research article a novel modulation classification...

Research ArticleA Novel Modulation Classification Approach UsingGabor Filter Network

Sajjad Ahmed Ghauri123 Ijaz Mansoor Qureshi45

Tanveer Ahmed Cheema15 and Aqdas Naveed Malik35

1 ISRA University Islamabad 44000 Pakistan2 School of Engineering amp Applied Sciences (SEAS) ISRA University Islamabad Campus I10 Markaz Islamabad 44000 Pakistan3 International Islamic University Islamabad 44000 Pakistan4AIR University Islamabad 44000 Pakistan5 Institute of Signals Systems and Soft Computing (ISSS) Islamabad Pakistan

Correspondence should be addressed to Sajjad Ahmed Ghauri sajjadghauri101gmailcom

Received 24 February 2014 Revised 16 June 2014 Accepted 17 June 2014 Published 14 July 2014

Academic Editor Nirupam Chakraborti

Copyright copy 2014 Sajjad Ahmed Ghauri et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

A Gabor filter network based approach is used for feature extraction and classification of digital modulated signals by adaptivelytuning the parameters of Gabor filter network Modulation classification of digitally modulated signals is done under the influenceof additive white Gaussian noise (AWGN)The modulations considered for the classification purpose are PSK 2 to 64 FSK 2 to 64and QAM 4 to 64 The Gabor filter network uses the network structure of two layers the first layer which is input layer constitutesthe adaptive feature extraction part and the second layer constitutes the signal classification part The Gabor atom parameters aretuned using Delta rule and updating of weights of Gabor filter using least mean square (LMS) algorithm The simulation resultsshow that proposed novel modulation classification algorithm has high classification accuracy at low signal to noise ratio (SNR) onAWGN channel

1 Introduction

Digital modulation is an important factor in communicationsystem Identification of received signal modulation in thepresence of channel noise in noncooperative communicationis a complex issue Before demodulation of received signalmodulation classification is done Modulation classificationis a technique that allows receiver to become cognizant ofcurrent status of transmitted data and channel Applicationsof modulation classification (MC) are in commercial sector(interference identification spectrummanagement)militarydomain and software defined radio (SDR) If receiversclassify the modulation scheme successfully the SDR can beused as a receiver for modification of demodulation partTheMC has applications also in cognitive radios (CR)

After the detection of received signal and before thedemodulation of received signal modulation classificationprocess is done Modulation classification process involves

two steps the first is feature extraction of the transmittedsignal and the second is classification of the signal based uponfeature extraction In the literature various methods havebeen proposed for classificationidentification of differentmodulation formats [1] Basically automatic modulationclassification process is distributed in two approaches [2] (1)log likelihood function based decision theoretic approach (2)extraction of features based pattern recognition approach

Log likelihood function based decision theoreticapproach has been proposed in [3ndash5] This approach isbasically a function of symbols which are to be transmittedas well as channel parameter The log likelihood functionis calculated under each modulation format (hypothesis)The modulation format which maximizes the likelihoodfunction is the decision The log likelihood function baseddecision algorithms are optimal because they minimize theprobability of error in classification of signal but they arecomputationally complex The log likelihood function based

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 643671 14 pageshttpdxdoiorg1011552014643671

2 The Scientific World Journal

decision theoretic approach requires a priori knowledgeabout the signal The likelihood functions become tussle andhard to implement because of channel conditions Extractionof features based pattern recognition approach is also knownas feature based (FB) approach The decision is made onthe observation of the extracted feature set FB approachis suboptimal method with reasonable computationalcomplexity as compared to log likelihood based algorithmsand also easy to implement [6 7]

In the literature the feature which was extracted fromthe transmitted signal is of many types such as higher ordermoments (HOM) higher order cummulants (HOC) up to8th order (HOM) [1] spectral features (120590ap 120590dp 120590aa 120590af120590fn and 120574max) [8] and cyclic features (spectral coherencefunction cyclic domain profile) [9] In [1 10] authors presentthe automaticmodulation classification algorithmwhich usesHOC for estimation of channel and pattern recognitionno a priori information is required In [11] HOC up to4th order are used for classification of modulations overan AWGN channel The features utilized in [9 12 13]are spectral features (120590ap 120590dp 120590aa 120590af 120590fn and 120574max) andcyclic features (spectral coherence function cyclic domainprofile) A summary of proposed algorithms based on time-frequency analysis wavelet transform higher order statistics(cummulants and moments) cyclo-stationarity propertiesand on spectral properties for modulation classification arein [14]

Themodulation identification of BPSKQPSK 16-PSK 2-16QAM GMSK and MSK modulations schemes under theeffect of noisy channel is considered in [15] using wavelettransform approach and statistical moments as features Theproposed algorithm performs 100 identification at SNRof 10 dB A hierarchical cyclostationary based algorithm isproposed to identify the wide range of unknown modulatedsignals presented in [16] The authors also assume no apriori information such as carrier frequency and carrierphase The modulation formats to be classified are AMBPSK OFDM CDMA 4ndash8 ASK 2ndash16 PSK 16 and 64 QAMmodulation formatsThe performance of proposed algorithmis investigated on fading channels The proposed algorithmin [17] uses higher order moments of continuous wavelettransform (CWT) as a feature set The classifier used ismultilayer feed forward neural network using resilient backpropagation algorithm The modulation formats consideredare M-ary shift keying without any priori information Theperformance of algorithm is evaluated on AWGN channelas well as fading channels In [18] FSK and AM signals arejointly detected and classified using first order cyclostation-arity The algorithm only requires approximate informationabout signal band width and carrier frequency and there isno need for time recovery in the proposed algorithm In[19] features are extracted based upon autocorrelation andcyclic autocorrelation for cyclic prefix guard time intervalOFDM signals to estimate the useful time interval the cyclicprefix duration and the number of subcarriers in frequencyselective channels Authors use time frequency analysis toextract features in [20] These extracted features are usedfor classification purpose The proposed algorithm has threemain tools a TF tool which computes the TF transform

extraction of features which gives main characteristics ofsignal and classifier part which discriminates with the help offeaturesThemodulation classification for the wireless sensornetworks is carried out in [21] usingmultisensor fusion basedmethod The classification performance is investigated onAWGN channel and fading channelThe a priori informationabout the signal such as timing synchronization phase jitterphase offset and frequency offset is considered for evalu-ation of correct classification The first signal classificationis done using 2nd 4th and 6th order cummulants andthen kernel thought is used to map the feature to higherdimensional space and optimum hyper plane is constructedusing SVM to classify the signals in [22] The classifier basedon back propagation neural network (BPNN) and trained byimproved particle swarm optimization (PSO) which is usedto optimal weights and threshold for BPNN is proposed in[23] The recognized modulation formats are 2ASK 4ASK2FSK 4FSK BPSK and QPSK The classifier designed forspace time block codes (STBC) system using multidimen-sional independent component analysis (ICA) is proposedin [24] The classifier is also based on maximum likelihoodon the condition of virtual channel matrix The featuresextracted for modulation identification are received signalpower distribution in [25] The classifier identifies only sixmodulation formats Higher order cummulants up to 4th and6th order are used to classify the modulation formats such asBPSK QPSK and higher order QAMrsquos [26] Cyclostationaryfeatures are also used to classify the BPSK and non-BPSK atlastmaximum likelihood detection algorithm is performed tofurther classification of QPSK and 16-QAMThe modulationclassification is done without having any information aboutnoise power energy of the transmitted signal and channelcoefficients [27] The modulation classification is carried outby minimizing the distance of log likelihood and expectedlog likelihood of the received data Modulation classificationis considered on frequency selective fading channel usingGibbs sampling method based on latent Dirichlet Bayesiannetwork in [28] Blind modulation classification problem isconsidered under the effect on frequency selective fadingchannels in [29] The features used for classification arecorrelation function of the received signal The modulationrecognition focuses on pattern recognitionmethod proposedin [30] the main purpose is to demonstrate the possibility ofrecognizing digital modulation formats at lower SNRs Themethod of modulation classification involves computationof the empirical characteristics function (ECF) from thereceived signal samples and employing constrained leastsquares (CLS) filtering in frequency domain [31]

For signal classification and representations adaptivetime frequency analysis including wavelet based filter bank[32] and Gabor based filter banks were used in [33 34]Recently in [35] authors proposed a Gabor atom basedupon neural network (GNN) for feature extraction andsignal classification Efficient feature extraction and higherrecognition rate have been achieved using GNN HoweverGNN consists of two layers the first layer is feature extractionand the second layer is of signal classification Using degreeof non-stationarity the Gabor filter is proposed in [36] forefficient classification

The Scientific World Journal 3

In this paper the authors have proposed joint approachfor feature extraction and classification formultisignal vectorGabor filter based approach is used to classify the digitalmodulated signal in the presence of AWGN channel TheGabor filter parameters are adjusted adaptively using theDelta ruleTheweights of the adaptive filter are adjusted usingleast mean square (LMS) algorithm The digital modulationsconsidered in this paper are PSK2 PSK4 PSK8 PSK16PSK32 PSK64 FSK2 FSK4 FSK8 FSK16 FSK32 FSK64QAM2 QAM4 QAM8 QAM 16 QAM 32 and QAM 64The proposed algorithm gives high classification accuracy atlower SNRs The mean square error (MSE) for training ofGabor filter network versus number of iterations as well asversus SNR for considered modulations is also shown Thesimulation results for testing of proposed algorithm showhigh classification accuracy

