Research Article A Real Valued Neural Network Based...

Research ArticleA Real Valued Neural Network Based Autoregressive EnergyDetector for Cognitive Radio Application

A J Onumanyi1 E N Onwuka1 A M Aibinu1 O C Ugweje2 and M J E Salami3

1 Department of Telecommunication Federal University of Technology Minna Niger State Nigeria2 Digital Bridge Institute Abuja Nigeria3 Department of Mechatronic Engineering International Islamic University Malaysia Kuala Lumpur Malaysia

Correspondence should be addressed to A J Onumanyi adeiza1yahoocom

Received 31 March 2014 Revised 9 June 2014 Accepted 1 July 2014 Published 29 October 2014

Academic Editor George Kyriacou

Copyright copy 2014 A J Onumanyi et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A real valued neural network (RVNN) based energy detector (ED) is proposed and analyzed for cognitive radio (CR) applicationThis was developed using a known two-layered RVNNmodel to estimate the model coefficients of an autoregressive (AR) systemBy using appropriate modules and a well-designed detector the power spectral density (PSD) of the AR system transfer functionwas estimated and subsequent receiver operating characteristic (ROC) curves of the detector generated and analyzed A highdetection performance with low false alarm rate was observed for varying signal to noise ratio (SNR) sample number and modelorder conditions The proposed RVNN based ED was then compared to the simple periodogram (SP) Welch periodogram (WP)multitaper (MT) Yule-Walker (YW) Burg (BG) and covariance (CV) based ED techniques The proposed detector showed betterperformance than the SP WP and MT while providing better false alarm performance than the YW BG and CV Data providedhere support the effectiveness of the proposed RVNN based ED for CR application

1 Introduction

The energy detector (ED) has been widely proposed forspectrum sensing (SS) in cognitive radio (CR) owing toits design simplicity fast sensing periodicity and ability todetect primary user (PU) signal without a priori knowledgeof its waveform structure (except for the knowledge of noisestatistics) [1ndash11] However the demand for fast sensing andhigh detection accuracy in CR has revealed particular limi-tations with the ED In fast sensing the ED tends to obtainfewer samples for spectral estimation which leads to reducedresolution and invariably poor detection performance [12ndash15] Also it is known that the ED performs poorly in lowsignal to noise ratio (SNR) conditions and fluctuating noiseenvironments [12ndash14] which results in increased false alarmrate These challenges have compelled the need for newimproved ED techniques capable of providing better localsensing results at acceptable detection and false alarm ratesin both low and high SNR conditions This serves as themotivation for our research

Towards developing an ED several usable spectrum esti-mation techniques are well-known and these can be broadlydivided into parametric and nonparametric techniquesSome examples of these nonparametric techniques includethe simple periodogram (SP)Welch periodogram (WP) andthe multitaper (MT) while parametric techniques includethe Yule-Walker (YW) Burg (BG) and covariance (CV)techniques Generally the ED has been widely assumed tobe based on the periodogram approach (developed either intime or in frequency domain) and this could be presum-ably responsible for its poor performance owing to knownlimitations of the periodogram for example large noisevariance [13 14] On the other hand few works have beenidentified on the use of parametric techniques particularlythe autoregressive (AR) technique in CR [16ndash22] Also thesefew works have focused more on its use in spectrum holeprediction rather than as an ED for CR application

In this work the focus is not on developing a new spec-trum estimation technique but rather on proposing the use ofa real valued neural network (RVNN) based autoregressive

Hindawi Publishing CorporationInternational Scholarly Research NoticesVolume 2014 Article ID 579125 11 pageshttpdxdoiorg1011552014579125

2 International Scholarly Research Notices

(AR) spectrum estimation technique for ED application inCR The choice of the RVNN based AR technique was basedon its advantage over the popular BG technique in solvingthe challenge of spectral line splitting at high SNR and largemodel order conditions [23] Consequently it was observedhere that such an advantage would lead to an improvedED with less probability of false alarms for CR applicationResults of this contribution are presented in Section 5 Alsowhile authors in [23] developed the RVNN technique andapplied it in voice activity detection in our own work wepropose necessary additions to standardize the approach as afully functional ED using an empirical threshold estimationtechnique for CR application The RVNN based AR modelcoefficient estimator developed in [23] has never been appliedas an ED for CR application hence its application wasconsidered here to exploit its inherent advantage Thereforeonce developed as a functional ED it was tested usingsimulated data particularly in low and high SNR conditionsand varying model order values as described in Section 4and results obtained with corresponding implications arepresented in Section 5 Appropriate conclusions are drawn inSection 6

2 Brief Review of Energy Detector Techniques

Energy detectors (ED) sense the presence or absence ofPU signals by estimating the energy content of a specifiedband using the power spectral density (PSD) measurementsand comparing with predetermined thresholds [12 14] Thisaids the CR device in vacating PU occupied bands to avoidinterference and use vacant bands to improve spectrumutilization Figures 1(a) and 1(b) provide a representation ofthis process Towards this goal signals above the thresholdtypically signify PU presence 119867

1 and below threshold

as noise 1198670 These hypotheses 119867

0and 119867

1are typically

represented as

1198670

119909 (119899) = 119908 (119899) (1)

1198671

119909 (119899) = 119904 (119899) + 119908 (119899) (2)

where 119908(119899) represents samples of additive white Gaussiannoise (AWGN) 119904(119899) denotes samples of PU signal and119909(119899) denotes samples of received signal at the CR inputconsidering a perfect channel

EDs are typically developed to decide on these hypotheseseither in time or in frequency domain In time domain itconsists of an input noise prefilter a magnitude square lawdevice an integrator and a detector as shown in Figure 2Thisapproach has been used in several works [12ndash15] and well-known for its simplicity and low design and developmentcost However it is based on the super heterodyne techniquewhich is limited by its slow voltage ramping response time [6]Such a delay might be intolerable for CR operation Anotherapproach is to realize the ED in the frequency domainusing the well-known periodogram as shown in Figure 3This provides an opportunity to achieve full digitizationof the detection process however this approach constrains

the sensing bandwidth owing to known limitations of typicalfast Fourier transform (FFT) realizations [8]

Another method identified for the ED in CR is theWelch periodogram (WP) approach [24] Particularly in [25]performance analysis was carried out on the use of WP inRayleigh fading channels while [26 27] used WP for OFDMsystems in CR These authors observed that WP operateswell for narrowband sensing however they conclude thatthe approach is limited by the excessive variance aroundthe true mean PSD value This increases the probabilityof false alarm of the system Another approach using theMultitaper (MT) technique was proposed in [28] with basicdescriptions provided from filter-bank theory point of viewThis technique was extended in [29] for signal detectionin CR and results were compared with the time domainbased ED It was observed that MT performed better in lowSNR conditions under Raleigh fading channels This wasbased on the techniquersquos dependence on both magnitudeand phase of received samples Also [30] provided animprovedMTmethod forCR application inwhich a recursivemethod to improve the accuracy of estimates while keepingreal-time properties uncompromised was proposed Authorscompared their technique with the SP and ordinary MT andobserved better performance for their improved MT

On the other hand the use of autoregressive (AR) meth-ods has been sparsely pursued especially for energy detectionin CR The AR methods present a class of techniquespopularly classified as parametric techniques Though notwidely used in CR we observed that [19ndash21] proposed ARfor spectrum hole detection in CR using time series forecast-ing Authors reported on the performance of the proposedapproach however it remains unclear how well such anapproach would perform in typical deployment conditionsAlso authors in [21 22] used particle andKalman filtering forspectrum availability forecasting In [17] authors presented acomparison of SP and Yule-Walker (YW) AR techniques andargued that better performance could be achieved by the YWif large model orders are considered However most of theseapplications have not considered AR application for ED inCR andhence it remains unknownhowwell such techniqueswould perform if employed Consequently we consideredthe use of a real valued neural network (RVNN) AR modelestimator [23] to develop a detector for CR application Thisapproach provides data reported in [23] which was leveragedupon here to develop an improved ED for CR Consequentlyit is the focus here to develop evaluate and analyze itsperformance for CR application

