recognition method )reshold settings canthen be determined depending on the distribution con-ditions of the extracted features )e threshold levels havebeen determined based on the projection of two linesupward and downward with effective space to avoidmisclassification )e lines are parallel to the SNR axis(within a certain range of SNR) )e created cluster regionis used to separate required class distribution samples(modulation format that required discrimination) )epoints are computed empirically on the y-axis (featuredistribution level) and this criterion will give a highlyeffective recognition rate even with a minimum value ofSNR

Table 1 represents the feature threshold values whichwere set empirically )e Boolean equations (12)ndash(16) il-lustrated the logical decision process while Figure 7 showsthe block diagram of the M-QAM logarithmic recognitionalgorithm which is posterior to easily implement an ex-tension of the proposed method in real time

Algorithm 1 formally describes the procedures for thefeature extraction and the decision for modulation recogni-tion On the contrary in the feature extracting procedure theinput is represented by the data row after modulated with M-QAM However si dx signal passes through a noisy channelsi dxprime and the first step in extracting is fetching C111113864

C22C33C44 after computing the cumulant vector of signals

Scientific Programming 3

the process of the logarithmic classifier is begun and testedif fa0ltfx(φ0) if so index1 1 for the 4-QAM signal

Else if fxigefx(φi)ampampfxi

lefx(φi) indexi iprime where2nprimeQAM nprime gt 2 igt 1 iprime gt 1

)e same procedure is carried out for fai fbi

fci fdi

with the increase in the index i until i 8Algorithm 2 formally describes the procedure of de-

ciding which classifier has a better probability to discrimi-nate the required modulation format )e outcome of theclassifier to recognize a single class is boosted by one two orall classifiers )is operation depends on feature distributioncurves for each class Let us suppose that their featuredistribution curves have no overlapping parts and the curvesare approximately parallel to the SNR axis (within a certain

range of SNR) All classifiers set ldquotruerdquo )e input isfai

fbi fci

fdi with i index

If(indexfai iprime)||(indexfbi

iprime)||(indexfci iprime)||

(indexfci iprime) is true then increase the index CCindex SNR

)is procedure continues until fai fbi

fci fdi

i8Algorithm 2 has been developed to shorten the execution

time of signal recognition and classifier speed incrementand moreover to improve the accuracy of the classifierAlgorithm 2 can be summarized as follows the comparisonis achieved by logical operation of the sequential statusfai

fbi fci

fdii As result if either present statue could not

recognize the candidate class in both cases of signalnoisepower ratio is greater or less than 0 dB To overcome thatsituation other classifiers strengthened the present status

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM

256 QAM512 QAM1024 QAM

005

115

225

335

445

555

6

ndash5ndash4ndash3ndash2ndash1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20SNR (dB)

f b

Figure 2 Feature ldquofbrdquo distribution curve vs SNR with the test of10000 signal realizations from 4sim1024-QAM each consistingsignal length N 4096 with a phase offset of ldquoπ6rdquo

0123456789

1011121314151617


f d

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


Figure 4 Feature ldquofdrdquo distribution curve vs SNR with the test of10000 signal realizations from 4sim1024-QAM each consistingsignal length N 4096 with a phase offset of ldquoπ6rdquo

0

1

2

3

4

5

6

7

8

9

10


f c

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


Figure 3 Feature ldquofcrdquo distribution curve vs SNR with the test of10000 signal realizations from 4sim1024-QAM each consistingsignal length N 4096 with a phase offset of ldquoπ6rdquo

0

05

1

15

2

25

3

35


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


f a

Figure 1 Feature ldquofardquo distribution curve vs SNR with the test of10000 signal realizations from 4sim1024-QAM each consistingsignal length N 4096 with a phase offset of ldquoπ6rdquo


and boosted the probability of the correct recognition ratebefore deciding the correct modulation

)e mathematical expression of the decision boundaryof the logarithmic classifier algorithm of the higher orderQAM signals is expressed below For instance for an inputfeature Dx

(1) the threshold levels are concluded from theresults in Table 1 at i 0 and expressed as logical status

Dx(1) fa gefa φ0( 1113857ampfa ltfa φ2( 11138571113858 1113859 (11)

Remark iprime (i + 1) for 4-QAM iprime 1 likewise the ex-pression of Dx

(i)gt1 is as follows

Da(i+1) fa gefa φiminus1( 1113857ampfa ltfa φi+1( 11138571113858 1113859 (12)

Db(i+1) fb gefb φiminus1( 1113857ampfb ltfb φi+1( 11138571113858 1113859 (13)

Dc(i+1) fc gefc φiminus1( 1113857ampfc ltfc φi+1( 11138571113858 1113859 (14)

Start

Calculate logarithmic features fa fb fc fd

D1

4 QAM

Yes

No D2 D3

D6 D5 D4

D7 D8 D9

No

128 QAM

Yes

8 QAM

Yes

16 QAM

Yes

512 QAM

Yes

64 QAM

Yes

32 QAM

Yes

256 QAM

Yes

No

1024 QAM

Yes

OthersNoNo

No

NoNo

No

Figure 6 Flowchart of the M-QAM recognition algorithm

AMC module

Signal preprocessing

Classifier

Demodulation Output data

Rx

Rx receiver side AMC automatic modulation classification

Feature computation

Receiverenergydetectordownconverter

bandpass filter

Classes

Figure 5 Procedure for automatic modulation classification


Feature boundary based on logic status

Constellation shape with

AWGN

Data normalized

Logarithmic features fa fb fc fd

Modulation type

Decision boundaryDa (i + 1)

PCC ()

PCC probability of correct classificationfx feature data vector

Decision boundaryDb (i + 1)

Decision boundaryDc (i + 1)

Decision boundaryDd (i + 1)

Figure 7 )e block diagram of our logarithmic classification system

Input generate digital M-QAM modulation signalsDx d1 d2 d3 di and x isin a b c d M 2n n 2 3 4 5 6 7 8 9 10si dx si row of data after modulated by M-QAM signalOutput v isin index fai

fbi fci

fdi1113966 1113967 output boundary with indexi

Step 1 si dxprime corrupted by Gaussian random noise

Calculate cumulants C11 C22 C33 and C44Step 2 fai

log10[|C11i(si)|] fbi

log10[|C22i(si)|]

fci log10[|C33i

(si)|] fdi log10[|C44i

(si)|] Step 3 If fa0

ltfx(φ0)1113966 1113967 4-QAMindexi 1Step 4 Else If fxi

gefx(φi)ampampfxilefx(φi)1113966 1113967

where 2nprimeQAM nprime gt 2 igt 1 iprime gt 1indexi iprimeStep 5 Return v

ALGORITHM 1 Logarithmic classifier of higher order QAM modulation signals

Table 1 Optimum threshold values to each logarithmic feature

I fa fb fc fd

0 05 15 15 31 095 22 3 52 13 27 4 643 152 31 5 764 18 37 63 95 22 43 66 106 25 48 75 117 3 57 9 128 45 75 125 155

Input v isin index fai fbi

fci fdi

1113966 1113967i input boundary with indexi

Output PCCi probability of correct recognition

Step 1 If (indexfai iprime)||(indexfbi

iprime)||(indexfci iprime)||(indexfdi

iprime)CCindex SNR CCi + 1 correct rate countsEndStep 2 Return Pcc

ALGORITHM 2 Choose a higher and better classifier


Dd(i+1) fd gefd φiminus1( 1113857ampfd ltfd φi+1( 11138571113858 1113859 (15)