The rest of the paper is organized as follows Section 2represents the system model Section 3 represents the Gaborfilter for classification and feature extraction In Section 4Gabor filter training and testing algorithm is presentedSection 5 discusses the performance of proposed classifier inthe presence of AWGN while the whole paper is concludedin Section 5

2 System Model

The generalized expression for signal received is given by

119903 (119899) = 119909 (119899) + 119892 (119899) (1)

where 119903(119899) is complex baseband envelop of received signal119892(119899) is the additive white Gaussian noise with zero mean anda variance of 120590119892

2 and 119909(119899) is given by

119909 (119899) = 120572119890119894(119908119900119899119879+120579119899)

119895=infin

sum119895=minusinfin

119909 (119897) ℎ (119899120591 minus 119895120591 + 120598119879120591) (2)

where 119909(119897) = input symbol sequence which is drawn from setof119872 constellations of known symbols and it is not necessarythat symbols are equiprobable 120572 = amplitude of signal 119908119900 =angular frequency offset constant 120591 = symbol spacing 120579119899 =the phase jitter which varies from symbol to symbol ℎ(sdot sdot sdot ) =channel effects and 120598119879 = the timing jitter

The systemmodel for classification of modulation signalsis shown in Figure 1 First feature extracted from the receivedsignal which is corrupted by additive white Gaussian noiseafter extraction of these features the classification is basedupon the feature extracted The received signal may be PSKFSK or QAMmodulated

3 Gabor Filter for Classification andFeature Extraction

Gabor atom is efficient tool for feature extractionThe Gaboratom in simple form can be written as

119892119888120590119891 (119905) =1

radic120590119892(

119905 minus 119888

120590) 119890119895119891119905 (3)

Signal preprocessing

Feature extraction

Classification rule

PSK

FSK

QAM

2 to 64

2 to 64

4 to 64

Figure 1 System model for modulation classification

X

x1x2

x3x4

g1

g2

g3g4

gMxM

w1w2w3w4

wM

120593i = xigi

yk =M

sumi=1

120593iwi

d

ek

Seria

l to

para

llel c

onve

rsio

n (S

TP)

Input signal

Figure 2 Gabor filter network with input layer which is featureextraction part weights and output layer are linear classificationpart

where 119892(119905) = 214119890minus1205871199052

and 119888 120590 and 119891 are shift parameterscale parameter and modulation parameter respectively

In Figure 2 Gabor filter network is shownwhich has two-layer filter The input to Gabor filter network is first serial toparallel converted 119909119894 119894 = 1 2 3 119872 and outputs are 119910119896119896 = 1 2 3 119873 Let 119892119894 119894 = 1 2 3 119872 be the 119894th classGabor atom and be defined as

119892119894 (119905) =1

radic120590119894119892(

119905 minus 119888119894

120590119894) 119890119895119891119894119905 (4)

The Gabor atom parameters (119888 120590 and 119891) are required to beadjusted until some cost function is minimized

The input layer has119872 nodes 1205931 1205932 1205933 120593119872 also calledGabor nodes The output of the 119894th Gabor atom node is 120593119894corresponding to input signal 119909119894 Thus output of Gabor atomis defined as

120593119894 =1003816100381610038161003816⟨119892119894 119909119894⟩

1003816100381610038161003816

120593119894 =

100381610038161003816100381610038161003816100381610038161003816int

1

radic120590119894119892lowast(119905 minus 119888119894

120590119894) 119890minus119895119891119894119905119909119894 (119905) 119889119905

100381610038161003816100381610038161003816100381610038161003816

(5)

The output layer consists of 119873 nodes 119910119896 119896 = 1 2 3 119872

and for convenience 119873 is usually set to 1 The output of theGabor atom node 120593119894 in the input layer is weighted by 119908119894 thatis

119910119896119899 =

119872

sum119894=1

120593119894119899119908119894119899 119899 = 1 2 3 119873 (6)

Gabor filter network consists of two layers the input layeris feature extraction and the second layer has Gabor filterweights which constitutes the linear classification part


X

Min

Input signal

Gabor 1

Gabor 2

Gabor 3

Gabor P

Figure 3 Testing scheme for modulation classification

Feature extraction using Gabor filter network is that bothGabor atom parameters and Gabor filter weights are adjustedtominimize the sum of squared errorThe difference betweenthe desired outputs 119889119896 and actual output of Gabor filter 119910119896 isdefined as

119890119896= 119889119896 minus 119910119896 (7)

In [35] the Gabor atom parameters and neural networkweights are adjusted simultaneously in training phase Sucha joint updating of Gabor atom parameters and neuralnetworks weights show some deficiencies These deficiencieswill cope when Gabor atom parameters and neural networksweights are adjusted separately [36]

In training phase of modulation classification the twoadaptive algorithms are performed by Gabor filter network(1) the updating of Gabor atom parameters (119888 120590 and 119891) (2)for given set of Gabor atom parameters algorithm updatesthe weight of Gabor filter

In testing phase shown in Figure 3 the modulated signalmay be PSK 2 to 64 FSK 2 to 64 and QAM 2 to 64 Themodulated signal is passed through Gabor filter networkthat updates 4 parameters (119888 120590 119891 and 119908) and based uponthese parameters error is calculated The minimum errorcorresponds to decision about the receive signal modulation

4 Testing and Training of Proposed Algorithm

The training of Gabor filter network is partitioned into twophases training of Gabor atom parameters (119888 120590 119891 and 119908)in the first phase and training the weights of adaptive filterin second phase The parameters of Gabor atom parameters(119888 120590 119891 119908) are tuned according to Delta rule and weights ofadaptive filter are adjusted by least means square algorithm

Let 120574119894 denote one of 119894th Gabor node parameters includingshift parameter 119888119894 scale parameter120590119894 andmodulation param-eter 119891119894 According to Delta rule

Δ120574119894 = minus120578120597119869 (119896)

120597120574119894 (8)

where 120578 is learning rateThe cost function is square of difference between desired

response and output of Gabor function that is

119869 (119896) = (119889 (119896) minus 119910 (119896))2 (9)

The partial derivatives of cost function with respect to shiftparameter 119888119894 scale parameter 120590119894 and modulation para +meter 119891119894 are as follows

Δ119888119894 = 119888119894 (119899 + 1) minus 119888119894 (119899) (10)

= minus120578119888

2

120597119869 (119896)

120597119888119894

= minus120578119888

2[120597119869 (119896)

120597120593119894

120597120593119894

120597119888119894]

(11)

Δ120590119894 = 120590119894 (119899 + 1) minus 120590119894 (119899) (12)

= minus120578120590

2

120597119869 (119896)

120597120590119894

= minus120578120590

2[120597119869 (119896)

120597120593119894

120597120593119894

120597120590119894]

(13)

Δ119891119894= 119891119894 (119899 + 1) minus 119891119894 (119899) (14)

= minus120578119891

2

120597119869 (119896)

120597119891119894

= minus120578119891

2[120597119869 (119896)

120597120593119894

120597120593119894

120597119891119894]

(15)

From (9)

120597119869 (119896)

120597120593119894=

120597

120597120593119894[(119889 (119896) minus 119910 (119896))

2]

120597119869 (119896)

120597120593119894= 2 [119889 (119896) minus 119910 (119896)]

120597

120597120593119894(119889 (119896) minus 119910 (119896))

120597119869 (119896)

120597120593119894= minus 2 [119889 (119896) minus 119910 (119896)]

120597

120597120593119894(119910 (119896))

(16)

From (6)

120597

120597120593119894(119910 (119896)) =

120597

120597120593119894

[

[

119872

sum119895=1

120593119895119908119895]

]

120597

120597120593119894(119910 (119896)) =

119872

sum119895=1

120575119894119895119908119895

120597

120597120593119894(119910 (119896)) = 119908119894

(17)

Putting (17) into (16) we get

120597119869 (119896)

120597120593119894= minus2(119889 (119896) minus 119910 (119896)) 119908

119894 (18)


From (11) (13) and (15)

Δ119888119894 = 120578119888(119889 (119896) minus 119910 (119896)) 119908119894120597120593119894

120597119888119894

Δ120590119894 = [120578120590(119889 (119896) minus 119910 (119896)) 119908119894]120597120593119894

120597120590119894

Δ119891119894= [120578119891(119889 (119896) minus 119910 (119896)) 119908119894]

120597120593119894

120597119891119894

119892119894 =1

radic120590119894119890minus120587((119905minus119888

119894)120590119894)2

cos (119891119894119905)

(19)

From (5)

120593119894 =

100381610038161003816100381610038161003816100381610038161003816119909119894

1


119894)120590119894)2

cos (119891119894119905)100381610038161003816100381610038161003816100381610038161003816 (20)

For real valued signals Gabor atom is also real in such caseThe partial derivatives of 120593119894 with respect to shift parame-

ter 119888119894 scale parameter 120590119894 and modulation parameter 119891119894 are asfollows

120597120593119894

120597119888119894=

120597

120597119888119894(119909119894119892119894)

=120597

120597119888119894[119909119894

1


119894)120590119894)2

cos (119891119894119905)]

=119909119894

radic120590119894cos (119891119894119905)

times [119890minus120587((119905minus119888

119894)120590119894)2

times minus120587(2(119905 minus 119888119894

120590119894))(minus

1

120590119894)]

=119909119894

radic120590119894cos (119891119894119905) [119890

minus120587((119905minus119888119894)120590119894)2

(2120587(119905 minus 119888119894

1205901198942))]