3 Development of the Real Valued NeuralNetwork Based Energy Detector

31 An Overview of the RVNN Based Autoregressive ModelEstimation Technique Theworking principles of the real val-ued neural network (RVVN) autoregressive (AR) coefficientestimation technique were based on [23] Thus we presenthere only specific details needed to develop the ED for CRapplication however for further details we refer to [23]

International Scholarly Research Notices 3

Channel negotiation is complete and declared free


CR node 1

Channel is utilized

CR base station

CR node 2

PU transmitter

PU receiver

(a)

PU receiver

PU signal present

Channel is vacated

Channel renegotiation


CR node 1

CR node 2

PU transmitter

CR base station

(b)

Figure 1 (a) Absence of PU signal permitting CR nodes to negotiate and utilize free band (b) Presence of PU signal triggers CR nodes torenegotiate and vacate band

Input signalY(t)

Noise prefilter

Square lawdevice ( )2

Analogintegrator

Decisionthreshold

OutputH0 or H1

Figure 2 Energy detection in time domain


Input signalY(t)

ADC K point FFTAverage M

bins N timesDecisionthreshold

Square lawdevice | |2

OutputH0 or H1

Figure 3 Energy detection using the simple periodogram (frequency domain approach)

1

2

M

Input section

Hidden layer

Output layer

Bias

Bias

Weights from each input to each hidden layer

Weights from each hidden node to output

layer

V21

V22

Vp1

Vp2

VpM

V2M

V11

V12

V1M

g01

g02

g0M

W11

W21

WM1

y(n minus 1)

y(n minus 2)

y(n minus p)

h01

y(n)

Figure 4 A two-layered RVNN network system

It is known that an AR system driven by white noise 119909(119899)

produces an output sequence 119910(119899) given as

119910 (119899) = minus

119875

sum

119896=1

119886119896119910 (119899 minus 119896) + 119887

0119909 (119899) (3)

where 119886119896 1 le 119896 le 119875 and 119887

0denotes the model coefficients

and119875 is themodel order By taking the 119911-transform of (3) andrearranging the terms therein the transfer function 119867(119911) ofthe AR-system can be obtained as

119867 (119911) =119884 (119911)

119883 (119911)=

1198870

1 + sum119875

119896=1119886119896119911minus119896

(4)

By assigning 1198870

= 1 119911 = 119890minus119895119908 and taking the square of (4)

we obtain the SNR as

SNR =

100381610038161003816100381610038161003816100381610038161003816

119884 (119895119908)

119883 (119895119908)

100381610038161003816100381610038161003816100381610038161003816

2

=1

100381610038161003816100381610038161 + sum

119875

119896=1119886119896119890minus119895119908119896

10038161003816100381610038161003816

2 (5)

To estimate the model coefficient 119886119896 we used a two-

layered RVNN as shown in Figure 4By observing Figure 4 the output sequence of the RVNN

system can be obtained as

119910 (119899) = 120572F(

119872

sum

119897=1

1199081198971

120579119897

+ ℎ01

) (6)

where F denotes the representation of a linear transferfunction 119872 is the number of neurons in the hidden layer1199081198971represents the weight connecting node 119897 in the hidden

to output layer ℎ01

is the bias term of the output neuron120579119897denotes the output of the hidden node 119897 and 120572 is the

adaptive coefficient of the linear output activation functionThe hidden node output 120579

119897is obtained as

120579119897

= 120573119897F(

119875

sum

119896=1

V119896119897

119910 (119899 minus 119896) + 1198920119897

) (7)

where V119896119897is the weight connecting input nodes 119896 to hidden

node 1198971198920119897is the bias of the hidden node and120573

119897is the adaptive

coefficient of the hidden node linear transfer function Byusing linear transfer activation functions in both hidden andoutput layer that is F(sdot) is linear and substituting (7) into (4)the output sequence is obtained as

119910 (119899)

= 120572F(

119872

sum

119897=1

1199081198971

(120573119897F(

119875

sum

119896=1

V119896119897

119910 (119899 minus 119896) + 1198920119897

)) + ℎ01

)

(8)


ADCRVNN

based AR coefficient estimator

Received signal

FFT Detector threshold

Discretized inputs

Estimated model

coefficients

TransferfunctionestimatorH(Z)

Squaringdevice | |2

OutputH0 or H1

Figure 5 The newly proposed RVNN based ED

By rearranging terms in (8) and comparing with (4) themodel coefficients 119886

119896can be expressed as

119886119896

= 120572

119872

sum

119897=1

1199081198971

120573119897V119896119897

(9)

Thus the AR model coefficients can be estimated fromthe synaptic weights and coefficients of the adaptive acti-vation function of a properly trained two-layered RVNNFurthermore by assuming that the model order 119875 is known apriori then the number of neurons in the hidden layer canbe determined by using the priori data length informationat the input To formulate the necessary constraints forproper evaluation of the system the solution to a set oflinear equations that gives the best performance over the apriori fixed model order was obtained We obtained this byconsidering a data set of length 119873 for which the requirednumber of training data set 119871 was obtained as

119871 = 119873 minus 119875 + 1 (10)

The required number of training equations 119873eq isexpressed as

119873eq = 119875 times 119871 (11)

and for 119872 hidden nodes the number of unknowns for thenetwork was obtained as

119873un = (119875 + 1) 119872 + 119872 + 1 (12)

It is known from [23] that the case of119873eq ≫ 119873un producesbetter results with respect to the unseen data Therefore byputting (11) and (12) into the inequality (119873eq ≫ 119873un) weobtained the optimum number of neurons 119872 to satisfy

119872 ≪(119875 times 119871) minus 1

119875 + 2 (13)

With these necessary parameters well established thealgorithm used for the RVNN system is as follows

(1) We normalized the input data sequence to band-limitthe acquired signal using the 119885-score normalizationtechnique Other techniques that could be used arethe MinndashMax sigmoidal or unitary data normaliza-tion techniques

(2) The data were formatted using frame blocking andappropriate windowing of data sequencing

(3) The optimum number of neurons was determinedusing (13)

(4) The model coefficient was estimated using (9)(5) Finally training of the RVNN system was done

using the back propagation (BP) supervised learningalgorithm

32 The RVNN Based Energy Detector With the RVNNmodel estimator in place we developed the RVNN based EDusing the proposed schematic of Figure 5 This was achievedby generating the power spectral density (PSD) of the systemusing (5) and introducing a well-designed detector basedon an empirical threshold estimation technique (details ofmethod in Section 42) An overview of the design process isas follows

(1) A simple analogue-digital-converter (ADC) was usedfor digitization Here the number of samples wasdetermined using the known Nyquist rate of 8KHzfor a maximum bandspan of 4KHz for widebandsimulation and 100Hz for narrowband simulation

(2) The fast Fourier transform (FFT) was used forthe frequency response estimation Appropriate zeropadding was employed for cases of fewer samples forFFT operation

(3) The transfer function estimator was realized using thefrequency response vector obtained from appropriateadaptive filtering of the FFT samples

(4) A simple square law device was introduced for per-forming the squaring operation

(5) The detector analyzer was realized using empiricallydeduced thresholds (details in Section 42)

(6) Our proposed detector of Figure 5 can be used for CRapplication anddetails ofmethods used for its analysisare presented in the next section

4 Method of Modelling and Simulation

In this section we provide details of simulation parametersand analytical models used for evaluating the performance ofour proposed detector and other methods for comparison

41 Hypothesis Testing Additive white Gaussian noise(AWGN) with zero mean and unit variance was used andthe probability of false alarm 119875FA conditioned for the null


0 500 1000 1500 2000 2500 3000 3500 4000Frequency (Hz)

Pow

er sp

ectr

a den

sity

(dB

Hz)

Threshold

minus50

minus45

minus40

minus35

minus30

minus25

Figure 6 Wideband spectrum sensing of 4 KHz showing two PUsignals at 600Hz and 15 KHz in AWGN (occupancy = 10)

hypothesis (1) was obtained using the expression forlarge time-bandwidth product given in [31] The 119875FA fornoise samples distributed according to a Gaussian variate119873(2119879119882 4119879119882) is given as [31]

119875FA =1

radic8120587119879119882

int

infin

119881119879

exp[minus(119910 minus 2119879119882)