Di Da(i+1) D

b(i+1)

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868Dc(i+1) D

d(i+1)

11138681113868111386811138681113868

11138681113868111386811138681113868 (16)

where fx(φi) is the threshold value to each of the logarithmicfeatures in which x isin a b c d and i 0 2 3 4 8 wherethe threshold count here is 8 and also iprime 1 2 3 4 9 isa class pattern number ofQAMsignals that is being recognized

Referring to the flowchart in Figure 7 and equations(12)ndash(16) under the effect of SNR theMonte Carlo simulationwas carried 10000 times realization for each one of the nine

M-QAM signals and then it was tested by using the proposedlogarithmic classifier and the phase was offset by using threedegrees starting from 16π as the reference point

)is work emerges some promising results and thesimulation results are arranged in Figures 8ndash15 )e moststriking result that formed in Figures 8ndash11 shows that whenSNR ge 5 the recognition rate of M-QAM signals can reachover 99 even with variation in both sample length andphase offset therefore the algorithm proposed in this paperis very efficient in recognizing these signals and in order toevaluate the performance of the proposed algorithma comparison is conducted in terms of the probability of

ndash10 ndash5 0 5 10 15 20SNR (dB)

0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


Figure 8 )e probability of correct classification rate vs SNR with 10000 signal realizations from 4sim1024-QAM each consisting signallength N 4096 and phase offset ldquoπ6rdquo

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)




correct classification (PCC) versus SNR which can be for-mulated as

PCC 1113944

j

k1p ωk ∣ ωk( 1113857P ωk( 1113857

probability of correct classification rate

PCC middot 100

(17)

In the same direction ldquoJrdquo is the modulation signalcandidate classification (ω1ω2ω3ωj) where P(ωk) is theprobability of the modulation scheme when (ωk) occurwhile P(ωk ∣ ωk) is the probability of correct classificationwhen an (ωk) constellation is sent [32]

5 Discussion

All the simulations have been done under the computersimulation environment)e experiments were carried out inthree stages in the presence of AWGN first extract the HOCfeatures and then pass through the feature modifier the latterwill be a logarithmic classifier based on HOC Second makea decision based on the threshold algorithm and thirdachieve the evaluation of PCC for each modulation type

It appears from the simulation results that the bestperformance curve is achieved in using the length of sample4096 samples )is was performed based on the fact thatincreasing the data set can overcome the overfitting prob-lem Nevertheless this performance has the highest

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


Figure 10 )e probability of correct classification rate vs SNR with 10000 signal realizations from 4sim1024-QAM consisting signal lengthN 4096 and phase offset ldquoπ3rdquo

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


Figure 11)e probability of correct classification rate vs SNR with 10000 signal realizations from 4sim1024-QAM each consisting variablesignal length from N 64 128 265 512 1024 2048 4096 and phase offset ldquoπ6rdquo


classification rate at a low SNR from ndash3 dB to 20 dB asshown in Figure 8

On the contrary the curves for variable sample length[64 128 256 512 1024 2048 and 4096] indicate a con-verged accuracy in the same test range of the SNR and thiscan be clearly observed in Figure 11

)e accuracy of classifications is lower when reducing thenumber of samples transmitted while in the proposed al-gorithm the sample length has been reduced to [2048 1024512 256] )e probability of the correct classification ratioranges from about 80 to 100 in the SNR range of 0 to20 dB as shown in Figures 12ndash15 respectively )is is mainlydue to the reason that we proposed a method which

considered that the HOCrsquos feature is based on logarithmicmodification this will create a new classifier known asa logarithmic classifier However when SNRgeminus5 the classifieraccuracy deteriorates but does not collapse the correct clas-sification rate that becomes below 75 and the phase offsetwill be considered as shown in Figure 9 in which the phaseoffset were π4 while in Figure 10 the phase offset is π3 )eproposed algorithm gives a consistent classification accuracyof about 997 in the range of SNR from 2dB to 20 dB

It was observed when the phase offset changed theprobability of the correct classification rate is almost equaland this was due to the high robustness of the proposedclassifier Eventually the superior performance of the

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


ndash10 ndash5 10 15 20SNR (dB)

0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

0 5

Figure 12 )e probability of correct classification rate vs SNR with 10000 signal realizations 4sim1024-QAM each consisting signal lengthN 256 and phase offset ldquoπ6rdquo

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5



proposed classifier changed the phase offset and also var-iability of the transmitted signal length is attributed to theefficient of the proposed logarithmic classifier

51 EvaluationAccuracy andComplexitywithOtherMethodsBecause of the complexity of the classification algorithm thisresearch suggests a different method of classifications toconventional modulation [10 11] which requires a differentlogarithmic operations Yet still it is crucial in terms of highprobabilities to correct the recognition rate and less processis required to calculate the cumulant orders at the sametime the other studies do not highlight these promising lines[21 23 33ndash35]

Although cumulant-based classifier methods were con-venient to cope with M-QAM modulation recognition yet itdoes not provide a sufficient classification rate M-QAMmodes under fading channel and it can even produce missingclassification in some circumstances while the logarithmicclassifier of M-QAM signals has a better probability of correctrecognition rate at SNR range between minus5dB and 20 dB

)e performance of the logarithmic classifier of M-QAMis superior in what was proposed in terms of its ability todistinguish between high order and very high order of QAMsignals and thus can be considered as one of the pillars forthe modulation techniques in the future due to un-precedented demand for the wireless communication

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5

Figure 14 )e probability of correct classification rate vs SNR with 10000 signal realizations from 4-1024-QAM each consisting signallength N 1024 and phase offset ldquoπ6rdquo

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5

Figure 15 )e Probability of correct classification rate vs SNR with 10000 signal realizations 4-1024-QAM each consisting signal lengthN 2048 and phase offset ldquoπ6rdquo


technology expecting to reach an estimated 76 billion by2020 [36]

According to Table 2 the fourth-order cumulantclassifier has the lowest complexity while the combina-tion between forth- sixth- and eighth-order cumulantsbased classifier has the highest complications due to the

use of exponential operations however it is worth toclarify that the logarithmic classifier in this research workdepends on unique combination between lowest andhighest orders of cumulant and this combination willcreate an integrity and a less complexity classifier system)e complexity of several methods proposed that

Table 2 Comparison between proposed classifier with other systems in the literature

ReferenceClassifier structure Modulation type System performance

Simulation toolFeatures Complexity M-QAM M-PSK SNR (dB) Accuracy ()

[33] C40 C41 C42 C60

C61 C62C63

High 16 64 4minus3 Not covering

MATLAB functionsare invoked to implement

and evaluatethe performance

0 Not coveringge+5 784ndash100

[34] C40 C41 C42 C60

C61 C62C63

High 16 64 2 4minus3 Not covering0 Not coveringge+5 898ndash100

[11] C11 C22 C33 C44 Medium 16sim256 Nominus3 98330 100ge+5 100

[35]C20 C21 C40 C41

C42 C60C61C62

C63

High 16 64 256 2 4 8minus3 Not covering0 776ge+5 9996

[23]