=1199091198945radic120590119894

cos (119891119894119905) 2120587 (119905 minus 119888119894) 119890minus120587((119905minus119888

119894)120590119894)2

120597120593119894

120597120590119894=

120597

120597120590119894[119909119894

1


119894)120590119894)2

cos (119891119894119905)]

= 119909119894 cos (119891119894119905)

times [1


119894)120590119894)2


120590119894))

times (minus(119905 minus 119888119894)

1205901198942

) + 119890minus120587((119905minus119888

119894)120590119894)2

times minus1

2120590119894minus32

]

=119909119894 cos (119891119894119905)


119894)120590119894)2

[2120587 (119905 minus 119888119894)

2

1205901198943

minus1

2120590119894]

120597120593119894

120597119891119894=

120597

120597119891119894[119909119894

1


119894)120590119894)2

cos (119891119894119905)]

= minus119905


119894)120590119894)2

sin (119891119894119905)

(21)

The Updating of Gabor atom parameters (shift parameter 119888119894scale parameter 120590119894 and modulation parameter 119891119894) accordingto Delta rule is as follows

Δ119888119894 = 120578119888(119889 (119896) minus 119910 (119896)) 119908119894

times [1199091198945radic120590119894


119894)120590119894)2

] (22)

119888119894 (119899 + 1) = 119888119894 (119899) + 120578119888(119889 (119896) minus 119910 (119896)) 119908119894

times [1199091198945radic120590119894


119894)120590119894)2

] (23)

Δ120590119894 = [120578120590(119889 (119896) minus 119910 (119896)) 119908119894]

times 119909119894 cos (119891119894119905)


119894)120590119894)2

times [2120587 (119905 minus 119888119894)

2

1205901198943

minus1

2120590119894]

(24)

120590119894 (119899 + 1) = 120590119894 (119899) + [120578120590(119889 (119896) minus 119910 (119896)) 119908119894]

times 119909119894 cos (119891119894119905)


119894)120590119894)2

times [2120587 (119905 minus 119888119894)

2

1205901198943

minus1

2120590119894]

(25)

Δ119891119894= [120578119891(119889 (119896) minus 119910 (119896)) 119908119894]

times minus119905


119894)120590119894)2

sin (119891119894119905) (26)

119891119894 (119899 + 1) = 119891119894 (119899) + [120578119891(119889 (119896) minus 119910 (119896)) 119908119894]

times minus119905


119894)120590119894)2

sin (119891119894119905) (27)

Equations (23) (25) and (27) show the updated shift param-eter scale parameter and modulation parameter of Gaborfilter network

The weights of adaptive filter are updated as follows

Δ119908119894 = 119908119894 (119899 + 1) minus 119908119894 (119899) (28)

= minus120578119908

2

120597119869 (119896)

120597119908119894

= minus120578119908

2

120597

120597119908119894[(119889 (119896) minus 119910 (119896))

2]

=120578119908

22 (119889 (119896) minus 119910 (119896))

120597

120597119908119894119910 (119896)


Step 1 Initialization of Gabor atom parameters (shift parameter 119888119894 scale parameter 120590

119894and modulation parameter 119891

119894)

and weights of Gabor filter (119908119894)

Step 2 Calculate the Gabor atom using (4) and using (20) compute all Gabor atom nodesStep 3 The Gabor atoms node (120593

119894) are now input to the Adaptive filter and adjust the weights of the adaptive filter

using LMS (28)ndash(32)Step 4 Evaluate error which is defined in (7) If error is less than chosen threshold then training of algorithm is stopped

and save Gabor atom parameters (119888119894 120590119894 119891119894) and Gabor filter weights (119908

119894)

Step 5 If error is not less than threshold repeat Step 3 by using the error calculated in Step 4Step 6 Tune the Gabor atom parameters (119888

119894 120590119894 119891119894) using (8) (23) (25) and (27)

Step 7 Save Gabor atom parameters (119888119894 120590119894 119891119894) and Gabor filter weights (119908

119894)

Algorithm 1 (Training of Gabor filter Network for Modulation Classification)

Step 1 Input Gabor atom parameters (119888119894 120590119894 119891119894) and Gabor filter weights (119908

119894)

Step 2 Calculate the Gabor atom nodes (120593119894)

Step 3 Evaluate the output of Gabor filter

119910119896=

119872

sum119894=1

120593119894119908119894

Step 4 Decision based upon checking all the outputs

Algorithm 2 (Testing of Gabor filter Network for Modulation Classification)

= 120578119908 (119889 (119896) minus 119910 (119896))120597

120597119908119894119910 (119896)

(29)

120597119910 (119896)

120597119908119894=

120597

120597119908119894

[

[

119872

sum119895=1

120593119895119908119895]

]

= 120593119894 (30)

Substituting (30) in (28) we get

Δ119908119894 = 120578119908 (119889 (119896) minus 119910 (119896)) 120593119894 (31)

From (28)

119908119894 (119899 + 1) = 119908119894 (119899) + 120578119908 (119889 (119896) minus 119910 (119896)) 120593119894 (32)

Equation (32) shows the weight updating of the adaptive filterusing least mean square algorithm

The proposed algorithm is for feature extraction andclassification of modulation formats (PSK 2 to 64 FSK 2to 64 and QAM 2 to 64) under the influence of AWGNchannel The proposed algorithm is divided in to two phasesthe first phase is for the training of Gabor filter network Intraining phase the parameters of Gabor filter network (shiftscale and modulation) are updated according to delta ruleThese parameters are now input to the adaptive filter whereweights of adaptive filter are adjusted using least mean squarealgorithm The error is now calculated if error is less thanthe threshold training process stops otherwise update theGabor filter parameters and weights of the adaptive filteraccording to Delta rule and LMS algorithm until the error

function is minimized The second phase is the test phaseof the algorithm where input modulated signal is fed to thetrained Gabor filter network The parameters of Gabor filternetwork and weights of the adaptive filter are updated anderror is calculated The minimum error corresponds to thedesired modulation format

The proposed algorithm for training and testing of Gaborfilter network for the problem of modulation classification ispresented as shown in Algorithms 1 and 2

5 Simulation Results

The modulation classification using Gabor filter is evaluatedin this section Firstly the training of algorithm is presentedand then the testing of algorithm in the presence of AWGNchannelThe probability of correct classification (PCC) in thepresence of AWGN channel is simulated here using Gaborfilter network The modulation schemes considered here aredivided in three scenarios that is PSK2 PSK4 PSK8 PSK16PSK 32 and PSK64 FSK2 FSK4 FSK8 FSK16 FSK 32 andFSK64 and QAM2 QAM4 QAM8 QAM16 QAM32 andQAM64 The PCC curves are simulated against number ofiterations and SNR for three different modulation scenarios

Tables 1ndash3 and Figures 4ndash9 show the training of Gaborfilter network for the considered modulation formats (PSKFSK and QAM) up to order 2 to 64 The Gabor filter net-work parameters (shift scale and modulation) are updatedaccording to each of which considered modulation formatsusing delta rule and also weights are updated for eachconsidered modulation format case using least mean square


Table 1 Updated Gabor filter atom parameters and weights for PSKmodulation 2ndash64

Shift parameter (119888)PSK2 PSK4 PSK8 PSK16 PSK32 PSK64554 507 577 565 481 527577 590 425 445 418 429469 424 433 520 456 556463 472 483 417 467 456502 429 500 408 513 459503 518 568 589 523 479516 509 589 491 579 463461 467 552 591 435 447448 459 513 562 561 447543 514 513 494 415 475

Scale parameter (120590)PSK2 PSK4 PSK8 PSK16 PSK32 PSK641563 1625 1025 1676 167 2451603 857 817 518 1353 16211487 1408 255 1887 678 533192 1827 1231 663 1333 466644 316 1189 1848 938 5941332 317 480 685 1190 2501149 1294 1283 1533 744 15291439 333 733 758 603 5211904 1423 739 513 1800 1281867 294 848 105 1256 259

Modulation parameter (119891)PSK2 PSK4 PSK8 PSK16 PSK32 PSK64235 minus005 080 314 minus053 182minus272 minus056 minus037 minus053 290 minus302191 252 minus190 095 minus133 minus224minus102 010 minus155 146 247 038173 108 183 151 minus075 minus189minus275 minus183 minus257 minus142 266 110047 020 minus279 minus221 054 minus157032 011 minus093 minus156 minus094 minus055188 033 minus259 031 minus128 068minus076 minus227 007 283 minus101 minus170

Weights (119908)PSK2 PSK4 PSK8 PSK16 PSK32 PSK645059 minus2625 minus0747 minus0119 0837 minus4310minus1823 minus1927 0671 0297 1309 minus30736844 minus2482 minus0533 minus0371 minus3033 83331847 2528 0499 minus0356 minus0894 minus38025384 minus0090 0677 minus0346 minus1484 14138671 1923 0256 minus0917 minus0843 38870058 minus2857 minus0703 minus0455 0449 minus1762minus1356 1852 minus0555 minus0487 minus1844 26821899 1055 0481 minus1498 0844 minus3901minus3603 minus2714 0402 minus0664 1832 2549

algorithmTheGabor atom parameters and weights of Gaborfilter (119888119894 120590119894 119891119894 and 119908119894) for the considered modulations are

Table 2 Updated Gabor filter atom parameters and weights for FSKmodulation 2ndash64