2

8119879119882] 119889119910 (14)

=1

2erf 119888 [

119881119879

minus 2119879119882

2radic2radic119879119882

] (15)

where 119879 denotes the observation interval 119882 the bandwidthbeing sensed 119881

119879the threshold and 119879119882 the time-bandwidth

product These were translated appropriately as follows 119879119882

is known as the total number of samples 119873 (at Nyquist rate)2119879119882 is the sample mean 120583 of the noise PSD and 4119879119882 isthe sample variance

2 of the noise PSD (the noise power)Hence we rewrite (15) as

119875FA =1

2erf 119888 [

119881119879

minus 120583

radic22] (16)

We note that the particular use of (15) according to[31] was based on the condition of a large time-bandwidthproduct meaning large sample number Next to estimatethe probability of detection 119875

119863 we considered a modulated

discrete signal 119878(119899119879) given as

119878 (119899119879) = 119860 (119905) cos (2120587119891119888119899119879) forall119899 = 0 1 119873 minus 1 (17)

where 119860(119905) represents the expression for the modulatingsignal 119891

119888the carrier frequency 119873 the total number of

samples and 119879 the sampling timeFor examination of the effect of wideband sensing we

considered two PU signals with equal amplitudes 1198601

=

1198602

= 10 dB and frequencies 1198911198881

= 600Hz 1198911198882

= 1500Hzestimated over a relatively wide sensing span of 4Hz using awideband occupancy of 10 as shown in Figure 6 We notethat though low frequencies were used the setup could easilyapply to high frequency bands with the same concept beingapplicable

For narrowband sensing a typical PU signal of band-width 119882 = 60Hz was simulated for a narrowband sweep of

0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Pow

er sp

ectr

a den

sity

(dB

Hz)

Threshold

minus34

minus32

minus30

minus28

minus26

minus24

minus22

minus20

minus18

Figure 7 Narrowband spectrum sensing of 100Hz showing PUbandwidth of 60Hz and guardbands of 20Hz on both sides

0010203040506070809

1

Prob

abili

ty o

f fal

se al

arm

Threshold value (dBHz)

Threshold value to achieve

false alarm of 001

minus42 minus40 minus38 minus36 minus34 minus32 minus30 minus28 minus26

Figure 8 Probability of false alarm for different thresholds using theRVNN based ED in wideband sensing

100Hzas shown in Figure 7 using theRVNNbasedEDTheseinput data were kept constant for all simulation conditionsand other EDs compared herein Then the 119875

119863was estimated

using [31]

119875119863

=1

2erf 119888 [

119881119879

minus 2119879119882 minus 120582

2radic2radic119879119882 + 120582

] (18)

where 120582 denotes the SNR for the estimated spectrum

42 Threshold Estimation An empirical threshold selectionmethod was employed here and 119875FA for each threshold wasestimated using (16) This was done by varying the thresholdvalues 119881

119879over the noise PSD and Figure 8 provides the result

obtained using the RVNN based ED in wideband sensing Bycomparing the threshold line in Figure 6 with Figure 8 it canbe easily observed that at a threshold of minus35 dBHz less noisesamples crossed the threshold (Figure 6) resulting in 119875FA lt

001 as seen in Figure 8 This provided a suitable thresholdfor estimating the detector performance

5 Results and Discussion

51 Varying AR Model Order on RVNN Based ED The effectof varying ARmodel order on the performance of the RVNNbased EDwas analyzed by inspecting the outcome of differentROCs under varying model order values This examination


0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Prob

abili

ty o

f det

ectio

n

Probability of false alarm

P = 10

P = 20

P = 30

P = 40

P = 50

Figure 9 ROC for RVNN based ED in narrowband sensing underlow SNR (0 dB) and sample number 119873 = 250

0 01 02 03 04 05 06 07 08 09 104

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 40

P = 50

P = 30

Figure 10 ROC for RVNN based ED in narrowband sensing underhigh SNR (10 dB) and sample number 119873 = 250

was essential to aid in the choice of optimum model orderfor CR operation Furthermore this effect was investigatedin both narrow and wideband sensing to determine whichscenario best supports the detector The detector was alsoexamined in low (0 dB) and high (10 dB) SNR conditionsrespectively It can be observed from Figures 9 and 11that the ROCs for different orders remained approximatelyequal for low SNR in both narrow and wideband sensingThis confirmed that at low SNR the PU signal is totallysubmerged in noise and cannot be differentiated by the use ofenergy levels alone resulting in 119875FA asymp 119875

119863 This also indicated

that irrespective of the approach the ED typically performspoorly in low SNR conditions However in narrowbandsensing high SNR and varying model order of Figure 10 theRVNN based ED was observed to perform well particularlyfor model order 119875 = 50 We also observed that thedifference in performance becomes practically negligible for119875 ge 40 Hence a minimum order of 119875 = 40 wasobserved to achieve high detection performance For thecase of wideband sensing high SNR and varying model

0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50

Figure 11 ROC for RVNNbased ED inwideband sensing under lowSNR (0 dB) and sample number 119873 = 250

order Figure 12 revealed a reverse in performance for themodel order values investigated here In this case modelorder 119875 = 50 was observed to perform poorly while 119875 =

20 provided better performance We note that this outcomewas based on the increased spectral leakage at lower orderwhich resulted in more samples crossing the threshold thanat 119875 = 50 This effect is evident owing to the large spectrumconsidered under wideband sensing as compared to thepercentage occupancy of the signal within the band Henceit can be inferred that the probability of false alarm wouldconsequently increase for such lower model orders than thehigher orders thus making it uncertain to strictly rely on theresults of an ROC curve alone However this observationwould be further studied and analysed in future worksBy comparison it was observed that narrowband sensingproduces better performance than wideband for the RVNNbased ED This can be conclusive if the sensing bandwidthof the narrowband detector corresponds typically to thetransmission bandwidth of the PU signal The implication ofthese results means that to use the RVNN based ED for CRnarrowband sensing at 119875 = 50 for short data length (fastsensing time) will be ideal to produce the best detectionperformance

52 Varying SampleNumber onRVNNBasedED To examinethis effect a fixed choice of AR model order 119875 = 50 wasselected for narrowband sensing while 119875 = 20 was chosenfor wideband sensing This ensured that the best modelorder values were used to examine the effect of sensing timethat is varying sample number Here we examined onlyfor the high SNR case (10 dB) knowing that performanceremains the same in low SNR conditions (seen in Figures9 and 11) By observing Figure 13 it was seen that detectionperformance of RVNN based ED improved with increase insample number 119873 However this increase became negligiblefor119873 ge 2000Wenote that this performancewas achieved for119875 = 50 Furthermore by using 119875 = 20 for wideband sensingFigure 14 revealed that high performance was sustained even


0 01 02 03 04 05 06 07 08 09 104

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50

Figure 12 ROC for RVNN based ED in wideband sensing underhigh SNR (10 dB) and sample number 119873 = 250

0 01 02 03 04 05 06 07 08 09 108

082084086088

09092094096098

1

N = 250

N = 1000

N = 2000

Prob

abili

ty o

f det

ectio

n


Figure 13 ROC for RVNN based ED in narrowband sensing underhigh SNR (10 dB) and 119875 = 50

0 01 02 03 04 05 06 07 08 09 1075

08

085

09

095

1

Prob

abili

ty o

f det

ectio

n


N= 250

N = 1000

N = 2000

Figure 14 ROC for RVNN based ED in wideband sensing underhigh SNR (10 dB) and 119875 = 20

0 01 02 03 04 05 06 07 08 09 1088

09

092

094

096

098

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

RVNN N= 2000

YW N= 2000

BG N= 2000

CV N= 2000

Figure 15 ROCs compared for different parametric based EDsusing 119875 = 50 in narrowband sensing

0 01 02 03 04 05 06 07 08 09 108

082084086088

09092094096098

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

RVNN N= 2000

YW N= 2000

BG N= 2000

CV N= 2000

Figure 16 ROCs compared for different parametric based EDs for119875 = 20 in wideband sensing

with a slight performance drop in comparison to narrowbandsensingThis implied that to use the RVNN based ED for fastsensing in CR narrowband sensing for 119875 = 50 remains ideal