C20 C21 C40 C41

C42 C60C61C62

C63 C80 C81C82

C83 C84

High 16 64 256 2 4 8and others

minus3 Not covering0 Not covering

ge+5 Unknown

[21] C20 C21 C41 C42

C63Medium 16 64 V29 4

minus3 600 81ge+5 90

[10] C20 C21 C40 C41

C42Medium 8 16 32 64 4 8 16 32 64

minus3 260 45ge+5 95

Proposedalgorithm

Logarithmiccumulant Medium (8sim1024) 4

minus3 75ndash950 80ndash98ge+5 100

ldquosimrdquo refers values from M-QAM to M-QAM and ldquordquo refers values M-QAM and M-QAM note that signal length N 4096

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

Figure 16 )e probability of correct classification rate vs SNR with 10000 signal realizations from 4sim1024-QAM each consisting signallength N 4096 and phase offset ldquoπ6rdquo under AWGN plus fast frequency selective Ricean fading channel with fD 5 kHz


occurred in previous work was compared in detail asshown in Table 2

)e results shown in Figures 16 and 17 indicate theperformance degradation of classification for QAMsignals versus their performance in the AWGN channelIt is not difficult to understand that the cause of theperformance degradation comes from the multipathchannel fading and Doppler fading effects model )eweakness performance of cumulant-based classifierswith fading channels has been documented in [22] )eonly exception in the logarithmic classifier that maintainsthe same level of classification accuracy is typically atSNR gt5 dB despite the different fading channel modelsused

6 Robustness Evaluation Cases

61 Under Different Channel Models Research in themodulation classification of digital signals approximatelystarted since forty years ago and the robustness evaluationof conventional AMC methods under the AWGN channelhas been well established in the literature [37ndash39] Similarlythe use of AWGN as the channel model is a common practicefor communication engineers and researchers [19 40]

In information theory the basic communication channelmodel AWGN that represents the effect of several randomprocesses occurring in nature is in the same direction by whichAWGN is used as a channel model where the communicationimpairment is an addition of white noise with a constantspectral density and normally distributed amplitude In thiswork the proposed logarithmic classifier has shown superiorperformance under the AWGN channel even with low SNRalso with variable lengths of the transmitted signal

Table 2 shows the robustness analysis among previousworks which were investigated in the development of themodulation classification algorithm It appears very clearly

that the logarithmic classifier has higher classification ac-curacy of modulation schemes 4-1024-QAM which alsoachieves a high percentage when the SNRge 5

Although AWGN alone could be a proper model to thedegradation of signals in free space yet the existence ofphysical obstructions such as building and towers can causemultipath propagation losses It implies that the signalreaches the receiver site via multiple propagation pathsRespecting to the relative lengths of the paths this could beeither constructive or destructive interference Furthermorerelative motion between the transmitter and receiver maycause the Doppler shift )e performance of the proposedclassifier is also investigated in the AWGN channel with fastfrequency-selective fading also with the effect of Rayleighand Rician magnitude channel fading while the phase wasrandomly distributed and was assumed to be constantthrough the symbol period which indicates no loss insignals Rician factor is defined as the ratio between thepower of the direct path and the power of the reflected pathswhich is a constant value Here it is assumed to be 3 dB

)e specification used was based on Molisch and hiscoworker research [41] with a symbol rate of 384 times 106symbols per second average path gains [0minus09minus49minus8

minus78minus239]dB path delays [0 2 8 12 23 37] times 10minus7 sec-onds and maximum Doppler shift of 5 kHz Figures 16 and17 depict the probability of correct recognition rate at signallength N 4096 in the AWGN plus fast frequency selectivewith 50 kHz of maximum Doppler shifts with Rician andRayleigh fading channels respectively Furthermore Fig-ures 18 and 19 show the probability of correct recognitionrate with variable signal lengths in AWGN plus fast fre-quency selective with 50 kHz of maximum Doppler shifts inRician and Rayleigh fading channels respectively

As could be observed in Figures 16 and 17 respectivelyunder signal propagation over multipath it gives an ac-cepted classification rate when SNR is not lower than 4 dB

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

Figure 17 )e probability of correct classification rate vs SNR with 10000 signal realizations from 4sim1024-QAM each consisting signallength N 4096 and phase offset ldquoπ6rdquo under AWGN plus fast frequency selective Rayleigh fading channel with fD 5 kHz


although with presence of effect of the Doppler shift Also itcould be observed in Figures 16 and 17 )e probability ofthe correct classification rate at SNR gt 4 dB is higher for theRician fading channels compared to the Rayleigh fadingchannels )is is because of the existence of the strong signaldue to the line of sight component It is well noted thata higher Doppler shift results in a lower probability ofcorrect classification [41] As well as contrast to that thelogarithmic classifier provides unexpected performance evenwith the existence of the Doppler shift and signal istransmitted with a variable length between 64-4096 It is

also important to underline that the proposed classifiervouchsafes satisfactory results under both fading channelenvironments Rician and Rayleigh

As could also be observed in Figures 16 and 17 mainly atSNR lower than minus2 dB the correct classification rate has fallenbelow 80 especially to 32 64 128 256 QAM signals )iscould be noted when the SNR is lower than 0dB

)e intraclass recognition of the modulation order usingthe logarithmic classifier gives different results depending onthe modulation type For example the simulations in thiswork illustrated that this recognition will be better for 1024-

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

Figure 19)e probability of correct classification rate vs SNR with 10000 signal realizations from 4sim1024-QAM each consisting variablesignal length from N 64 128 265 512 1024 2048 4096 and phase offset ldquoπ6rdquo under AWGN plus fast frequency selective Rayleigh fadingchannel with fD 5 kHz

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

Figure 18)e probability of correct classification rate vs SNR with 10000 signal realizations from 4sim1024-QAM each consisting variablesignal length from N 64 128 265 512 1024 2048 4096 and phase offset ldquoπ6rdquo under AWGN plus fast frequency selective Ricean fadingchannel with fD 5 kHz


QAM and 512-QAM schemes than other modulationschemes where the probability percent is high to correct theclassification rate Similarly the SNR is not lower than 0 dBand the results show that the probability of the recognitionrate gives the lowest percentage for 32-QAM and 64-QAMsignals which can be observed in Figures 16ndash19 It is alsoimportant to mention that the fluctuations in performancein the correct recognition rate is in higher order QAMsignals and that is due to the internal structures of thelogarithmic classifier

It seems that the effect of variation in the frequency offsetof the transmitted signals almost insignificantly influences thelogarithmic classifier although under SNRminus2 and randomsignal lengths Figures 20(a) and 20(b) depict the probabilityof the correct classification rate vs frequency offset and signallength N 4096 Likewise Figure 20(b) depicts the probabilityof the correct classification rate vs frequency offset witha variable signal length and the signals corrupted by AWGN)is end could be an important point to the proposedclassifier among the AMC methods that have tested the

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0 02 04 06 08 1 12 14 16 18 2Fre Quency offset times10ndash4

50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(a)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0 02 04 06 08 1 12 14 16 18 2Frequency offset times10ndash4

50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(b)