Shift parameter (119888)FSK2 FSK4 FSK8 FSK16 FSK32 FSK64425 436 535 467 574 422409 488 580 420 455 593458 459 554 594 401 589550 581 571 535 557 525446 555 460 583 459 596536 493 428 401 550 589427 449 416 431 515 595438 528 475 570 576 540435 503 441 504 539 477438 429 558 597 531 584

Scale parameter (120590)FSK2 FSK4 FSK8 FSK16 FSK32 FSK64444 646 680 1724 1965 12271422 253 357 373 625 1922211 802 1544 1010 1767 686589 1094 475 1142 403 6931921 230 1189 210 677 19961944 278 1426 546 412 14041774 484 1182 1050 396 587137 667 1098 1724 1769 5871953 1599 1396 873 1991 3741267 357 145 1457 365 1959

Modulation parameter (119891)FSK2 FSK4 FSK8 FSK16 FSK32 FSK64minus015 minus297 287 164 242 minus170115 277 084 076 minus148 minus207122 182 269 minus254 minus123 minus084minus150 291 minus067 237 077 310287 194 minus099 minus295 016 045066 208 229 004 minus300 minus256minus245 minus072 218 minus143 minus185 041019 287 minus123 259 205 minus109minus044 169 minus104 minus230 069 034255 minus076 141 minus180 079 minus054

Weights (119908)FSK2 FSK4 FSK8 FSK16 FSK32 FSK64minus2579 minus7096 0931 0124 minus0318 8540minus0490 minus0572 minus1195 minus0239 minus1668 5174minus1532 minus3564 minus1195 3627 4663 minus15706719 minus5807 minus1110 minus0984 minus2764 0566minus9317 4059 minus0083 minus0283 0840 minus2799minus8051 minus2456 0068 0990 3381 minus16280012 3768 0443 0242 4211 12898minus12209 1989 minus1487 1298 minus1675 minus62708351 5954 minus1451 minus0296 minus4969 4876minus4070 minus0026 0402 1027 minus5423 minus8421

stored The updated Gabor atom parameters and weightsof Gabor filter (119888119894 120590119894 119891119894 and 119908119894) are shown in Tables 1ndash3


Table 3 Updated Gabor filter atom parameters and weights forQAM 2ndash64

Shift parameter (119888)QAM2 QAM4 QAM8 QAM16 QAM32 QAM64554 507 577 565 481 527577 590 425 445 418 429469 424 433 520 456 556463 472 483 417 467 456502 429 500 408 513 459503 518 568 589 523 479516 509 589 491 579 463461 467 552 591 435 447448 459 513 562 561 447543 514 513 494 415 475

Scale parameter (120590)QAM2 QAM4 QAM8 QAM16 QAM32 QAM641563 1625 1025 1676 167 2451603 857 817 518 1353 16211487 1408 255 1887 678 533192 1827 1231 663 1333 466644 316 1189 1848 938 5941332 317 480 685 1190 2501149 1294 1283 1533 744 15291439 333 733 758 603 5211904 1423 739 513 1800 1281867 294 848 105 1256 259

Modulation parameter (119891)QAM2 QAM4 QAM8 QAM16 QAM32 QAM64235 minus005 080 314 minus053 182minus272 minus056 minus037 minus053 290 minus302191 252 minus190 095 minus133 minus224minus102 010 minus155 146 247 038173 108 183 151 minus075 minus189minus275 minus183 minus257 minus142 266 110047 020 minus279 minus221 054 minus157032 011 minus093 minus156 minus094 minus055188 033 minus259 031 minus128 068minus076 minus227 007 283 minus101 minus170

Weights (119908)QAM2 QAM4 QAM8 QAM16 QAM32 QAM64minus0031 minus0504 1009 minus1428 minus1095 0339minus0021 minus0446 minus0796 minus1339 minus0559 minus0835minus0043 minus0187 minus0285 minus0725 0304 04420194 0794 0299 minus1122 1359 minus05580354 1061 0664 minus0476 minus1109 05060250 minus0591 minus0306 0044 minus1357 minus02340097 minus0622 minus0380 1193 0290 00220007 0247 minus0769 minus0316 0624 minus01770245 0467 minus0608 0984 minus0334 06940046 minus0117 0536 0552 minus0294 0423

Figures 4ndash6 show the training of Gabor filter network fordifferent number of iterations in case of PSKmodulation FSK

modulation and QAM respectively The training process fordifferent SNRs is also shown in Figures 7ndash9 The trainingshows that the mean square error dies down as the numberof iterations is increased and also by increasing the SNRFigures 10ndash15 show the testing of Gabor filter network for theconsidered modulations formats (PSK 2 to 64 FSK 2 to 64and QAM 2 to 64) in the presence of AWGN channel Theprobability of correctness is plotted against signal to noiseratio (SNR) and different number of iterations to evaluate theclassification accuracy of the proposed Gabor filter networkThe simulations results show the classification accuracy forthe examples of PSK4 FSK16 and QAM32 which are 100for fixed SNR and different number of iterations

Table 1 shows the updated Gabor atom parameters for themodulation formats of PSK of order 2 to 64 Table 1 has fourparts the first part shows the updated scale parameter for PSK2 to 64 the second part shows the updated shift parameterthe third part shows the updated modulation parameter andthe forth part shows the updated weights of the adaptive filterAll values of updated Gabor filter parameters and weights ofadaptive filter are for minimummean square error

Table 2 shows the updatedGabor atomparameters for themodulation formats of FSK of order 2 to 64 Table 2 has fourparts the first part shows the updated scale parameter for FSK2 to 64 the second part shows the updated shift parameterthe third part shows the updated modulation parameter andthe forth part shows the updated weights of the adaptive filterAll values of updated Gabor filter parameters and weights ofadaptive filter are for minimummean square error

Table 3 shows the updatedGabor atomparameters for themodulation formats of QAM of order 2 to 64 Table 3 hasfour parts the first part shows the updated scale parameterfor QAM 2 to 64 the second part shows the updated shiftparameter the third part shows the updated modulationparameter and the forth part shows the updated weightsof the adaptive filter All values of updated Gabor filterparameters and weights of adaptive filter are for minimummean square error

Figure 4 shows the training of Gabor filter network forthe case of PSK modulation format having order 2 to 64for different number of iterations at fixed SNR of 10 dB Theparameters of Gabor filter network are trained for greaterthan 50 iterations for the case of PSK 2 4 and 8 while for thePSK 16 32 and 64 the training of Gabor filter network is forless than 50 iterations The mean square error is minimizedand approaches to zero for all curves shown in Figure 4 as anumber of iterations are increased

Figure 5 shows the Gabor filter network training for thecase of FSK modulation format having order 2 to 64 for fixednumber of iterations As shown in Figure 5 the mean squareerror is approaching to zero when a number of iterations areincreased The training of Gabor filter network is done formaximum 50 iterations for the FSK modulation case

Figure 6 shows the training of Gabor filter network forQAM case with fixed SNR of 10 dB and different iterationsThe training of Gabor filter network shows minimized meansquare error for all curves shown in Figure 6with less numberof iterations In Figure 6 QAM 16 32 and 64 are trained for


4

3

2

1

00 50 100 150 200 250

Number of iterations

Mea

n sq

uare

erro

rM

ean

squa

re er

ror

0 50 100 150 200 250


6

5

4

3

2

1

00 50 100 150 200 250


10

8

6

4

2

0

0 50 100 150 200 250


6

5

4

3

2

1

00 50 100 150 200 250


20

15

10

5

00 50 100 150 200 250


20

15

10

5

0

PSK2 PSK4 PSK8

PSK16 PSK32 PSK64

Figure 4 Training of Gabor filter parameters and weights for modulation classification in case of PSKmodulation 2ndash64 for different numberof iterations at SNR = 10 dB

08

06

04

02

0

08

06

04

02

0

0 50 100 150 200 250


0 50 100 150 200 250

Number of iterations0 50 100 150 200 250


0 50 100 150 200 250



Mea

n sq

uare

erro

rM

ean

squa

re er

ror

0 50 100 150 200 250


1

08

06

04

02

0

2

15

1

05

0

1

08

06

04

02

0

2

15

1

05

0

FSK2 FSK4 FSK8

FSK16 FSK32 FSK64

Figure 5 Training of Gabor filter parameters and weights for modulation classification in case of FSKmodulation 2ndash64 for different numberof iterations at SNR = 10 dB

20 iterations and QAM 2 4 and 8 are trained for above 50iterations

Figure 7 shows the training of Gabor filter networkparameters and weights of adaptive filter in case of PSKmod-ulation up to order 2 to 64with fixed number of iterations anddifferent SNRs As signal to noise ratio is varied from 0 to 20themean square error approaching towards zeroThe trainingof proposed algorithm for all cases of considered modulationis done successfully and Figure 7 shows that the proposed

algorithm for the modulation classification is trained at SNRof 10 dB

Figure 8 shows the training of Gabor filter networkparameters and weights of adaptive filter in case of FSKmod-ulation up to order 2 to 64 with fixed number of iterationsand different SNRs The training of FSK modulation formatsis done at SNR of 10ndash15 dB

The training of Gabor filter network for QAM 2 to 64 atdifferent SNRs and fixed number of iterations is shown in


10

8

6

4

2

0

8

6

4

2

0

8

6

4

2

0

30

25

20

15

10

5

0

25

20

15

10

5

0

8

6

4

2

00 50 100 150 200 250




0 50 100 150 200 250




Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64

Figure 6 Training ofGabor filter parameters andweights formodulation classification in case ofQAM2ndash64 for different number of iterationsat SNR = 10 dB