53 Comparison with Other Parametric Based ED TechniquesThe RVNN based ED was compared with the Yule-Walker(YW) Burg (BG) and covariance (CV) based approachesNarrowband sensing was examined using model order 119875 =

50 while 119875 = 20 was chosen for wideband sensingFigure 15 revealed a close comparative performance betweenall techniques for fasting sensing time (119873 = 250) Furthercomparison was conducted for long sensing time (119873 = 2000)

and once again performance level was close However it wasobserved that performance increased for all techniques withincrease in sample number This implied that long sensingtime improved the performance of the RVNN based ED andother techniques For wideband sensing Figure 16 revealeda close detection performance between RVNN based ED and


0010203040506070809

1

Prob

abili

ty o

f fal

se al

arm

Threshold value (dBm)minus30 minus25 minus20 minus15 minus10 minus5 0

RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

Figure 17 Comparison of probability of false alarm for differentparametric based techniques for the case of narrowband sensing at119873 = 250

other parametric techniques however a 2drop in detectionperformance was observed with respect to BG YW andCV Comparatively the RVNN based ED produced similardetection performance to acceptable specifications (119875

119863gt 09

at 119875FA = 01) along with other techniques In addition it isshown in Figure 17 that the proposed technique provides a10 average reduction in 119875FA at thresholds below minus20 dBmthan YW BG andCVThis revealed a possible 1 dB reductionin threshold level to achieve 119875FA = 01 as compared toother parametric techniques studied here This means thatthe RVNN based ED provides better sensitivity than YW BGand CV based approaches Also we note that YW BG andCV have tendencies to overestimate the magnitude responseof a signal which resulted in the observed better ROC per-formance of YW BG and CV over the proposed techniquein Figures 15 and 16 Nevertheless higher SNR estimationand consequently improved ROC can be achieved for theRVNNbased ED by including appropriate amplifiers after thesquare law device in Figure 5 On the other hand false alarmsare more difficult to address and cannot be solved by simpleamplification as proposed because both noise and signals willbe amplified accordingly except if noise reduction techniquesare used Consequently reducing 119875FA could depend moreon threshold selection or on the underlying nature of thedetectorTherefore Figure 17 emphasizes a critical advantageof the RVNN based ED over other parametric techniquesespecially in providing an inherent capacity to reduce the 119875FAlevel and prevent possible interference to primary user (PU)signalsThis is a highly desirable feature of any good detectorfor CR application

54 Comparison with Nonparametric Techniques Finally theRVNN based ED was compared with nonparametric tech-niques such as the simple periodogram (SP) Welch peri-odogram (WP) and multitaper (MT) For narrowband sens-ing Figure 18 revealed that the RVNN based ED performedbetter than the nonparametric techniques compared hereexcept for WP which performed slightly better This wasdue to the high variance estimation obtained in the WP

0 01 02 03 04 05 06 07 08 09 107

073076079082085088091094097

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000

Figure 18 ROCs compared between RVNN based ED and othernonparametric techniques in narrowband for 119875 = 50

0 01 02 03 04 05 06 07 08 09 105

06

07

08

09

1Pr

obab

ility

of d

etec

tion


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000

Figure 19 ROCs compared between RVNN based ED and othernonparametric techniques for wideband sensing for 119875 = 20

which made more noise samples to cross the threshold thanin the RVNN based ED In wideband sensing Figure 19revealed that the RVNN based ED performed better thanother nonparametric techniques

6 Conclusion

In this paper a real valued neural network (RVNN) basedenergy detector (ED) has been proposed simulated andanalyzed The choice of the RVNN method for estimatingthe coefficients of an autoregressive (AR) system was basedon its inherent ability to solve the challenge of line splittingand spectral shifting as reported in [23] Thus our developedRVNN based ED was examined using different simulationparameters for different sensing conditions We observedthat for model order 119875 = 50 the proposed detector provideda high detection performance in narrowband sensing and


similar performance in wideband sensing for 119875 = 20 Fur-thermore the detector was compared with other parametricbased techniques like the Yule-Walker (YW) Burg (BG) andcovariance (CV)methods A close performance was achievedbetween our proposed ED and others with less than 5drop in ROC performance observed with respect to YWBG and CV However a 10 reduction in false alarm wasobserved for the RVNN based ED over other parametrictechniques This result presents an important advantage inusing the proposed technique for CR application becausetechniques with less false alarms are highly desirable Finallyit was compared with some nonparametric techniques likethe simple periodogram (SP)Welch periodogram (WP) andthe multitaper (MT) Our proposed detector provided a 10detection performance gain over these techniques except innarrowband and fast sensing case where WP provided about2 detection increase than the RVNN based ED This wasattributed to the high estimated noise variance level whichconsequently resulted in increased false alarm rates in WPThe study reported here indicates that the RVNN based EDprovides a new option for spectrum sensing in CR Howeverwe note that attention was not given here to the degree ofdesign complexity with respect to choice of higher modelorder Though it has been shown in [17] that computationaldemand in terms of number of multiplications is less thanthe periodogram likewise for the storage demand no closedform model exists to describe complexity for higher modelorder This might not necessarily affect detection or falsealarm performance but might affect timing performanceHowever this remains to be studied and provides an oppor-tunity for future research investigations in the field of ARapplication in CR

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publishing of this paper

Acknowledgment

This work was supported under the University Board ofResearch (UBR) grant award from the Federal University ofTechnology Minna Nigeria

References

[1] M Lopez-Benıtez and F Casadevall ldquoOn the spectrum occu-pancy perception of cognitive radio terminals in realisticscenariosrdquo in Proceedings of the 2nd International Workshop onCognitive Information Processing (CIP rsquo10) Special Session onNEWCOMTF pp 99ndash104 Elba Italy June 2010

[2] A J Onumanyi E N Onwuka O Ugweje and M J ESalami ldquoSpectroscopicmeasurements and analysis of frequencyoccupancy a case study of Minna Niger Staterdquo in Proceedingsof the 3rd Biennial Engineering Conference pp 30ndash35 FederalUniversity of Technology Minna Nigeria 2013

[3] R Urban T Kriz and M Cap ldquoIndoor broadband spectrumsurveymeasurements for the improvement of wireless systemsrdquoin Proceedings of the Progress in Electromagnetics Research

Symposium (PIERS rsquo13) pp 376ndash380 Taipei Taiwan March2013

[4] MNMehdawi K Riley A PaulsonM Fanan andMAmmarldquoSpectrum occupancy survey in HULL-UK for cognitive radioapplications measurement amp analysisrdquo International Journal ofScientific amp Technology Research vol 2 no 4 pp 231ndash236 2013

[5] D Datla A M Wyglinski and G J Minden ldquoA spectrum sur-veying framework for dynamic spectrum access networksrdquoIEEE Transactions on Vehicular Technology vol 58 no 8 pp4158ndash4168 2009

[6] J Polson and B A Fette ldquoCognitive techniques position aware-nessrdquo Cognitive Radio Technology pp 265ndash288 2009

[7] BWang and K J R Liu ldquoAdvances in cognitive radio networksa surveyrdquo IEEE Journal on Selected Topics in Signal Processingvol 5 no 1 pp 5ndash23 2011

[8] YHur J ParkWWoo J S Lee K Lim andC Lee ldquoA cognitiveradio (CR) system employing a dual-stage spectrum sensingtechnique AMulti-Resolution Spectrum Sensing (MRSS) and aTemporal Signature Detection (TSD) techniquerdquo in Proceedingsof the IEEE Global Telecommunications Conference (GLOBE-COM rsquo06) pp 1ndash5 San Francisco Calif USA December 2006

[9] M Nekovee ldquoMechanism design for cognitive radio networksrdquoin Proceedings of the Conference on Complexity in Engineering(COMPENG 10) pp 12ndash17 Rome Italy February 2010

[10] E Hossain D Niyato and D I Kim ldquoEvolution and futuretrends of research in cognitive radio a contemporary surveyrdquoWireless Communications and Mobile Computing 2013