Figure 20 (a) Probability of the correct classification rate vs frequency offset and signal length N 4096 (b) Probability of the correctclassification rate vs frequency offset with variable signal lengths from N 64 128 265 512 1024 2048 4096 with a phase offset of ldquoπ6rdquo4sim1024-QAM with 10000 signal under AWGNmdashonly SNRminus2 dB


influence of the offset frequency to the transmitted signal Inthe same direction Figure 21 shows a change in the number oftransmitted symbols vs probability of the correct classificationrate It also well-observed that the proposed method hasa better classification rate than the proposed algorithm does[23] Even with this it is a very difficult circumstance withSNRminus2 dB in the AWGN channel Eventually the loga-rithmic classification algorithm is not the best one On thecontrary it facilitated the process of classification of higherorder QAM signals Nevertheless degradation points of thelogarithmic classifier are that it is a channel-dependentmodelAny variations in the type of noise (colored vs AWGN) thenumber of transmitted signals present in the channel and thetype of possible modulated signals require an overhaul of allfour tree threshold levels

7 General Trends

Unlike the traditional AMC algorithms the logarithmicclassifier has functional features which make them thepreferable classifier for the medium and higher order of M-QAM modulation schemes Likewise the logarithmic clas-sifier is very useful for channels that only receive corruptionby AWGN )e prominent results related to the AWGNchannel without fading effect have shown unexpected per-formance Although the classification of higher order mod-ulation signals is more challenging than to lower order signalsdue to the distance between the constellation points is smallbut on the contrary it appears nonreal convergence duringthe evaluation of the robustness of the logarithmic classifier)e probability of correct classification suffered from dis-parity especially for lower order modulation schemes at theexpense of schemes that have smaller constellation pointdistance therefore from this end it might be concluded thatmore research is needed on the logarithmic classifier par-ticularly SNR 0 Although cumulant-based classifier

schemes with many variations is the convenient way to copewith M-QAMmodulation schemes signal cumulant featuresor uncoordinated combination between cumulants andmoments does not provide sufficient classification undermultipath fading channels and can even produce contrast inthe classification rate It is also notable that this classifiertechnique is not unique in terms of fixed threshold and thereexist various ways to determine threshold levels automaticallyin order to improve the classification sense to the desiredmodulation schemes However the comprehensive reviewreveals that the logarithmic classifier with fixed threshold hasovercome all weaknesses points even with a severe noisyenvironment moreover under multipath propagationchannels On the contrary this work has provided referencesthat help researchers make progress toward in the direction ofdeveloped new generation of AMC systems which is called asthe logarithmic classifier

8 Conclusion

)is paper provides a method that transacts with themodulation recognition of higher order M-QAM signalsunder the effect of AWGN on a channel environmentthrough the usage of classifier which is cumulant-basednatural logarithmic characteristics with fixed thresholds

)e combination of higher order cumulant and prop-erties of the logarithmic functions created a new generationof the cumulant-based classifier who provides a superiorperformance to classify the higher order M-QAM signalseven with a low range of SNR

)e simulation results indicate that the correct classificationrate can reach over 92 at an SNR of 4dB under the AWGNeven as it seems moderate over different fading channels

According to a comparison with the recently proposedalgorithms in the literature the performance of the loga-rithmic classifier was efficient and also less complex

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


1000 2000 3000 4000 5000 6000 7000 8000 9000 10000Numbers of symbols

50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

Figure 21 )e probability of the correct classification rate vs the number of symbols SNR with 10000 signal realizations from 4sim1024-QAM phase offset ldquoπ6rdquo and signal degradation using AWGNmdashonly SNRminus2 dB


Abbreviations

AMC Automatic modulation classificationHOM Higher order momentsHOC Higher order cumulantM-QAM Multilevel quadrature amplitude modulationAWGN Additive white Gaussian noiseN Signal lengthCxpq nth order statistical cumulant with q-conjugate

orderMxpq nth order statistical moment with q-conjugate

orderfx Logarithmic feature transformer and

x isin a b c d

i )reshold count integer numberiprime Number of class pattern status of the

modulation schemePCC Probability of correct classificationfD Maximum Doppler shiftMsimM M-QAM M-QAMSNR Signal-to-noise ratio

Data Availability

No data were used to support this study thereby this paperprovides a new entry for the M-QAM modulation recog-nition algorithm )e higher order 4sim1024-QAM signalsare considered and new attributes were extracted fromsignals ldquoMATLAB Communications Toolboxrdquo was used toevaluate the proposed method Raw data are randomlygenerated by fetching the random function in the simulationprogram For more details contact the authors

Conflicts of Interest

)e authors declare that they have no conflicts of interest

References

[1] O A Dobre A Abdi Y Bar-Ness and W Su ldquoSurvey ofautomatic modulation classification techniques classicalapproaches and new trendsrdquo IET Communications vol 1no 2 pp 137ndash156 2007

[2] Z Xing and Y Gao ldquoMethod to reduce the signal-to-noiseratio required for modulation recognition based on loga-rithmic propertiesrdquo IET Communications vol 12 no 11pp 1360ndash1366 2018

[3] J A Sills ldquoMaximum-likelihood modulation classification forPSKQAMrdquo in Proceedings of the IEEE Military Communi-cations Conference Proceedings MILCOM 1999 vol 1pp 217ndash220 Atlantic City NJ USA October-November 1999

[4] F Hameed O Dobre and D Popescu ldquoOn the likelihood-based approach to modulation classificationrdquo IEEE Trans-actions on Wireless Communications vol 8 no 12pp 5884ndash5892 2009

[5] W Wei and J M Mendel ldquoA new maximum-likelihoodmethod for modulation classificationrdquo in Proceedings of the1995 Conference Record of the Twenty-Ninth Asilomar Con-ference on Signals Systems and Computers vol 2 pp 1132ndash1136 Pacific Grove CA USA October 1995

[6] E E Azzouz and A K Nandi ldquoAutomatic identification ofdigital modulation typesrdquo Signal Processing vol 47 no 1pp 55ndash69 1995

[7] M Abdelbar W H Tranter L Fellow T Bose andS Member ldquoCooperative cumulants-based modulationclassification in distributed networksrdquo IEEE Transactions onCognitive Communications and Networking vol 4 no 3pp 446ndash461 2018

[8] J L Xu W Su and M Zhou ldquoLikelihood-ratio approaches toautomatic modulation classificationrdquo IEEE Transactions onSystems Man and Cybernetics Part C (Applications andReviews) vol 41 no 4 pp 455ndash469 2011

[9] H Hosseinzadeh F Razzazi and A Haghbin ldquoA self trainingapproach to automatic modulation classification based onsemi-supervised online passive aggressive algorithmrdquo WirelessPersonal Communications vol 82 no 3 pp 1303ndash1319 2015

[10] A Swami and B M Sadler ldquoHierarchical digital modulationclassification using cumulantsrdquo IEEE Transactions on Com-munications vol 48 no 3 pp 416ndash429 2000

[11] I A Hashim J W Abdul Sadah T R Saeed and J K AlildquoRecognition of QAM signals with low SNR using a combinedthreshold algorithmrdquo IETE Journal of Research vol 61 no 1pp 65ndash71 2015

[12] M L Dukiu and G B Markoviu ldquoAutomatic modulationclassification using cumulants with repeated classificationattemptsrdquo in 20th Telecommunications Forum (TELFOR)vol 4 pp 424ndash427 2012