04

03

02

01

0

08

06

04

02

0

25

2

15

1

05

0

5

4

3

2

1

0

10

8

6

4

2

0

15

10

5

0

SNRminus10 minus5 0 5 10 15 20





FSK2 FSK4 FSK8


FSK16 FSK32 FSK64

Mea

n sq

uare

erro

rM

ean

squa

re er

ror

Figure 7 Training of Gabor filter parameters and weights for modulation classification in case of PSK modulation 2ndash64 at different SNRsand fixed number of iterations

Figure 9The parameters of Gabor filter network and weightsof the adaptive filter are updated and mean square error isminimized as SNR is increased from 0 to 20 dB

The example considered in Figures 10 and 11 is PSK4The probability of correctness versus different number ofiterations at SNR = 10 dB is shown in Figure 10 while PCCcurve versus SNR at fixed number of iterations is shown inFigure 11 The PCC in Figure 10 is approximately 1 when thenumber of iterations is increased up to 200 From Figures 10and 11 the classification performance of Gabor filter networkfor the PSK modulation scenario under the effect of white

Gaussian noise channel is approximately 100 at lower SNRIn Figures 10 and 11 the example considered are PSK4 and it isshown form the results that PSK4 classified correctly amongclass of PSK modulation formats having order 2 to 64

In Figures 12 and 13 the probability of correctness forFSK modulation scenario is shown for different numberof iterations and SNR The example considered is FSK16The PCC curve shows that the classification performanceis approximately 100 at SNR = 15 dB for fixed number ofiterations The probability of correctness is approximately 1in Figure 12 when a number of iterations are increased up to


04

03

02

01

0Mea

n sq

uare

erro

rM

ean

squa

re er

ror







25

2

15

1

05

0

8

6

4

2

0

12

10

8

6

4

2

0

1

08

06

04

02

0

6

5

4

3

2

1

0

FSK2 FSK4 FSK8

FSK16 FSK32 FSK64

Figure 8 Training of Gabor filter parameters and weights for modulation classification in case of FSK modulation 2ndash64 at different SNRsand fixed number of iterations

02

015

01

005

0

04

03

02

01

0

08

06

04

02

0

04

03

02

01

0

05

04

03

02

01

0

08

06

04

02

0







Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64

Figure 9 Training of Gabor filter parameters and weights for modulation classification in case of QAM 2ndash64 at different SNRs and fixednumber of iterations

10908070605040302010

20 40 60 80 100 120 140 160 180 200


Prob

abili

ty o

f cor

rect

ness

(PCC

) Probability of correctness in PSK modulation classification

Figure 10 Probability of correctness (PCC) versus number of iterations at SNR = 10 dB for PSK4 example


1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)minus10 minus5 0 5 10 15 20

SNR (dB)

Probability of correctness in case of PSK

Figure 11 Probability of correctness (PCC) versus SNR for fixed number of iterations in PSK4 example

1

09

08

07

06

05

04

Prob

abili

ty o

f cor

rect

ness

(PCC

)

200 40 60 80 100 120 140 160 180 200


Probability of correctness in case of FSK modulation

Figure 12 Probability of correctness (PCC) versus number of iterations at SNR = 10 dB for FSK16 example

1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)

SNR (dB)minus10 minus5 0 5 10 15 20

Probability of correctness in case of FSK

Figure 13 Probability of correctness (PCC) versus SNR for fixed number of iterations in FSK16 example

200 The FSK 16 example is classified accurately among thegroup of considered modulation formats

In Figures 14 and 15 the example considered is QAM32for classification purposeThe classification curve in the formof PCC versus different number of iterations at fixed SNR of10 dB is shown in Figure 14 while in Figure 15 PCC curvesversus SNR at fixed number of iterations are shown Theclassification of Gabor filter network in case of QAM is quitebetter with the existing modulation classification techniques

The simulation results show the 100 classification accu-racy of the proposed algorithm The features extracted fromthe proposed architecture and classifier based upon Gaborfilter network provide correct classification among group

of considered modulation formats Moreover the receivedsignal is corrupted by additive white Gaussian noise butthe classification accuracy is approximately 100 at lowerSNRsThe algorithm is also computationally less complex andclassification accuracy is attained at less number of iterations

6 Conclusion

In this paper proposed classifier which is Gabor filter basedis used for feature extraction and also for the classificationpurpose The Gabor filter input layer constitutes the featureextraction part (119888119894 120590119894 and 119891119894) whereas weights (119908119894) between


1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)0 20 40 60 80 100 120 140 160 180 200


Probability of correctness in case of QAM

Figure 14 Probability of correctness (PCC) versus number of iterations at SNR = 10 dB for QAM32 example


Probability of correctness in case of QAM1

09

08

07

06

05

04

03

02Prob

abili

ty o

f cor

rect

ness

(PCC

)

Figure 15 Probability of correctness (PCC) versus SNR for fixednumber of iterations in QAM32 example

Gabor atom nodes and output of the Gabor filter constitutethe linear classification part The feature extraction layerand classification part search for the optimal Gabor atomparameters and weights of the Gabor filter so that erroris to be minimized The considered modulations such asPSK2 PSK4 PSK8 PSK16 PSK32 PSK64 QAM2 QAM4QAM8 QAM 16 QAM 32 QAM 64 FSK2 FSK4 FSK8FSK16 FSK32 and FSK64 are classified under the effects ofAWGN channel The classifier proposed here is very effectiveperformance in considered scenarios of modulation Theproposed novel Gabor filter based modulation classificationtechnique shows 100 classification accuracy at lower SNR

Conflict of Interests

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

References

[1] S A Ghauri I M Qureshi A N Malik and T A CheemaldquoHigher order cummulants based digital modulation recogni-tion schemerdquo Research Journal of Applied Sciences Engineeringamp Technology vol 6 no 20 pp 3910ndash3915 2013

[2] S A Ghauri and I M Qureshi ldquoAutomatic classification ofdigital modulated signals using linear discriminant analysis

on AWGN channelrdquo in Proceedings of the 1st InternationalConference on Information and Communication TechnologyTrends (ICICTT 13) September 2013

[3] T Yucek and H Arslan ldquoA novel sub-optimum maximum-likelihood modulation classification algorithm for adaptiveOFDM systemsrdquo in Proceedings of the IEEE Wireless Commu-nications and Networking Conference (WCNC rsquo04) vol 2 pp739ndash744 March 2004

[4] P Panagiotou A Anastasopoulos and A Polydoros ldquoLikeli-hood ratio tests for modulation classificationrdquo in Proceedings ofthe 21st Century Military Communications (MILCOM rsquo00) vol2 pp 670ndash674 Los Angeles Calif USA October 2000

[5] W Wei and J M Mendel ldquoMaximum-likelihood classificationfor digital amplitude-phasemodulationsrdquo IEEE Transactions onCommunications vol 48 no 2 pp 189ndash193 2000

[6] P Marchand C Le Martret and J Lacoume ldquoClassificationof linear modulation by a combination of different orderscyclic cumulantsrdquo in Proceedings of the IEEE Signal ProcessingWorkshop on Higher-Order Statistics (SPW-HOS rsquo97) pp 47ndash51July 1997

[7] O A Dobre Y Bar-Ness and W Su ldquoHigher-order cycliccummulants for high order modulation classificationrdquo in Pro-ceedings of the IEEEMilitary Communications Conference (MIL-COM rsquo03) vol 1 pp 112ndash117 Boston Mass USA October 2003

[8] E E Azzouz and A K Nandi ldquoProcedure for automatic recog-nition of analogue and digital modulationrdquo IEE Proceedings-Communications vol 143 no 5 pp 259ndash266 1996

[9] B Ramkumar ldquoAutomatic modulation classification for cogni-tive radios using cyclic feature detectionrdquo IEEE Circuits andSystems Magazine vol 9 no 2 pp 27ndash45 2009

[10] S Xi andHCWu ldquoRobust automaticmodulation classificationusing cumulant features in the presence of fading channelsrdquo inProceedings of the IEEEWireless Communications and Network-ing Conference (WCNC rsquo06) vol 4 pp 2094ndash2099 April 2006

[11] H Wu M Saquib and Z Yun ldquoNovel automatic modulationclassification using cumulant features for communications viamultipath channelsrdquo IEEE Transactions on Wireless Communi-cations vol 7 no 8 pp 3098ndash3105 2008

[12] L Qian and C Zhu ldquoModulation classification based on cyclicspectral features and neural networkrdquo in Proceedings of the 3rdInternational Congress on Image and Signal Processing (CISP rsquo10)pp 3601ndash3605 Yantai China October 2010

[13] M L D Wong and A K Nandi ldquoAutomatic digital modulationrecognition using artificial neural network and genetic algo-rithmrdquo Signal Processing vol 84 no 2 pp 351ndash365 2004


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

[15] P Prakasam andM Madheswaran ldquoDigital modulation identi-fication model using wavelet transform and statistical parame-tersrdquo Journal of Computer Systems Networks and Communica-tions vol 2008 Article ID 175236 8 pages 2008

[16] Z Wu E Like V D Chakravarthy and P Ratazzi ldquoSignalclassification in fading channels using cyclic spectral analysisrdquoEurasip Journal on Wireless Communications and Networkingvol 2009 Article ID 879812 pp 1ndash14 2009