[11] I F Akyildiz W Lee M C Vuran and S Mohanty ldquoNeXt gen-erationdynamic spectrum accesscognitive radio wireless net-works a surveyrdquo Computer Networks vol 50 no 13 pp 2127ndash2159 2006

[12] R Umar andA U H Sheikh ldquoA comparative study of spectrumawareness techniques for cognitive radio oriented wirelessnetworksrdquo Physical Communication vol 9 pp 148ndash170 2013

[13] T Dhope and D Simunic ldquoSpectrum sensing algorithm forcognitive radio networks for dynamic spectrum access for IEEE80211af standardrdquo International Journal of Research andReviewsin Wireless Sensor Networks vol 2 no 1 pp 77ndash84 2012

[14] D Cabric S MMishra and RW Brodersen ldquoImplementationissues in spectrum sensing for cognitive radiosrdquo in Proceedingsof the Conference Record of the 38th Asilomar Conference onSignals Systems and Computers pp 772ndash776 Pacific GroveCalif USA November 2004

[15] A Ghasemi and E S Sousa ldquoOptimization of spectrum sensingfor opportunistic spectrum access in cognitive radio networksrdquoin Proceedings of the 4th Annual IEEE Consumer Communica-tions and Networking Conference pp 1022ndash1026 January 2007

[16] D G Altman and J M Bland ldquoParametric V non-parametricmethods for data analysisrdquo BMJ vol 338 Article ID a3167 2009

[17] S Kay ldquoDetection of a Sinuisoid inWhite Noise by Autoregres-sive Spectrum Analysisrdquo Proceeding of the IEEE InternationalConference on Acoustics Speech and Signal Processing (ICASSP80) pp 658ndash661 1980

[18] P Stoica and L M Randolph Spectral Analysis of SignalsPearsonPrentice Hall Upper Saddle River NJ USA 2005

[19] A Gorcin H Celebi K A Qaraqe and H Arslan ldquoAn autore-gressive approach for spectrum occupancy modeling and pre-diction based on synchronous measurementsrdquo in Proceedingsof the IEEE 22nd International Symposium on Personal Indoorand Mobile Radio Communications (PIMRC 11) pp 705ndash709Toronto Canada September 2011


[20] Z Wen T Luo W Xiang S Majhi and Y Ma ldquoAutoregressivespectrum hole predictionmodel for cognitive radio systemsrdquo inProceedings of the IEEE International Conference on Communi-cations Workshops (ICC rsquo08) pp 154ndash157 May 2008

[21] CDong YDong andLWang ldquoAutoregressive channel predic-tion model for cognitive radiordquo in Proceedings of the 5th Inter-national Conference on Wireless Communications Networkingand Mobile Computing (WiCOM rsquo09) pp 1ndash4 Beijing ChinaSeptember 2009

[22] C Dong Y Dong LWang Z Yang andH Zhang ldquoParticle fil-tering based autoregressive channel prediction modelrdquo Journalof Electronics vol 27 no 3 pp 316ndash320 2010

[23] AM Aibinu M J E Salami and A A Shafie ldquoArtificial neuralnetwork based autoregressive modeling technique with appli-cation in voice activity detectionrdquo Engineering Applications ofArtificial Intelligence vol 25 no 6 pp 1265ndash1276 2012

[24] P Welch ldquoThe use of fast fourier transform for the estimationof power spectra a method based on time averaging overshortmodified periodogramsrdquo IEEETransactions onAudio andElectroacoustics vol 15 no 2 pp 70ndash73 1967

[25] M Matinmikko H Sarvanko M Mustonen and A MammelaldquoPerformance of spectrum sensing using welchrsquos periodogramin rayleigh fading channelrdquo in Proceedings of the 4th Interna-tional Conference on Cognitive Radio Oriented Wireless Net-works and Communications 5 p 1 Hannover Germany June2009

[26] I Harjula AHekkalaMMatinmikko andMMustonen ldquoPer-formance evaluation of spectrum sensing using welch peri-odogram for OFDM signalsrdquo in Proceedings of the IEEE 73rdVehicular Technology Conference (VTC rsquo11) pp 1ndash5 May 2011

[27] N Wang and G Yue ldquoOptimal threshold of Welchrsquos periodo-gram for sensing OFDM signals at low SNR levelsrdquo in Proceed-ings of the 19th European Wireless Conference (EW) pp 1ndash5Guildford UK April 2013

[28] S Haykin ldquoThe multitaper method for accurate spectrumsensing in cognitive radio environmentsrdquo in Proceeding of the41st Asilomar Conference on Signals Systems and Computers ofthe IEEE Conference Record (ACSSC 07) pp 436ndash439 PacificGrove Calif USA November 2007

[29] J Wang and Q T Zhang ldquoA multitaper spectrum baseddetector for cognitive radiordquo in Proceedings of the IEEEWirelessCommunications and Networking Conference (WCNC rsquo09) pp1ndash5 April 2009

[30] H Gao M Wu C Xu and Q Wu ldquoAn improved multitapermethod for spectrum sensing in cognitive radio networksrdquoin Proceedings of the 3rd IEEE International Conference onComputer Science and Information Technology (ICCSIT 10) pp393ndash396 Chengdu China July 2010

[31] H Urkowitz ldquoEnergy detection of unknown deterministicsignalsrdquo Proceedings of the IEEE vol 55 no 4 pp 523ndash531 1967

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



(AR) spectrum estimation technique for ED application inCR The choice of the RVNN based AR technique was basedon its advantage over the popular BG technique in solvingthe challenge of spectral line splitting at high SNR and largemodel order conditions [23] Consequently it was observedhere that such an advantage would lead to an improvedED with less probability of false alarms for CR applicationResults of this contribution are presented in Section 5 Alsowhile authors in [23] developed the RVNN technique andapplied it in voice activity detection in our own work wepropose necessary additions to standardize the approach as afully functional ED using an empirical threshold estimationtechnique for CR application The RVNN based AR modelcoefficient estimator developed in [23] has never been appliedas an ED for CR application hence its application wasconsidered here to exploit its inherent advantage Thereforeonce developed as a functional ED it was tested usingsimulated data particularly in low and high SNR conditionsand varying model order values as described in Section 4and results obtained with corresponding implications arepresented in Section 5 Appropriate conclusions are drawn inSection 6

2 Brief Review of Energy Detector Techniques

Energy detectors (ED) sense the presence or absence ofPU signals by estimating the energy content of a specifiedband using the power spectral density (PSD) measurementsand comparing with predetermined thresholds [12 14] Thisaids the CR device in vacating PU occupied bands to avoidinterference and use vacant bands to improve spectrumutilization Figures 1(a) and 1(b) provide a representation ofthis process Towards this goal signals above the thresholdtypically signify PU presence 119867

1 and below threshold

as noise 1198670 These hypotheses 119867

0and 119867

1are typically

represented as

1198670

119909 (119899) = 119908 (119899) (1)

1198671

119909 (119899) = 119904 (119899) + 119908 (119899) (2)

where 119908(119899) represents samples of additive white Gaussiannoise (AWGN) 119904(119899) denotes samples of PU signal and119909(119899) denotes samples of received signal at the CR inputconsidering a perfect channel

EDs are typically developed to decide on these hypotheseseither in time or in frequency domain In time domain itconsists of an input noise prefilter a magnitude square lawdevice an integrator and a detector as shown in Figure 2Thisapproach has been used in several works [12ndash15] and well-known for its simplicity and low design and developmentcost However it is based on the super heterodyne techniquewhich is limited by its slow voltage ramping response time [6]Such a delay might be intolerable for CR operation Anotherapproach is to realize the ED in the frequency domainusing the well-known periodogram as shown in Figure 3This provides an opportunity to achieve full digitizationof the detection process however this approach constrains

the sensing bandwidth owing to known limitations of typicalfast Fourier transform (FFT) realizations [8]