[13] D S Chirov ldquoApplication of the decision trees to recognizethe types of digital modulation of radio signals in cognitivesystems of HF communicationrdquo in Proceedings of the 2018Systems of Signal Synchronization Generating and Processingin Telecommunications pp 1ndash6 Minsk Belarus July 2018

[14] B GMobasseri ldquoConstellation shape as a robust signature fordigital modulation recognitionrdquo in Proceedings of the IEEEConference on Military Communications MILCOM 1999pp 442ndash446 Piscataway NJ USA October-November 1999

[15] B G Mobasseri ldquoDigital modulation classification usingconstellation shaperdquo Signal Processing vol 80 no 2pp 251ndash277 2000

[16] C Yin B Li Y Li and B Lan ldquoModulation classification ofMQAM signals based on density spectrum of the constella-tionsrdquo in Proceedings of the 2010 2nd International Conferenceon Future Computer and Communication ICFCC 2010 vol 3pp 57ndash61 Wuhan China May 2010

[17] A Fehske J Gaeddert and J H Reed ldquoA new approach tosignal classification using spectral correlation and neuralnetworksrdquo in Proceedings of the First IEEE InternationalSymposium on New Frontiers in Dynamic Spectrum AccessNetworks DySPAN 2005 pp 144ndash150 Baltimore MD USANovember 2005

[18] W C Headley J D Reed and C R C Da Silva ldquoDistributedcyclic spectrum feature-based modulation classificationrdquo inProceedings of the 2008 IEEE Wireless Communications andNetworking Conference pp 1200ndash1204 Las Vegas NV USAMarch-April 2008

[19] Y Yuan P Zhao B Wang and B Wu ldquoHybrid maximumlikelihood modulation classification for continuous phasemodulationsrdquo IEEE Communications Letters vol 20 no 3pp 450ndash453 2016

[20] H T Fu QWan and R Shi ldquoModulation classification basedon cyclic spectral features for co-channel time-frequencyoverlapped two-signalrdquo in Proceedings of the 2009 Pacific-AsiaConference on Circuits Communications and Systems PACCS2009 pp 31ndash34 Chengdu China May 2009


[21] O A Dobre M Oner S Rajan and R Inkol ldquoCyclo-stationarity-based robust algorithms for QAM signal iden-tificationrdquo IEEE Communications Letters vol 16 no 1pp 12ndash15 2012

[22] O A Dobre A Abdi Y Bar-Ness and W Su ldquoCyclo-stationarity-based modulation classification of linear digitalmodulations in flat fading channelsrdquo Wireless PersonalCommunications vol 54 no 4 pp 699ndash717 2010

[23] O A Dobre Y Bar-Ness and W Su ldquoHigher-order cycliccumulants for high order modulation classificationrdquo inProceedings of the 2003 IEEE conference on Military com-munications MILCOM 2003 pp 112ndash117 Boston MA USAOctober 2003

[24] C M Spooner ldquoOn the utility of sixth-order cyclic cumulantsfor RF signal classificationrdquo in Proceedings of the ConferenceRecord-Asilomar Conference on Signals Systems and Com-puters vol 1 pp 890ndash897 Pacific Grove CA USA November2001

[25] F Ghofrani A Jamshidi and A Keshavarz-Haddad ldquoIn-ternet traffic classification using hidden naive Bayes modelrdquoin Proceedings of the ICEE 2015 23rd Iranian Conference onElectrical Engineering vol 10 pp 235ndash240 Tehran Iran May2015

[26] F Ghofrani A Keshavarz-Haddad and A Jamshidi ldquoIn-ternet traffic classification using multiple classifiersrdquo inProceedings of the 2015 7th International Conference onKnowledge and Smart Technology (KST) IKT 2015 Chonburi)ailand January 2015

[27] S Norouzi A Jamshidi and A R Zolghadrasli ldquoAdaptivemodulation recognition based on the evolutionary algo-rithmsrdquo Applied Soft Computing vol 43 pp 312ndash319 2016

[28] H Agirman-Tosun Y Liu A M Haimovich et al ldquoMod-ulation classification of MIMO-OFDM signals by in-dependent component analysis and support vectormachinesrdquo in Proceedings of the 2011 Conference Record of theForty Fifth Asilomar Conference on Signals Systems andComputers (ASILOMAR) pp 1903ndash1907 Pacific Grove CAUSA November 2011

[29] D Boutte and B Santhanam ldquoA hybrid ICA-SVM approachto continuous phase modulation recognitionrdquo IEEE SignalProcessing Letters vol 16 no 5 pp 402ndash405 2009

[30] B Ramkumar ldquoAutomatic modulation classification forcognitive radios using cyclic feature detectionrdquo IEEE Circuitsand Systems Magazine vol 9 no 2 pp 27ndash45 2009

[31] A Ali F Yangyu and S Liu ldquoAutomatic modulation clas-sification of digital modulation signals with stacked autoen-codersrdquo Digital Signal Processing vol 71 pp 108ndash116 2017

[32] S Xi and H-C Wu ldquoRobust automatic modulation classi-fication using cumulant features in the presence of fadingchannelsrdquo in Proceedings of theIEEE Wireless Communica-tions and Networking Conference 2006 WCNC 2006pp 2094ndash2099 Las Vegas NV USA April 2006

[33] Z Zhu M Waqar Aslam and A K Nandi ldquoGenetic algo-rithm optimized distribution sampling test for M-QAMmodulation classificationrdquo Signal Processing vol 94 no 1pp 264ndash277 2014

[34] N Ahmadi and R Berangi ldquoModulation classification ofQAM and PSK from their constellation using Genetic Al-gorithm and hierarchical clusteringrdquo in Proceedings of the2008 3rd International Conference on Information amp Com-munication Technologies from Ceory to Applicationsvol 11670 Damascus Syria April 2008

[35] A Abdelmutalab K Assaleh and M El-Tarhuni ldquoAutomaticmodulation classification based on high order cumulants and

hierarchical polynomial classifiersrdquo Physical Communicationvol 21 pp 10ndash18 2016

[36] M H Alsharif and R Nordin ldquoEvolution towards fifthgeneration (5G) wireless networks current trends and chal-lenges in the deployment of millimetre wave massive MIMOand small cellsrdquo Telecommunication Systems vol 64 no 4pp 617ndash637 2017

[37] C-S Park J-H Choi S-P Nah W Jang and D Y KimldquoAutomatic modulation recognition of digital signals usingwavelet features and SVMrdquo in Proceedings of the 2008 10thInternational Conference on Advanced CommunicationTechnology vol 1 pp 387ndash390 Gangwon-Do South KoreaFebruary 2008

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

[39] L Zhou Z Sun and W Wang ldquoLearning to short-timeFourier transform in spectrum sensingrdquo Physical Commu-nication vol 25 pp 420ndash425 2017

[40] M H Valipour MM Homayounpour andM A MehralianldquoAutomatic digital modulation recognition in presence ofnoise using SVM and PSOrdquo in Proceedings of the 6th In-ternational Symposium on Telecommunications IST 2012pp 378ndash382 Tehran Iran November 2012

[41] A F Molisch K Balakrishnan D Cassioli and C-C ChongldquoIEEE 802154a channel model-final reportrdquo Environmentspp 1ndash40 2005


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Submit your manuscripts atwwwhindawicom

project and was documented since 1969 and nowadays theAMC is extensively used and well known for communica-tion engineers as a significant part in the internal design ofintelligent radio systems [3 4]