[17] W Hamouda K Hassan I Dayoub and M BerbineauldquoAutomatic modulation recognition using wavelet transformand neural networks in wireless systemsrdquo Eurasip Journal onAdvances in Signal Processing vol 2010 Article ID 532898 2010

[18] O A Dobre S Rajan and R Inkol ldquoJoint signal detection andclassification based on first-order cyclostationarity for cognitiveradiosrdquo Eurasip Journal on Advances in Signal Processing vol2009 Article ID 656719 2009

[19] V Le Nir T Van Waterschoot J Duplicy and M MoonenldquoBlind coarse timing offset estimation for CP-OFDM and ZP-OFDMtransmission over frequency selective channelsrdquoEurasipJournal onWireless Communications and Networking vol 2009Article ID 262813 2009

[20] M Gandetto M Guainazzo and C S Regazzoni ldquoUse of timefrequency analysis and neural networks for mode identificationin a wireless software defined radio approachrdquo EURASIP Jour-nal on Applied Signal Processing pp 1778ndash1790 2014

[21] Y Zhang N Ansari and W Su ldquoMulti-sensor signal fusionbased modulation classification by using wireless sensor net-worksrdquo in Proceedings of the IEEE International Conference onCommunications (ICC rsquo11) pp 1ndash5 Kyoto Japan June 2011

[22] X Zhou Y Wu and B Yang ldquoSignal classification methodbased on SVM and higher order cummulatntsrdquoWireless SensorNetworks vol 2 pp 48ndash52 2010

[23] L Cheng and J Liu ldquoAn optimal neural network classifier forautomaticmodulation recognitionrdquoTELKOMNIKA IndonesianJournal of Electrical Engineering vol 12 no 2 pp 1343ndash13522014

[24] M Luo L Li G Qian and J Lu ldquoA blindmodulation identifica-tion algorithm for STBC systems using multidimensional ICArdquoConcurrency Computation Practice and Experience vol 26 no8 pp 1490ndash1505 2014

[25] J Liu Z Dong K P Zhong et al ldquoModulation formatidentification based on received signal power distributions fordigital coherent reciversrdquo in Proceedings of the Optical FiberConferences pp 9ndash13 2014

[26] J Sanderson X Li Z Q Liu and Z Q Wu ldquoHierarchical blindmodulation classification for underwater acoustic communica-tion signal via cyclostationary andmaximal likelihood analysisrdquoin Proceedings of the IEEEMilitary Communications Conference(MILCOM rsquo13) pp 29ndash34 2013

[27] E Soltan Mohammadi and M Naraghi-Por ldquoBlind modulationclassification over fading channels using expectationmaximiza-tionrdquo IEEE Communication Letters vol 17 no 9 pp 1692ndash16952013

[28] Y Liu O Simeone A M Haimouich and W Su ldquoModulationclassification via Gibbs sampling based on a Latent DirichletBayesian Networkrdquo IEEE Signal Processing Letters vol 21 no9 pp 1135ndash1139 2014

[29] M Marcy and O A Dobre ldquoBlind modulation classificationfor single and multiple antenna system over frequency selectivechannelsrdquo IEEE Signal Processing Letters vol 21 no 9 pp 1098ndash1102 2014

[30] J P Jide ldquoAutomatic recognition of both inter and intra classesof digital modulated signals using artificial neural netowrkrdquoJournal of Engineering Science and Technology vol 9 no 2 pp273ndash285 2014

[31] B Dulek O Ozdemir P K Varshney and W Su ldquoA novelapproach to dictionary construction for automatic modulationclassificationrdquo Journal of the Franklin Institute vol 351 no 5 pp2991ndash3012 2014

[32] J Zhang G G Walter Y Miao and W N W Lee ldquoWaveletneural networks for function learningrdquo IEEE Transactions onSignal Processing vol 43 no 6 pp 1485ndash1497 1995

[33] S Qain and D Chen ldquoJoint time frequency analysisrdquo SignalProcessing Magazine vol 16 pp 52ndash67 1999

[34] T G Sayan K Leblebicioglu and T Ince ldquoElectromagnetictarget classification using time-frequency analysis and neuralnetworksrdquoMicrowave andOptical Technology Letters vol 21 no1 pp 63ndash69 1999

[35] Y Shi and X Zhang ldquoA Gabor atom network for signalclassification with application in radar target recognitionrdquo IEEETransactions on Signal Processing vol 49 no 12 pp 2994ndash30042001

[36] F Zhu X Zhang and Y Hu ldquoGabor filter approach to jointfeature extraction and target recognitionrdquo IEEE Transactions onAerospace and Electronic Systems vol 45 no 1 pp 17ndash30 2009

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decision theoretic approach requires a priori knowledgeabout the signal The likelihood functions become tussle andhard to implement because of channel conditions Extractionof features based pattern recognition approach is also knownas feature based (FB) approach The decision is made onthe observation of the extracted feature set FB approachis suboptimal method with reasonable computationalcomplexity as compared to log likelihood based algorithmsand also easy to implement [6 7]

In the literature the feature which was extracted fromthe transmitted signal is of many types such as higher ordermoments (HOM) higher order cummulants (HOC) up to8th order (HOM) [1] spectral features (120590ap 120590dp 120590aa 120590af120590fn and 120574max) [8] and cyclic features (spectral coherencefunction cyclic domain profile) [9] In [1 10] authors presentthe automaticmodulation classification algorithmwhich usesHOC for estimation of channel and pattern recognitionno a priori information is required In [11] HOC up to4th order are used for classification of modulations overan AWGN channel The features utilized in [9 12 13]are spectral features (120590ap 120590dp 120590aa 120590af 120590fn and 120574max) andcyclic features (spectral coherence function cyclic domainprofile) A summary of proposed algorithms based on time-frequency analysis wavelet transform higher order statistics(cummulants and moments) cyclo-stationarity propertiesand on spectral properties for modulation classification arein [14]

Themodulation identification of BPSKQPSK 16-PSK 2-16QAM GMSK and MSK modulations schemes under theeffect of noisy channel is considered in [15] using wavelettransform approach and statistical moments as features Theproposed algorithm performs 100 identification at SNRof 10 dB A hierarchical cyclostationary based algorithm isproposed to identify the wide range of unknown modulatedsignals presented in [16] The authors also assume no apriori information such as carrier frequency and carrierphase The modulation formats to be classified are AMBPSK OFDM CDMA 4ndash8 ASK 2ndash16 PSK 16 and 64 QAMmodulation formatsThe performance of proposed algorithmis investigated on fading channels The proposed algorithmin [17] uses higher order moments of continuous wavelettransform (CWT) as a feature set The classifier used ismultilayer feed forward neural network using resilient backpropagation algorithm The modulation formats consideredare M-ary shift keying without any priori information Theperformance of algorithm is evaluated on AWGN channelas well as fading channels In [18] FSK and AM signals arejointly detected and classified using first order cyclostation-arity The algorithm only requires approximate informationabout signal band width and carrier frequency and there isno need for time recovery in the proposed algorithm In[19] features are extracted based upon autocorrelation andcyclic autocorrelation for cyclic prefix guard time intervalOFDM signals to estimate the useful time interval the cyclicprefix duration and the number of subcarriers in frequencyselective channels Authors use time frequency analysis toextract features in [20] These extracted features are usedfor classification purpose The proposed algorithm has threemain tools a TF tool which computes the TF transform

extraction of features which gives main characteristics ofsignal and classifier part which discriminates with the help offeaturesThemodulation classification for the wireless sensornetworks is carried out in [21] usingmultisensor fusion basedmethod The classification performance is investigated onAWGN channel and fading channelThe a priori informationabout the signal such as timing synchronization phase jitterphase offset and frequency offset is considered for evalu-ation of correct classification The first signal classificationis done using 2nd 4th and 6th order cummulants andthen kernel thought is used to map the feature to higherdimensional space and optimum hyper plane is constructedusing SVM to classify the signals in [22] The classifier basedon back propagation neural network (BPNN) and trained byimproved particle swarm optimization (PSO) which is usedto optimal weights and threshold for BPNN is proposed in[23] The recognized modulation formats are 2ASK 4ASK2FSK 4FSK BPSK and QPSK The classifier designed forspace time block codes (STBC) system using multidimen-sional independent component analysis (ICA) is proposedin [24] The classifier is also based on maximum likelihoodon the condition of virtual channel matrix The featuresextracted for modulation identification are received signalpower distribution in [25] The classifier identifies only sixmodulation formats Higher order cummulants up to 4th and6th order are used to classify the modulation formats such asBPSK QPSK and higher order QAMrsquos [26] Cyclostationaryfeatures are also used to classify the BPSK and non-BPSK atlastmaximum likelihood detection algorithm is performed tofurther classification of QPSK and 16-QAMThe modulationclassification is done without having any information aboutnoise power energy of the transmitted signal and channelcoefficients [27] The modulation classification is carried outby minimizing the distance of log likelihood and expectedlog likelihood of the received data Modulation classificationis considered on frequency selective fading channel usingGibbs sampling method based on latent Dirichlet Bayesiannetwork in [28] Blind modulation classification problem isconsidered under the effect on frequency selective fadingchannels in [29] The features used for classification arecorrelation function of the received signal The modulationrecognition focuses on pattern recognitionmethod proposedin [30] the main purpose is to demonstrate the possibility ofrecognizing digital modulation formats at lower SNRs Themethod of modulation classification involves computationof the empirical characteristics function (ECF) from thereceived signal samples and employing constrained leastsquares (CLS) filtering in frequency domain [31]