Another method identified for the ED in CR is theWelch periodogram (WP) approach [24] Particularly in [25]performance analysis was carried out on the use of WP inRayleigh fading channels while [26 27] used WP for OFDMsystems in CR These authors observed that WP operateswell for narrowband sensing however they conclude thatthe approach is limited by the excessive variance aroundthe true mean PSD value This increases the probabilityof false alarm of the system Another approach using theMultitaper (MT) technique was proposed in [28] with basicdescriptions provided from filter-bank theory point of viewThis technique was extended in [29] for signal detectionin CR and results were compared with the time domainbased ED It was observed that MT performed better in lowSNR conditions under Raleigh fading channels This wasbased on the techniquersquos dependence on both magnitudeand phase of received samples Also [30] provided animprovedMTmethod forCR application inwhich a recursivemethod to improve the accuracy of estimates while keepingreal-time properties uncompromised was proposed Authorscompared their technique with the SP and ordinary MT andobserved better performance for their improved MT

On the other hand the use of autoregressive (AR) meth-ods has been sparsely pursued especially for energy detectionin CR The AR methods present a class of techniquespopularly classified as parametric techniques Though notwidely used in CR we observed that [19ndash21] proposed ARfor spectrum hole detection in CR using time series forecast-ing Authors reported on the performance of the proposedapproach however it remains unclear how well such anapproach would perform in typical deployment conditionsAlso authors in [21 22] used particle andKalman filtering forspectrum availability forecasting In [17] authors presented acomparison of SP and Yule-Walker (YW) AR techniques andargued that better performance could be achieved by the YWif large model orders are considered However most of theseapplications have not considered AR application for ED inCR andhence it remains unknownhowwell such techniqueswould perform if employed Consequently we consideredthe use of a real valued neural network (RVNN) AR modelestimator [23] to develop a detector for CR application Thisapproach provides data reported in [23] which was leveragedupon here to develop an improved ED for CR Consequentlyit is the focus here to develop evaluate and analyze itsperformance for CR application

3 Development of the Real Valued NeuralNetwork Based Energy Detector

31 An Overview of the RVNN Based Autoregressive ModelEstimation Technique Theworking principles of the real val-ued neural network (RVVN) autoregressive (AR) coefficientestimation technique were based on [23] Thus we presenthere only specific details needed to develop the ED for CRapplication however for further details we refer to [23]




CR node 1

Channel is utilized

CR base station

CR node 2

PU transmitter

PU receiver

(a)

PU receiver

PU signal present

Channel is vacated



CR node 1

CR node 2

PU transmitter

CR base station

(b)


Input signalY(t)

Noise prefilter


Analogintegrator

Decisionthreshold

OutputH0 or H1



Input signalY(t)




OutputH0 or H1


1

2

M

Input section

Hidden layer

Output layer

Bias

Bias



layer

V21

V22

Vp1

Vp2

VpM

V2M

V11

V12

V1M

g01

g02

g0M

W11

W21

WM1

y(n minus 1)

y(n minus 2)

y(n minus p)

h01

y(n)




119910 (119899) = minus

119875

sum

119896=1

119886119896119910 (119899 minus 119896) + 119887

0119909 (119899) (3)

where 119886119896 1 le 119896 le 119875 and 119887



119867 (119911) =119884 (119911)

119883 (119911)=

1198870

1 + sum119875

119896=1119886119896119911minus119896

(4)




SNR =

100381610038161003816100381610038161003816100381610038161003816

119884 (119895119908)

119883 (119895119908)

100381610038161003816100381610038161003816100381610038161003816

2

=1

100381610038161003816100381610038161 + sum

119875

119896=1119886119896119890minus119895119908119896

10038161003816100381610038161003816

2 (5)




119910 (119899) = 120572F(

119872

sum

119897=1

1199081198971

120579119897

+ ℎ01

) (6)






120579119897

= 120573119897F(

119875

sum

119896=1

V119896119897

119910 (119899 minus 119896) + 1198920119897

) (7)





119910 (119899)

= 120572F(

119872

sum

119897=1

1199081198971

(120573119897F(

119875

sum

119896=1

V119896119897

119910 (119899 minus 119896) + 1198920119897

)) + ℎ01

)

(8)


ADCRVNN


Received signal


Discretized inputs

Estimated model

coefficients


Squaringdevice | |2

OutputH0 or H1




119886119896

= 120572

119872

sum

119897=1

1199081198971

120573119897V119896119897

(9)


119871 = 119873 minus 119875 + 1 (10)


119873eq = 119875 times 119871 (11)


119873un = (119875 + 1) 119872 + 119872 + 1 (12)


119872 ≪(119875 times 119871) minus 1

119875 + 2 (13)


















0 500 1000 1500 2000 2500 3000 3500 4000Frequency (Hz)

Pow

er sp

ectr

a den

sity

(dB

Hz)

Threshold

minus50

minus45

minus40

minus35

minus30

minus25



119875FA =1

radic8120587119879119882

int

infin

119881119879

exp[minus(119910 minus 2119879119882)

2

8119879119882] 119889119910 (14)

=1

2erf 119888 [

119881119879

minus 2119879119882


] (15)






119875FA =1

2erf 119888 [

119881119879

minus 120583

radic22] (16)




119878 (119899119879) = 119860 (119905) cos (2120587119891119888119899119879) forall119899 = 0 1 119873 minus 1 (17)





=

1198602


= 600Hz 1198911198882



0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Pow

er sp

ectr

a den

sity

(dB

Hz)

Threshold

minus34

minus32

minus30

minus28

minus26

minus24

minus22

minus20

minus18


0010203040506070809

1

Prob

abili

ty o

f fal

se al

arm



false alarm of 001




119863was estimated

using [31]

119875119863

=1

2erf 119888 [

119881119879

minus 2119879119882 minus 120582

2radic2radic119879119882 + 120582

] (18)









0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50


0 01 02 03 04 05 06 07 08 09 104

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 40

P = 50

P = 30





0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50






0 01 02 03 04 05 06 07 08 09 104

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50


0 01 02 03 04 05 06 07 08 09 108

082084086088

09092094096098

1

N = 250

N = 1000

N = 2000

Prob

abili

ty o

f det

ectio

n



0 01 02 03 04 05 06 07 08 09 1075

08

085

09

095

1

Prob

abili

ty o

f det

ectio

n


N= 250

N = 1000

N = 2000


0 01 02 03 04 05 06 07 08 09 1088

09

092

094

096

098

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

RVNN N= 2000

YW N= 2000

BG N= 2000

CV N= 2000


0 01 02 03 04 05 06 07 08 09 108

082084086088

09092094096098

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

RVNN N= 2000

YW N= 2000

BG N= 2000

CV N= 2000







0010203040506070809

1

Prob

abili

ty o

f fal

se al

arm


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250



119863gt 09



0 01 02 03 04 05 06 07 08 09 107

073076079082085088091094097

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000


0 01 02 03 04 05 06 07 08 09 105

06

07

08

09

1Pr

obab

ility

of d

etec

tion


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000



6 Conclusion






Acknowledgment


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












CR node 1

Channel is utilized

CR base station

CR node 2

PU transmitter

PU receiver

(a)

PU receiver

PU signal present

Channel is vacated



CR node 1

CR node 2

PU transmitter

CR base station

(b)


Input signalY(t)

Noise prefilter


Analogintegrator

Decisionthreshold

OutputH0 or H1



Input signalY(t)




OutputH0 or H1


1

2

M

Input section

Hidden layer

Output layer

Bias

Bias



layer

V21

V22

Vp1

Vp2

VpM

V2M

V11

V12

V1M

g01

g02

g0M

W11

W21

WM1

y(n minus 1)

y(n minus 2)

y(n minus p)

h01

y(n)




119910 (119899) = minus

119875

sum

119896=1

119886119896119910 (119899 minus 119896) + 119887

0119909 (119899) (3)

where 119886119896 1 le 119896 le 119875 and 119887



119867 (119911) =119884 (119911)

119883 (119911)=

1198870

1 + sum119875

119896=1119886119896119911minus119896

(4)




SNR =

100381610038161003816100381610038161003816100381610038161003816

119884 (119895119908)

119883 (119895119908)

100381610038161003816100381610038161003816100381610038161003816

2

=1

100381610038161003816100381610038161 + sum

119875

119896=1119886119896119890minus119895119908119896

10038161003816100381610038161003816

2 (5)




119910 (119899) = 120572F(

119872

sum

119897=1

1199081198971

120579119897

+ ℎ01

) (6)