Currently digital modulation identification algorithms canbe split into two techniques a maximum likelihood hypothesismethod which is based on decision theory [5] and statisticalpattern recognition which relies upon the feature extractionideas [6 7] in uncooperative channel environment )e al-gorithms of the pattern recognition technique are usually usedin practical application and that is due to the absence of priorknowledge from received modulation signals [8] )e dis-crimination method has particularly beneficial features forpattern recognition which are initially extracted from thevectors of data and the identification of the signal modulationmode that was completed upon the coverage between char-acteristic parameters and limits of the extracted features whichwas considered as the knownmode of the modulation type [9]

In the last five years a new modulation classificationtechnique has been proposed at the same time with the evo-lution of the automatic digital signal modulation recognitionalgorithms research and this new modulation offers a newtrend of complicated signal sets and higher order modulationsignals )e most commonly used features are high-ordercumulants (HOC) and high-order moment (HOM) [10] )eHOC-based techniques show superior performance to classifythe digital modulation signals at a low signal-to-noise ratio(SNR) these algorithms were documented in literature[11ndash13] Nevertheless they were not appropriate to classifyhigher-order M-QAM modulation formats Constellationshape varies from one modulation signal type to another inorder to be considered as a robust signature

)e constellation shape was used in the algorithms inreferences [14ndash16] to recognize various types of higher ordermodulation including 8-PSK and 16-QAM )e recognitionof success rate probabilities is around 95 but it still requiredmore SNR which may reach 4 dB However the constellationshape can be classified into M-PSK and M-QAM and at thesame time they are sensitive to several wireless channels thatcould seriously make confusions in work these comprisefrequency offset phase rotation and the application of raisedcosine roll-off filters Under this situation the symbol rate andfrequency offset setting must be more accurate during theperiods of presentment and at the same time the most widelyused features are a cyclic spectrum and cyclic frequency thatcould help multiple unwanted signals to be detected with eachof temporal and frequency-based overlaps [17ndash20]

In 2012 Dobber and his coworkers [21] suggested twonovel algorithms for the recognition of 4-QAM 16-QAM64-QAM and QAMV29 modulation schemes also other[22 23] authors suggested to use higher order cycliccumulants (CCs) which were obtained from received signalsas features for modulation classification Also this had beenput forward in [24] which presents a method to classifya number of mixed modulation schemes with an assort-ment of N-class problems and this technique alsoachieved a notable performance at low ranges of SNR Dueto the development of algorithms in machine learning the

researchers had started to design classification algorithmsbased on some aspects of machine learning which improvedthe classification ability and gives further pros to the clas-sifier in terms of distinguished types of modulation signals

Some investigations which were achieved on the behav-iors of hidden naive Bayes (HNB) [25] and on combination ofnaive Bayes (NB) and other types of classifiers to create a newclassifier named multiple classifier [26] certified that suchclassifier types were highly effective compared to conventionalclassifiers in terms of a small number of training iterations

Supervised learning technique was combined witha modified K-means algorithm that is based on four famousoptimization algorithms )is modification presented a newgeneration of the AMC technique Likewise artificial neuralnetworks (ANNs) with genetic algorithms were studied andconsidered by Norouz and his coworkers [27] and alsosupport vector machine (SVM) classifier in [28 29]

)e ways based on ANN and SVM show a superiorperformance although there is less prior information ofsignal features However multiple training samples anda long training period are necessary to accomplish sufficientlearning which increases the computational complexity andmakes the processing time longer

In the last five years researches widely explored the newtechniques in order to reduce the required SNR and make itmore efficient of recognition capability through focusing onrobust features and classifier designs One of the weak pointsof the previous algorithms is that the nature of the decision-tree is that it requires fixed threshold values due to thefeatures that had been proposed by the authors and thesefeatures are highly sensitive to any changes in SNR that canmake the threshold values be valid for small ranges of SNRabove to 10 dB However there had been no work until nowthat concentrates on the recognition of higher order QAMsignals in terms of the shape of feature distribution curves

In fact this assumption gives a good understanding of thebehavior of systems and reflects their major trends thereforeunder the circumstance of a channel corrupted by AWGNthis paper derived a relationship among of the higher ordercumulant as features and threshold levels in order to evaluatethe performance ofM-QAMmodulation recognition technique

2 Mathematical Analyses

21 Logarithmic Calculation Below are some theoreticalanalyses that assumes two logarithmic functions denotedf1(x1) and f2(x2) carrying different variable ldquox1 x2rdquo buthave the same base value ldquonrdquo which can be written as follows

f1 x1( 1113857 logn x11113858 1113859

f1 x2( 1113857 logn x21113858 1113859(1)

where the range of variables x1 ne x2 and the base value isconsidered to be the same )e ratio between f1(x1)andf2(x2) can be expressed as

W x1 x2( 1113857 logn x11113858 1113859

logn x21113858 1113859ln x11113858 1113859ln(n)

ln x21113858 1113859ln(n) (2)



logn x11113858 1113859 ln x11113858 1113859

ln(n) (3)


W x1 x2( 1113857 ln x11113858 1113859ln(n)

ln x21113858 1113859ln(n) (4)


W x1 x2( 1113857 ln x11113858 1113859

ln x21113858 1113859 (5)






lowast( 1113857 M11



220 minus 2M

211


lowast y(n)


minus 9M22M11 + 18 M20( 11138572M11 + 12M

311


lowast y(n)

lowast y(n)


240


420 minus 144M

411 minus 432M

220M

211

+ 12M40M220 + 192M31M11M20 + 144M22M

211

+ 72M22M220

(6)




fa log10 C111113868111386811138681113868

11138681113868111386811138681113960 1113961 (7)

fb log10 C221113868111386811138681113868

11138681113868111386811138681113960 1113961 (8)

fc log10 C331113868111386811138681113868

11138681113868111386811138681113960 1113961 (9)

fd log10 C441113868111386811138681113868

11138681113868111386811138681113960 1113961 (10)











fci fdi




fbi fci

fdi with i index





fci fdi



fbi fci



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


005

115

225

335

445

555

6


f b


0123456789

1011121314151617


f d

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

1

2

3

4

5

6

7

8

9

10


f c

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

05

1

15

2

25

3

35


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


f a












Start


D1

4 QAM

Yes

No D2 D3

D6 D5 D4

D7 D8 D9

No

128 QAM

Yes

8 QAM

Yes

16 QAM

Yes

512 QAM

Yes

64 QAM

Yes

32 QAM

Yes

256 QAM

Yes

No

1024 QAM

Yes

OthersNoNo

No

NoNo

No


AMC module


Classifier


Rx


Feature computation


bandpass filter

Classes





AWGN

Data normalized


Modulation type


PCC ()







fbi fci





log10[|C22i(si)|]

fci log10[|C33i








I fa fb fc fd

0 05 15 15 31 095 22 3 52 13 27 4 643 152 31 5 764 18 37 63 95 22 43 66 106 25 48 75 117 3 57 9 128 45 75 125 155


fci fdi









Di Da(i+1) D

b(i+1)

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868Dc(i+1) D

d(i+1)

11138681113868111386811138681113868

11138681113868111386811138681113868 (16)






0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





PCC 1113944

j

k1p ωk ∣ ωk( 1113857P ωk( 1113857


PCC middot 100

(17)