For signal classification and representations adaptivetime frequency analysis including wavelet based filter bank[32] and Gabor based filter banks were used in [33 34]Recently in [35] authors proposed a Gabor atom basedupon neural network (GNN) for feature extraction andsignal classification Efficient feature extraction and higherrecognition rate have been achieved using GNN HoweverGNN consists of two layers the first layer is feature extractionand the second layer is of signal classification Using degreeof non-stationarity the Gabor filter is proposed in [36] forefficient classification




2 System Model


119903 (119899) = 119909 (119899) + 119892 (119899) (1)


2 and 119909(119899) is given by

119909 (119899) = 120572119890119894(119908119900119899119879+120579119899)

119895=infin


119909 (119897) ℎ (119899120591 minus 119895120591 + 120598119879120591) (2)





119892119888120590119891 (119905) =1

radic120590119892(

119905 minus 119888

120590) 119890119895119891119905 (3)


Feature extraction

Classification rule

PSK

FSK

QAM

2 to 64

2 to 64

4 to 64


X

x1x2

x3x4

g1

g2

g3g4

gMxM

w1w2w3w4

wM

120593i = xigi

yk =M

sumi=1

120593iwi

d

ek

Seria

l to

para

llel c

onve

rsio

n (S

TP)

Input signal


where 119892(119905) = 214119890minus1205871199052



119892119894 (119905) =1

radic120590119894119892(

119905 minus 119888119894

120590119894) 119890119895119891119894119905 (4)



120593119894 =1003816100381610038161003816⟨119892119894 119909119894⟩

1003816100381610038161003816

120593119894 =

100381610038161003816100381610038161003816100381610038161003816int

1


120590119894) 119890minus119895119891119894119905119909119894 (119905) 119889119905

100381610038161003816100381610038161003816100381610038161003816

(5)



119910119896119899 =

119872

sum119894=1

120593119894119899119908119894119899 119899 = 1 2 3 119873 (6)



X

Min

Input signal

Gabor 1

Gabor 2

Gabor 3

Gabor P



119890119896= 119889119896 minus 119910119896 (7)







Δ120574119894 = minus120578120597119869 (119896)

120597120574119894 (8)



119869 (119896) = (119889 (119896) minus 119910 (119896))2 (9)


Δ119888119894 = 119888119894 (119899 + 1) minus 119888119894 (119899) (10)

= minus120578119888

2

120597119869 (119896)

120597119888119894

= minus120578119888

2[120597119869 (119896)

120597120593119894

120597120593119894

120597119888119894]

(11)

Δ120590119894 = 120590119894 (119899 + 1) minus 120590119894 (119899) (12)

= minus120578120590

2

120597119869 (119896)

120597120590119894

= minus120578120590

2[120597119869 (119896)

120597120593119894

120597120593119894

120597120590119894]

(13)

Δ119891119894= 119891119894 (119899 + 1) minus 119891119894 (119899) (14)

= minus120578119891

2

120597119869 (119896)

120597119891119894

= minus120578119891

2[120597119869 (119896)

120597120593119894

120597120593119894

120597119891119894]

(15)

From (9)

120597119869 (119896)

120597120593119894=

120597

120597120593119894[(119889 (119896) minus 119910 (119896))

2]

120597119869 (119896)

120597120593119894= 2 [119889 (119896) minus 119910 (119896)]

120597

120597120593119894(119889 (119896) minus 119910 (119896))

120597119869 (119896)

120597120593119894= minus 2 [119889 (119896) minus 119910 (119896)]

120597

120597120593119894(119910 (119896))

(16)

From (6)

120597

120597120593119894(119910 (119896)) =

120597

120597120593119894

[

[

119872

sum119895=1

120593119895119908119895]

]

120597

120597120593119894(119910 (119896)) =

119872

sum119895=1

120575119894119895119908119895

120597

120597120593119894(119910 (119896)) = 119908119894

(17)


120597119869 (119896)

120597120593119894= minus2(119889 (119896) minus 119910 (119896)) 119908

119894 (18)


From (11) (13) and (15)

Δ119888119894 = 120578119888(119889 (119896) minus 119910 (119896)) 119908119894120597120593119894

120597119888119894

Δ120590119894 = [120578120590(119889 (119896) minus 119910 (119896)) 119908119894]120597120593119894

120597120590119894

Δ119891119894= [120578119891(119889 (119896) minus 119910 (119896)) 119908119894]

120597120593119894

120597119891119894

119892119894 =1


119894)120590119894)2

cos (119891119894119905)

(19)

From (5)

120593119894 =

100381610038161003816100381610038161003816100381610038161003816119909119894

1


119894)120590119894)2

cos (119891119894119905)100381610038161003816100381610038161003816100381610038161003816 (20)



120597120593119894

120597119888119894=

120597

120597119888119894(119909119894119892119894)

=120597

120597119888119894[119909119894

1


119894)120590119894)2

cos (119891119894119905)]

=119909119894

radic120590119894cos (119891119894119905)


119894)120590119894)2


120590119894))(minus

1

120590119894)]

=119909119894

radic120590119894cos (119891119894119905) [119890

minus120587((119905minus119888119894)120590119894)2

(2120587(119905 minus 119888119894

1205901198942))]

=1199091198945radic120590119894


119894)120590119894)2

120597120593119894

120597120590119894=

120597

120597120590119894[119909119894

1


119894)120590119894)2

cos (119891119894119905)]

= 119909119894 cos (119891119894119905)

times [1


119894)120590119894)2


120590119894))


1205901198942

) + 119890minus120587((119905minus119888

119894)120590119894)2

times minus1

2120590119894minus32

]

=119909119894 cos (119891119894119905)


119894)120590119894)2

[2120587 (119905 minus 119888119894)

2

1205901198943

minus1

2120590119894]

120597120593119894

120597119891119894=

120597

120597119891119894[119909119894

1


119894)120590119894)2

cos (119891119894119905)]

= minus119905


119894)120590119894)2

sin (119891119894119905)

(21)


Δ119888119894 = 120578119888(119889 (119896) minus 119910 (119896)) 119908119894

times [1199091198945radic120590119894


119894)120590119894)2

] (22)

119888119894 (119899 + 1) = 119888119894 (119899) + 120578119888(119889 (119896) minus 119910 (119896)) 119908119894

times [1199091198945radic120590119894


119894)120590119894)2

] (23)

Δ120590119894 = [120578120590(119889 (119896) minus 119910 (119896)) 119908119894]

times 119909119894 cos (119891119894119905)


119894)120590119894)2

times [2120587 (119905 minus 119888119894)

2

1205901198943

minus1

2120590119894]

(24)

120590119894 (119899 + 1) = 120590119894 (119899) + [120578120590(119889 (119896) minus 119910 (119896)) 119908119894]

times 119909119894 cos (119891119894119905)


119894)120590119894)2

times [2120587 (119905 minus 119888119894)

2

1205901198943

minus1

2120590119894]

(25)

Δ119891119894= [120578119891(119889 (119896) minus 119910 (119896)) 119908119894]

times minus119905


119894)120590119894)2

sin (119891119894119905) (26)

119891119894 (119899 + 1) = 119891119894 (119899) + [120578119891(119889 (119896) minus 119910 (119896)) 119908119894]

times minus119905


119894)120590119894)2

sin (119891119894119905) (27)



Δ119908119894 = 119908119894 (119899 + 1) minus 119908119894 (119899) (28)

= minus120578119908

2

120597119869 (119896)

120597119908119894

= minus120578119908

2

120597

120597119908119894[(119889 (119896) minus 119910 (119896))

2]

=120578119908

22 (119889 (119896) minus 119910 (119896))

120597

120597119908119894119910 (119896)




119894)






119894)


119894 120590119894 119891119894) using (8) (23) (25) and (27)


119894)



119894)



119910119896=

119872

sum119894=1

120593119894119908119894



= 120578119908 (119889 (119896) minus 119910 (119896))120597

120597119908119894119910 (119896)

(29)

120597119910 (119896)

120597119908119894=

120597

120597119908119894

[

[

119872

sum119895=1

120593119895119908119895]

]

= 120593119894 (30)


Δ119908119894 = 120578119908 (119889 (119896) minus 119910 (119896)) 120593119894 (31)

From (28)

119908119894 (119899 + 1) = 119908119894 (119899) + 120578119908 (119889 (119896) minus 119910 (119896)) 120593119894 (32)




