120579119897

= 120573119897F(

119875

sum

119896=1

V119896119897

119910 (119899 minus 119896) + 1198920119897

) (7)





119910 (119899)

= 120572F(

119872

sum

119897=1

1199081198971

(120573119897F(

119875

sum

119896=1

V119896119897

119910 (119899 minus 119896) + 1198920119897

)) + ℎ01

)

(8)


ADCRVNN


Received signal


Discretized inputs

Estimated model

coefficients


Squaringdevice | |2

OutputH0 or H1




119886119896

= 120572

119872

sum

119897=1

1199081198971

120573119897V119896119897

(9)


119871 = 119873 minus 119875 + 1 (10)


119873eq = 119875 times 119871 (11)


119873un = (119875 + 1) 119872 + 119872 + 1 (12)


119872 ≪(119875 times 119871) minus 1

119875 + 2 (13)


















0 500 1000 1500 2000 2500 3000 3500 4000Frequency (Hz)

Pow

er sp

ectr

a den

sity

(dB

Hz)

Threshold

minus50

minus45

minus40

minus35

minus30

minus25



119875FA =1

radic8120587119879119882

int

infin

119881119879

exp[minus(119910 minus 2119879119882)

2

8119879119882] 119889119910 (14)

=1

2erf 119888 [

119881119879

minus 2119879119882


] (15)






119875FA =1

2erf 119888 [

119881119879

minus 120583

radic22] (16)




119878 (119899119879) = 119860 (119905) cos (2120587119891119888119899119879) forall119899 = 0 1 119873 minus 1 (17)





=

1198602


= 600Hz 1198911198882



0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Pow

er sp

ectr

a den

sity

(dB

Hz)

Threshold

minus34

minus32

minus30

minus28

minus26

minus24

minus22

minus20

minus18


0010203040506070809

1

Prob

abili

ty o

f fal

se al

arm



false alarm of 001




119863was estimated

using [31]

119875119863

=1

2erf 119888 [

119881119879

minus 2119879119882 minus 120582

2radic2radic119879119882 + 120582

] (18)









0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50


0 01 02 03 04 05 06 07 08 09 104

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 40

P = 50

P = 30





0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50






0 01 02 03 04 05 06 07 08 09 104

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50


0 01 02 03 04 05 06 07 08 09 108

082084086088

09092094096098

1

N = 250

N = 1000

N = 2000

Prob

abili

ty o

f det

ectio

n



0 01 02 03 04 05 06 07 08 09 1075

08

085

09

095

1

Prob

abili

ty o

f det

ectio

n


N= 250

N = 1000

N = 2000


0 01 02 03 04 05 06 07 08 09 1088

09

092

094

096

098

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

RVNN N= 2000

YW N= 2000

BG N= 2000

CV N= 2000


0 01 02 03 04 05 06 07 08 09 108

082084086088

09092094096098

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

RVNN N= 2000

YW N= 2000

BG N= 2000

CV N= 2000







0010203040506070809

1

Prob

abili

ty o

f fal

se al

arm


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250



119863gt 09



0 01 02 03 04 05 06 07 08 09 107

073076079082085088091094097

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000


0 01 02 03 04 05 06 07 08 09 105

06

07

08

09

1Pr

obab

ility

of d

etec

tion


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000



6 Conclusion






Acknowledgment


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Input signalY(t)




OutputH0 or H1


1

2

M

Input section

Hidden layer

Output layer

Bias

Bias



layer

V21

V22

Vp1

Vp2

VpM

V2M

V11

V12

V1M

g01

g02

g0M

W11

W21

WM1

y(n minus 1)

y(n minus 2)

y(n minus p)

h01

y(n)




119910 (119899) = minus

119875

sum

119896=1

119886119896119910 (119899 minus 119896) + 119887

0119909 (119899) (3)

where 119886119896 1 le 119896 le 119875 and 119887



119867 (119911) =119884 (119911)

119883 (119911)=

1198870

1 + sum119875

119896=1119886119896119911minus119896

(4)




SNR =

100381610038161003816100381610038161003816100381610038161003816

119884 (119895119908)

119883 (119895119908)

100381610038161003816100381610038161003816100381610038161003816

2

=1

100381610038161003816100381610038161 + sum

119875

119896=1119886119896119890minus119895119908119896

10038161003816100381610038161003816

2 (5)




119910 (119899) = 120572F(

119872

sum

119897=1

1199081198971

120579119897

+ ℎ01

) (6)






120579119897

= 120573119897F(

119875

sum

119896=1

V119896119897

119910 (119899 minus 119896) + 1198920119897

) (7)





119910 (119899)

= 120572F(

119872

sum

119897=1

1199081198971

(120573119897F(

119875

sum

119896=1

V119896119897

119910 (119899 minus 119896) + 1198920119897

)) + ℎ01

)

(8)


ADCRVNN


Received signal


Discretized inputs

Estimated model

coefficients


Squaringdevice | |2

OutputH0 or H1




119886119896

= 120572

119872

sum

119897=1

1199081198971

120573119897V119896119897

(9)


119871 = 119873 minus 119875 + 1 (10)


119873eq = 119875 times 119871 (11)


119873un = (119875 + 1) 119872 + 119872 + 1 (12)


119872 ≪(119875 times 119871) minus 1

119875 + 2 (13)


















0 500 1000 1500 2000 2500 3000 3500 4000Frequency (Hz)

Pow

er sp

ectr

a den

sity

(dB

Hz)

Threshold

minus50

minus45

minus40

minus35

minus30

minus25



119875FA =1

radic8120587119879119882

int

infin

119881119879

exp[minus(119910 minus 2119879119882)

2

8119879119882] 119889119910 (14)

=1

2erf 119888 [

119881119879

minus 2119879119882


] (15)






119875FA =1

2erf 119888 [

119881119879

minus 120583

radic22] (16)




119878 (119899119879) = 119860 (119905) cos (2120587119891119888119899119879) forall119899 = 0 1 119873 minus 1 (17)





=

1198602


= 600Hz 1198911198882



0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Pow

er sp

ectr

a den

sity

(dB

Hz)

Threshold

minus34

minus32

minus30

minus28

minus26

minus24

minus22

minus20

minus18


0010203040506070809

1

Prob

abili

ty o

f fal

se al

arm



false alarm of 001




119863was estimated

using [31]

119875119863

=1

2erf 119888 [

119881119879

minus 2119879119882 minus 120582

2radic2radic119879119882 + 120582

] (18)









0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50


0 01 02 03 04 05 06 07 08 09 104

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 40

P = 50

P = 30





0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50






0 01 02 03 04 05 06 07 08 09 104

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50


0 01 02 03 04 05 06 07 08 09 108

082084086088

09092094096098

1

N = 250

N = 1000

N = 2000

Prob

abili

ty o

f det

ectio

n



0 01 02 03 04 05 06 07 08 09 1075

08

085

09

095

1

Prob

abili

ty o

f det

ectio

n


N= 250

N = 1000

N = 2000


0 01 02 03 04 05 06 07 08 09 1088

09

092

094

096

098

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

RVNN N= 2000

YW N= 2000

BG N= 2000

CV N= 2000


0 01 02 03 04 05 06 07 08 09 108

082084086088

09092094096098

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

RVNN N= 2000

YW N= 2000

BG N= 2000

CV N= 2000







0010203040506070809

1

Prob

abili

ty o

f fal

se al

arm


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250



119863gt 09



0 01 02 03 04 05 06 07 08 09 107

073076079082085088091094097

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000


0 01 02 03 04 05 06 07 08 09 105

06

07

08

09

1Pr

obab

ility

of d

etec

tion


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000



6 Conclusion






Acknowledgment


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










ADCRVNN


Received signal


Discretized inputs

Estimated model

coefficients


Squaringdevice | |2

OutputH0 or H1




119886119896

= 120572

119872

sum

119897=1

1199081198971

120573119897V119896119897

(9)


119871 = 119873 minus 119875 + 1 (10)


119873eq = 119875 times 119871 (11)


119873un = (119875 + 1) 119872 + 119872 + 1 (12)


119872 ≪(119875 times 119871) minus 1

119875 + 2 (13)


