5 Discussion



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)









4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5









[33] C40 C41 C42 C60

C61 C62C63





[34] C40 C41 C42 C60

C61 C62C63



[35]C20 C21 C40 C41

C42 C60C61C62

C63


[23]

C20 C21 C40 C41

C42 C60C61C62

C63 C80 C81C82

C83 C84



ge+5 Unknown

[21] C20 C21 C41 C42

C63Medium 16 64 V29 4

minus3 600 81ge+5 90

[10] C20 C21 C40 C41

C42Medium 8 16 32 64 4 8 16 32 64

minus3 260 45ge+5 95

Proposedalgorithm




4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)














4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(a)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(b)




7 General Trends



8 Conclusion





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



Abbreviations




x isin a b c d



Data Availability




References


















































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in





logn x11113858 1113859 ln x11113858 1113859

ln(n) (3)


W x1 x2( 1113857 ln x11113858 1113859ln(n)

ln x21113858 1113859ln(n) (4)


W x1 x2( 1113857 ln x11113858 1113859

ln x21113858 1113859 (5)






lowast( 1113857 M11



220 minus 2M

211


lowast y(n)


minus 9M22M11 + 18 M20( 11138572M11 + 12M

311


lowast y(n)

lowast y(n)


240


420 minus 144M

411 minus 432M

220M

211

+ 12M40M220 + 192M31M11M20 + 144M22M

211

+ 72M22M220

(6)




fa log10 C111113868111386811138681113868

11138681113868111386811138681113960 1113961 (7)

fb log10 C221113868111386811138681113868

11138681113868111386811138681113960 1113961 (8)

fc log10 C331113868111386811138681113868

11138681113868111386811138681113960 1113961 (9)

fd log10 C441113868111386811138681113868

11138681113868111386811138681113960 1113961 (10)











fci fdi




fbi fci

fdi with i index





fci fdi



fbi fci



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


005

115

225

335

445

555

6


f b


0123456789

1011121314151617


f d

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

1

2

3

4

5

6

7

8

9

10


f c

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

05

1

15

2

25

3

35


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


f a












Start


D1

4 QAM

Yes

No D2 D3

D6 D5 D4

D7 D8 D9

No

128 QAM

Yes

8 QAM

Yes

16 QAM

Yes

512 QAM

Yes

64 QAM

Yes

32 QAM

Yes

256 QAM

Yes

No

1024 QAM

Yes

OthersNoNo

No

NoNo

No


AMC module


Classifier


Rx


Feature computation


bandpass filter

Classes





AWGN

Data normalized


Modulation type


PCC ()







fbi fci





log10[|C22i(si)|]

fci log10[|C33i








I fa fb fc fd

0 05 15 15 31 095 22 3 52 13 27 4 643 152 31 5 764 18 37 63 95 22 43 66 106 25 48 75 117 3 57 9 128 45 75 125 155


fci fdi









Di Da(i+1) D

b(i+1)

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868Dc(i+1) D

d(i+1)

11138681113868111386811138681113868

11138681113868111386811138681113868 (16)






0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





PCC 1113944

j

k1p ωk ∣ ωk( 1113857P ωk( 1113857


PCC middot 100

(17)


5 Discussion



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)









4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5









[33] C40 C41 C42 C60

C61 C62C63





[34] C40 C41 C42 C60

C61 C62C63



[35]C20 C21 C40 C41

C42 C60C61C62

C63


[23]

C20 C21 C40 C41

C42 C60C61C62

C63 C80 C81C82

C83 C84



ge+5 Unknown

[21] C20 C21 C41 C42

C63Medium 16 64 V29 4

minus3 600 81ge+5 90

[10] C20 C21 C40 C41

C42Medium 8 16 32 64 4 8 16 32 64

minus3 260 45ge+5 95

Proposedalgorithm




4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)














4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(a)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(b)




7 General Trends



8 Conclusion





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



Abbreviations




x isin a b c d



Data Availability




References


















































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in








fci fdi




fbi fci

fdi with i index





fci fdi



fbi fci



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


005

115

225

335

445

555

6


f b


0123456789

1011121314151617


f d

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

1

2

3

4

5

6

7

8

9

10


f c

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

05

1

15

2

25

3

35


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


f a












Start


D1

4 QAM

Yes

No D2 D3

D6 D5 D4

D7 D8 D9

No

128 QAM

Yes

8 QAM

Yes

16 QAM

Yes

512 QAM

Yes

64 QAM

Yes

32 QAM

Yes

256 QAM

Yes

No

1024 QAM

Yes

OthersNoNo

No

NoNo

No


AMC module


Classifier


Rx


Feature computation


bandpass filter

Classes





AWGN

Data normalized


Modulation type


PCC ()







fbi fci





log10[|C22i(si)|]

fci log10[|C33i








I fa fb fc fd

0 05 15 15 31 095 22 3 52 13 27 4 643 152 31 5 764 18 37 63 95 22 43 66 106 25 48 75 117 3 57 9 128 45 75 125 155


fci fdi









Di Da(i+1) D

b(i+1)

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868Dc(i+1) D

d(i+1)

11138681113868111386811138681113868

11138681113868111386811138681113868 (16)






0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





PCC 1113944

j

k1p ωk ∣ ωk( 1113857P ωk( 1113857


PCC middot 100

(17)


5 Discussion



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)









4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5









[33] C40 C41 C42 C60

C61 C62C63





[34] C40 C41 C42 C60

C61 C62C63



[35]C20 C21 C40 C41

C42 C60C61C62

C63


[23]

C20 C21 C40 C41

C42 C60C61C62

C63 C80 C81C82

C83 C84



ge+5 Unknown

[21] C20 C21 C41 C42

C63Medium 16 64 V29 4

minus3 600 81ge+5 90

[10] C20 C21 C40 C41

C42Medium 8 16 32 64 4 8 16 32 64

minus3 260 45ge+5 95

Proposedalgorithm




4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)














4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(a)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(b)




7 General Trends



8 Conclusion





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



Abbreviations




x isin a b c d



Data Availability




References


















































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in













Start


D1

4 QAM

Yes

No D2 D3

D6 D5 D4

D7 D8 D9

No

128 QAM

Yes

8 QAM

Yes

16 QAM

Yes

512 QAM

Yes

64 QAM

Yes

32 QAM

Yes

256 QAM

Yes

No

1024 QAM

Yes

OthersNoNo

No

NoNo

No


AMC module


Classifier


Rx


Feature computation


bandpass filter

Classes





AWGN

Data normalized


Modulation type


PCC ()







fbi fci





log10[|C22i(si)|]

fci log10[|C33i








I fa fb fc fd

0 05 15 15 31 095 22 3 52 13 27 4 643 152 31 5 764 18 37 63 95 22 43 66 106 25 48 75 117 3 57 9 128 45 75 125 155


fci fdi









Di Da(i+1) D

b(i+1)

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868Dc(i+1) D

d(i+1)

11138681113868111386811138681113868

11138681113868111386811138681113868 (16)






0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





PCC 1113944

j

k1p ωk ∣ ωk( 1113857P ωk( 1113857


PCC middot 100

(17)


5 Discussion



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)









4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5









[33] C40 C41 C42 C60

C61 C62C63





[34] C40 C41 C42 C60

C61 C62C63



[35]C20 C21 C40 C41

C42 C60C61C62

C63


[23]