0 500 1000 1500 2000 2500 3000 3500 4000Frequency (Hz)

Pow

er sp

ectr

a den

sity

(dB

Hz)

Threshold

minus50

minus45

minus40

minus35

minus30

minus25



119875FA =1

radic8120587119879119882

int

infin

119881119879

exp[minus(119910 minus 2119879119882)

2

8119879119882] 119889119910 (14)

=1

2erf 119888 [

119881119879

minus 2119879119882


] (15)






119875FA =1

2erf 119888 [

119881119879

minus 120583

radic22] (16)




119878 (119899119879) = 119860 (119905) cos (2120587119891119888119899119879) forall119899 = 0 1 119873 minus 1 (17)





=

1198602


= 600Hz 1198911198882



0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Pow

er sp

ectr

a den

sity

(dB

Hz)

Threshold

minus34

minus32

minus30

minus28

minus26

minus24

minus22

minus20

minus18


0010203040506070809

1

Prob

abili

ty o

f fal

se al

arm



false alarm of 001




119863was estimated

using [31]

119875119863

=1

2erf 119888 [

119881119879

minus 2119879119882 minus 120582

2radic2radic119879119882 + 120582

] (18)









0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50


0 01 02 03 04 05 06 07 08 09 104

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 40

P = 50

P = 30





0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50






0 01 02 03 04 05 06 07 08 09 104

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50


0 01 02 03 04 05 06 07 08 09 108

082084086088

09092094096098

1

N = 250

N = 1000

N = 2000

Prob

abili

ty o

f det

ectio

n



0 01 02 03 04 05 06 07 08 09 1075

08

085

09

095

1

Prob

abili

ty o

f det

ectio

n


N= 250

N = 1000

N = 2000


0 01 02 03 04 05 06 07 08 09 1088

09

092

094

096

098

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

RVNN N= 2000

YW N= 2000

BG N= 2000

CV N= 2000


0 01 02 03 04 05 06 07 08 09 108

082084086088

09092094096098

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

RVNN N= 2000

YW N= 2000

BG N= 2000

CV N= 2000







0010203040506070809

1

Prob

abili

ty o

f fal

se al

arm


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250



119863gt 09



0 01 02 03 04 05 06 07 08 09 107

073076079082085088091094097

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000


0 01 02 03 04 05 06 07 08 09 105

06

07

08

09

1Pr

obab

ility

of d

etec

tion


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000



6 Conclusion






Acknowledgment


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 500 1000 1500 2000 2500 3000 3500 4000Frequency (Hz)

Pow

er sp

ectr

a den

sity

(dB

Hz)

Threshold

minus50

minus45

minus40

minus35

minus30

minus25



119875FA =1

radic8120587119879119882

int

infin

119881119879

exp[minus(119910 minus 2119879119882)

2

8119879119882] 119889119910 (14)

=1

2erf 119888 [

119881119879

minus 2119879119882


] (15)






119875FA =1

2erf 119888 [

119881119879

minus 120583

radic22] (16)




119878 (119899119879) = 119860 (119905) cos (2120587119891119888119899119879) forall119899 = 0 1 119873 minus 1 (17)





=

1198602


= 600Hz 1198911198882



0 10 20 30 40 50 60 70 80 90 100Frequency (Hz)

Pow

er sp

ectr

a den

sity

(dB

Hz)

Threshold

minus34

minus32

minus30

minus28

minus26

minus24

minus22

minus20

minus18


0010203040506070809

1

Prob

abili

ty o

f fal

se al

arm



false alarm of 001




119863was estimated

using [31]

119875119863

=1

2erf 119888 [

119881119879

minus 2119879119882 minus 120582

2radic2radic119879119882 + 120582

] (18)









0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50


0 01 02 03 04 05 06 07 08 09 104

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 40

P = 50

P = 30





0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50






0 01 02 03 04 05 06 07 08 09 104

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50


0 01 02 03 04 05 06 07 08 09 108

082084086088

09092094096098

1

N = 250

N = 1000

N = 2000

Prob

abili

ty o

f det

ectio

n



0 01 02 03 04 05 06 07 08 09 1075

08

085

09

095

1

Prob

abili

ty o

f det

ectio

n


N= 250

N = 1000

N = 2000


0 01 02 03 04 05 06 07 08 09 1088

09

092

094

096

098

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

RVNN N= 2000

YW N= 2000

BG N= 2000

CV N= 2000


0 01 02 03 04 05 06 07 08 09 108

082084086088

09092094096098

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

RVNN N= 2000

YW N= 2000

BG N= 2000

CV N= 2000







0010203040506070809

1

Prob

abili

ty o

f fal

se al

arm


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250



119863gt 09



0 01 02 03 04 05 06 07 08 09 107

073076079082085088091094097

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000


0 01 02 03 04 05 06 07 08 09 105

06

07

08

09

1Pr

obab

ility

of d

etec

tion


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000



6 Conclusion






Acknowledgment


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50


0 01 02 03 04 05 06 07 08 09 104

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 40

P = 50

P = 30





0 01 02 03 04 05 06 07 08 09 10

010203040506070809

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50






0 01 02 03 04 05 06 07 08 09 104

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50


0 01 02 03 04 05 06 07 08 09 108

082084086088

09092094096098

1

N = 250

N = 1000

N = 2000

Prob

abili

ty o

f det

ectio

n



0 01 02 03 04 05 06 07 08 09 1075

08

085

09

095

1

Prob

abili

ty o

f det

ectio

n


N= 250

N = 1000

N = 2000


0 01 02 03 04 05 06 07 08 09 1088

09

092

094

096

098

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

RVNN N= 2000

YW N= 2000

BG N= 2000

CV N= 2000


0 01 02 03 04 05 06 07 08 09 108

082084086088

09092094096098

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

RVNN N= 2000

YW N= 2000

BG N= 2000

CV N= 2000







0010203040506070809

1

Prob

abili

ty o

f fal

se al

arm


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250



119863gt 09



0 01 02 03 04 05 06 07 08 09 107

073076079082085088091094097

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000


0 01 02 03 04 05 06 07 08 09 105

06

07

08

09

1Pr

obab

ility

of d

etec

tion


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000



6 Conclusion






Acknowledgment


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 01 02 03 04 05 06 07 08 09 104

05

06

07

08

09

1

Prob

abili

ty o

f det

ectio

n


P = 10

P = 20

P = 30

P = 40

P = 50


0 01 02 03 04 05 06 07 08 09 108

082084086088

09092094096098

1

N = 250

N = 1000

N = 2000

Prob

abili

ty o

f det

ectio

n



0 01 02 03 04 05 06 07 08 09 1075

08

085

09

095

1

Prob

abili

ty o

f det

ectio

n


N= 250

N = 1000

N = 2000


0 01 02 03 04 05 06 07 08 09 1088

09

092

094

096

098

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

RVNN N= 2000

YW N= 2000

BG N= 2000

CV N= 2000


0 01 02 03 04 05 06 07 08 09 108

082084086088

09092094096098

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250

RVNN N= 2000

YW N= 2000

BG N= 2000

CV N= 2000







0010203040506070809

1

Prob

abili

ty o

f fal

se al

arm


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250



119863gt 09



0 01 02 03 04 05 06 07 08 09 107

073076079082085088091094097

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000


0 01 02 03 04 05 06 07 08 09 105

06

07

08

09

1Pr

obab

ility

of d

etec

tion


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000



6 Conclusion






Acknowledgment


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0010203040506070809

1

Prob

abili

ty o

f fal

se al

arm


RVNN N= 250

YW N= 250

BG N= 250

CV N= 250



119863gt 09



0 01 02 03 04 05 06 07 08 09 107

073076079082085088091094097

1

Prob

abili

ty o

f det

ectio

n


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000


0 01 02 03 04 05 06 07 08 09 105

06

07

08

09

1Pr

obab

ility

of d

etec

tion


RVNN N= 250

SP N= 250

WP N= 250

MT N= 250

RVNN N= 2000

SP N= 2000

WP N= 2000

MT N= 2000



6 Conclusion






Acknowledgment


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Acknowledgment


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article A Real Valued Neural Network Based...

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Transcript of Research Article A Real Valued Neural Network Based...