C20 C21 C40 C41

C42 C60C61C62

C63 C80 C81C82

C83 C84



ge+5 Unknown

[21] C20 C21 C41 C42

C63Medium 16 64 V29 4

minus3 600 81ge+5 90

[10] C20 C21 C40 C41

C42Medium 8 16 32 64 4 8 16 32 64

minus3 260 45ge+5 95

Proposedalgorithm




4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)














4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(a)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(b)




7 General Trends



8 Conclusion





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



Abbreviations




x isin a b c d



Data Availability




References


















































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in






AWGN

Data normalized


Modulation type


PCC ()







fbi fci





log10[|C22i(si)|]

fci log10[|C33i








I fa fb fc fd

0 05 15 15 31 095 22 3 52 13 27 4 643 152 31 5 764 18 37 63 95 22 43 66 106 25 48 75 117 3 57 9 128 45 75 125 155


fci fdi









Di Da(i+1) D

b(i+1)

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868Dc(i+1) D

d(i+1)

11138681113868111386811138681113868

11138681113868111386811138681113868 (16)






0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





PCC 1113944

j

k1p ωk ∣ ωk( 1113857P ωk( 1113857


PCC middot 100

(17)


5 Discussion



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)









4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5









[33] C40 C41 C42 C60

C61 C62C63





[34] C40 C41 C42 C60

C61 C62C63



[35]C20 C21 C40 C41

C42 C60C61C62

C63


[23]

C20 C21 C40 C41

C42 C60C61C62

C63 C80 C81C82

C83 C84



ge+5 Unknown

[21] C20 C21 C41 C42

C63Medium 16 64 V29 4

minus3 600 81ge+5 90

[10] C20 C21 C40 C41

C42Medium 8 16 32 64 4 8 16 32 64

minus3 260 45ge+5 95

Proposedalgorithm




4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)














4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(a)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(b)




7 General Trends



8 Conclusion





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



Abbreviations




x isin a b c d



Data Availability




References


















































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in





Di Da(i+1) D

b(i+1)

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868Dc(i+1) D

d(i+1)

11138681113868111386811138681113868

11138681113868111386811138681113868 (16)






0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





PCC 1113944

j

k1p ωk ∣ ωk( 1113857P ωk( 1113857


PCC middot 100

(17)


5 Discussion



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)









4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5









[33] C40 C41 C42 C60

C61 C62C63





[34] C40 C41 C42 C60

C61 C62C63



[35]C20 C21 C40 C41

C42 C60C61C62

C63


[23]

C20 C21 C40 C41

C42 C60C61C62

C63 C80 C81C82

C83 C84



ge+5 Unknown

[21] C20 C21 C41 C42

C63Medium 16 64 V29 4

minus3 600 81ge+5 90

[10] C20 C21 C40 C41

C42Medium 8 16 32 64 4 8 16 32 64

minus3 260 45ge+5 95

Proposedalgorithm




4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)














4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(a)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(b)




7 General Trends



8 Conclusion





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



Abbreviations




x isin a b c d



Data Availability




References


















































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in





PCC 1113944

j

k1p ωk ∣ ωk( 1113857P ωk( 1113857


PCC middot 100

(17)


5 Discussion



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)









4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5









[33] C40 C41 C42 C60

C61 C62C63





[34] C40 C41 C42 C60

C61 C62C63



[35]C20 C21 C40 C41

C42 C60C61C62

C63


[23]

C20 C21 C40 C41

C42 C60C61C62

C63 C80 C81C82

C83 C84



ge+5 Unknown

[21] C20 C21 C41 C42

C63Medium 16 64 V29 4

minus3 600 81ge+5 90

[10] C20 C21 C40 C41

C42Medium 8 16 32 64 4 8 16 32 64

minus3 260 45ge+5 95

Proposedalgorithm




4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)














4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(a)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(b)




7 General Trends



8 Conclusion





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



Abbreviations




x isin a b c d



Data Availability




References


















































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in









4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5









[33] C40 C41 C42 C60

C61 C62C63





[34] C40 C41 C42 C60

C61 C62C63



[35]C20 C21 C40 C41

C42 C60C61C62

C63


[23]

C20 C21 C40 C41

C42 C60C61C62

C63 C80 C81C82

C83 C84



ge+5 Unknown

[21] C20 C21 C41 C42

C63Medium 16 64 V29 4

minus3 600 81ge+5 90

[10] C20 C21 C40 C41

C42Medium 8 16 32 64 4 8 16 32 64

minus3 260 45ge+5 95

Proposedalgorithm




4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)














4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(a)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(b)




7 General Trends



8 Conclusion





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



Abbreviations




x isin a b c d



Data Availability




References


















































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in








4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM


0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


0 5









[33] C40 C41 C42 C60

C61 C62C63





[34] C40 C41 C42 C60

C61 C62C63



[35]C20 C21 C40 C41

C42 C60C61C62

C63


[23]

C20 C21 C40 C41

C42 C60C61C62

C63 C80 C81C82

C83 C84



ge+5 Unknown

[21] C20 C21 C41 C42

C63Medium 16 64 V29 4

minus3 600 81ge+5 90

[10] C20 C21 C40 C41

C42Medium 8 16 32 64 4 8 16 32 64

minus3 260 45ge+5 95

Proposedalgorithm




4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)














4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(a)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(b)




7 General Trends



8 Conclusion





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



Abbreviations




x isin a b c d



Data Availability




References


















































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in










[33] C40 C41 C42 C60

C61 C62C63





[34] C40 C41 C42 C60

C61 C62C63



[35]C20 C21 C40 C41

C42 C60C61C62

C63


[23]

C20 C21 C40 C41

C42 C60C61C62

C63 C80 C81C82

C83 C84



ge+5 Unknown

[21] C20 C21 C41 C42

C63Medium 16 64 V29 4

minus3 600 81ge+5 90

[10] C20 C21 C40 C41

C42Medium 8 16 32 64 4 8 16 32 64

minus3 260 45ge+5 95

Proposedalgorithm




4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)














4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(a)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(b)




7 General Trends



8 Conclusion





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



Abbreviations




x isin a b c d



Data Availability




References


















































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in















4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)







4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(a)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(b)




7 General Trends



8 Conclusion





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



Abbreviations




x isin a b c d



Data Availability




References


















































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in








4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)


4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



0

10

20

30

40

50

60

70

80

90

100

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(a)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(b)




7 General Trends



8 Conclusion





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



Abbreviations




x isin a b c d



Data Availability




References


















































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in






4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(a)

4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)

(b)




7 General Trends



8 Conclusion





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



Abbreviations




x isin a b c d



Data Availability




References


















































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in





7 General Trends



8 Conclusion





4 QAM8 QAM16 QAM

32 QAM64 QAM128 QAM



50

55

60

65

70

75

80

85

90

95

100

105

Prob

abili

ty o

f cor

rect

clas

sific

atio

n ra

te (

)



Abbreviations




x isin a b c d



Data Availability




References


















































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




Abbreviations




x isin a b c d



Data Availability




References


















































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in
































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




AnM-QAMSignalModulationRecognitionAlgorithmin AWGNChannel

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Transcript of AnM-QAMSignalModulationRecognitionAlgorithmin AWGNChannel