4

3

2

1

00 50 100 150 200 250


Mea

n sq

uare

erro

rM

ean

squa

re er

ror

0 50 100 150 200 250


6

5

4

3

2

1

00 50 100 150 200 250


10

8

6

4

2

0

0 50 100 150 200 250


6

5

4

3

2

1

00 50 100 150 200 250


20

15

10

5

00 50 100 150 200 250


20

15

10

5

0

PSK2 PSK4 PSK8

PSK16 PSK32 PSK64


08

06

04

02

0

08

06

04

02

0

0 50 100 150 200 250


0 50 100 150 200 250



0 50 100 150 200 250



Mea

n sq

uare

erro

rM

ean

squa

re er

ror

0 50 100 150 200 250


1

08

06

04

02

0

2

15

1

05

0

1

08

06

04

02

0

2

15

1

05

0

FSK2 FSK4 FSK8

FSK16 FSK32 FSK64








10

8

6

4

2

0

8

6

4

2

0

8

6

4

2

0

30

25

20

15

10

5

0

25

20

15

10

5

0

8

6

4

2

00 50 100 150 200 250




0 50 100 150 200 250




Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64


04

03

02

01

0

08

06

04

02

0

25

2

15

1

05

0

5

4

3

2

1

0

10

8

6

4

2

0

15

10

5

0






FSK2 FSK4 FSK8


FSK16 FSK32 FSK64

Mea

n sq

uare

erro

rM

ean

squa

re er

ror







04

03

02

01

0Mea

n sq

uare

erro

rM

ean

squa

re er

ror







25

2

15

1

05

0

8

6

4

2

0

12

10

8

6

4

2

0

1

08

06

04

02

0

6

5

4

3

2

1

0

FSK2 FSK4 FSK8

FSK16 FSK32 FSK64


02

015

01

005

0

04

03

02

01

0

08

06

04

02

0

04

03

02

01

0

05

04

03

02

01

0

08

06

04

02

0







Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64


10908070605040302010

20 40 60 80 100 120 140 160 180 200


Prob

abili

ty o

f cor

rect

ness

(PCC




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)minus10 minus5 0 5 10 15 20

SNR (dB)



1

09

08

07

06

05

04

Prob

abili

ty o

f cor

rect

ness

(PCC

)

200 40 60 80 100 120 140 160 180 200




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)








6 Conclusion



1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)0 20 40 60 80 100 120 140 160 180 200






09

08

07

06

05

04

03

02Prob

abili

ty o

f cor

rect

ness

(PCC

)





References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












2 System Model


119903 (119899) = 119909 (119899) + 119892 (119899) (1)


2 and 119909(119899) is given by

119909 (119899) = 120572119890119894(119908119900119899119879+120579119899)

119895=infin


119909 (119897) ℎ (119899120591 minus 119895120591 + 120598119879120591) (2)





119892119888120590119891 (119905) =1

radic120590119892(

119905 minus 119888

120590) 119890119895119891119905 (3)


Feature extraction

Classification rule

PSK

FSK

QAM

2 to 64

2 to 64

4 to 64


X

x1x2

x3x4

g1

g2

g3g4

gMxM

w1w2w3w4

wM

120593i = xigi

yk =M

sumi=1

120593iwi

d

ek

Seria

l to

para

llel c

onve

rsio

n (S

TP)

Input signal


where 119892(119905) = 214119890minus1205871199052



119892119894 (119905) =1

radic120590119894119892(

119905 minus 119888119894

120590119894) 119890119895119891119894119905 (4)



120593119894 =1003816100381610038161003816⟨119892119894 119909119894⟩

1003816100381610038161003816

120593119894 =

100381610038161003816100381610038161003816100381610038161003816int

1


120590119894) 119890minus119895119891119894119905119909119894 (119905) 119889119905

100381610038161003816100381610038161003816100381610038161003816

(5)



119910119896119899 =

119872

sum119894=1

120593119894119899119908119894119899 119899 = 1 2 3 119873 (6)



X

Min

Input signal

Gabor 1

Gabor 2

Gabor 3

Gabor P



119890119896= 119889119896 minus 119910119896 (7)







Δ120574119894 = minus120578120597119869 (119896)

120597120574119894 (8)



119869 (119896) = (119889 (119896) minus 119910 (119896))2 (9)


Δ119888119894 = 119888119894 (119899 + 1) minus 119888119894 (119899) (10)

= minus120578119888

2

120597119869 (119896)

120597119888119894

= minus120578119888

2[120597119869 (119896)

120597120593119894

120597120593119894

120597119888119894]

(11)

Δ120590119894 = 120590119894 (119899 + 1) minus 120590119894 (119899) (12)

= minus120578120590

2

120597119869 (119896)

120597120590119894

= minus120578120590

2[120597119869 (119896)

120597120593119894

120597120593119894

120597120590119894]

(13)

Δ119891119894= 119891119894 (119899 + 1) minus 119891119894 (119899) (14)

= minus120578119891

2

120597119869 (119896)

120597119891119894

= minus120578119891

2[120597119869 (119896)

120597120593119894

120597120593119894

120597119891119894]

(15)

From (9)

120597119869 (119896)

120597120593119894=

120597

120597120593119894[(119889 (119896) minus 119910 (119896))

2]

120597119869 (119896)

120597120593119894= 2 [119889 (119896) minus 119910 (119896)]

120597

120597120593119894(119889 (119896) minus 119910 (119896))

120597119869 (119896)

120597120593119894= minus 2 [119889 (119896) minus 119910 (119896)]

120597

120597120593119894(119910 (119896))

(16)

From (6)

120597

120597120593119894(119910 (119896)) =

120597

120597120593119894

[

[

119872

sum119895=1

120593119895119908119895]

]

120597

120597120593119894(119910 (119896)) =

119872

sum119895=1

120575119894119895119908119895

120597

120597120593119894(119910 (119896)) = 119908119894

(17)


120597119869 (119896)

120597120593119894= minus2(119889 (119896) minus 119910 (119896)) 119908

119894 (18)


From (11) (13) and (15)

Δ119888119894 = 120578119888(119889 (119896) minus 119910 (119896)) 119908119894120597120593119894

120597119888119894

Δ120590119894 = [120578120590(119889 (119896) minus 119910 (119896)) 119908119894]120597120593119894

120597120590119894

Δ119891119894= [120578119891(119889 (119896) minus 119910 (119896)) 119908119894]

120597120593119894

120597119891119894

119892119894 =1


119894)120590119894)2

cos (119891119894119905)

(19)

From (5)

120593119894 =

100381610038161003816100381610038161003816100381610038161003816119909119894

1


119894)120590119894)2

cos (119891119894119905)100381610038161003816100381610038161003816100381610038161003816 (20)



120597120593119894

120597119888119894=

120597

120597119888119894(119909119894119892119894)

=120597

120597119888119894[119909119894

1


119894)120590119894)2

cos (119891119894119905)]

=119909119894

radic120590119894cos (119891119894119905)


119894)120590119894)2


120590119894))(minus

1

120590119894)]

=119909119894

radic120590119894cos (119891119894119905) [119890

minus120587((119905minus119888119894)120590119894)2

(2120587(119905 minus 119888119894

1205901198942))]

=1199091198945radic120590119894


119894)120590119894)2

120597120593119894

120597120590119894=

120597

120597120590119894[119909119894

1


119894)120590119894)2

cos (119891119894119905)]

= 119909119894 cos (119891119894119905)

times [1


119894)120590119894)2


120590119894))


1205901198942

) + 119890minus120587((119905minus119888

119894)120590119894)2

times minus1

2120590119894minus32

]

=119909119894 cos (119891119894119905)


119894)120590119894)2

[2120587 (119905 minus 119888119894)

2

1205901198943

minus1

2120590119894]

120597120593119894

120597119891119894=

120597

120597119891119894[119909119894

1


119894)120590119894)2

cos (119891119894119905)]

= minus119905


119894)120590119894)2

sin (119891119894119905)

(21)


Δ119888119894 = 120578119888(119889 (119896) minus 119910 (119896)) 119908119894

times [1199091198945radic120590119894


119894)120590119894)2

] (22)

119888119894 (119899 + 1) = 119888119894 (119899) + 120578119888(119889 (119896) minus 119910 (119896)) 119908119894

times [1199091198945radic120590119894


119894)120590119894)2

] (23)

Δ120590119894 = [120578120590(119889 (119896) minus 119910 (119896)) 119908119894]

times 119909119894 cos (119891119894119905)


119894)120590119894)2

times [2120587 (119905 minus 119888119894)

2

1205901198943

minus1

2120590119894]

(24)

120590119894 (119899 + 1) = 120590119894 (119899) + [120578120590(119889 (119896) minus 119910 (119896)) 119908119894]

times 119909119894 cos (119891119894119905)


119894)120590119894)2

times [2120587 (119905 minus 119888119894)

2

1205901198943

minus1

2120590119894]

(25)

Δ119891119894= [120578119891(119889 (119896) minus 119910 (119896)) 119908119894]

times minus119905


119894)120590119894)2

sin (119891119894119905) (26)

119891119894 (119899 + 1) = 119891119894 (119899) + [120578119891(119889 (119896) minus 119910 (119896)) 119908119894]

times minus119905


119894)120590119894)2

sin (119891119894119905) (27)



Δ119908119894 = 119908119894 (119899 + 1) minus 119908119894 (119899) (28)

= minus120578119908

2

120597119869 (119896)

120597119908119894

= minus120578119908

2

120597

120597119908119894[(119889 (119896) minus 119910 (119896))

2]

=120578119908

22 (119889 (119896) minus 119910 (119896))

120597

120597119908119894119910 (119896)




119894)






119894)


119894 120590119894 119891119894) using (8) (23) (25) and (27)


119894)



119894)



119910119896=

119872

sum119894=1

120593119894119908119894



= 120578119908 (119889 (119896) minus 119910 (119896))120597

120597119908119894119910 (119896)

(29)

120597119910 (119896)

120597119908119894=

120597

120597119908119894

[

[

119872

sum119895=1

120593119895119908119895]

]

= 120593119894 (30)


Δ119908119894 = 120578119908 (119889 (119896) minus 119910 (119896)) 120593119894 (31)

From (28)

119908119894 (119899 + 1) = 119908119894 (119899) + 120578119908 (119889 (119896) minus 119910 (119896)) 120593119894 (32)




































4

3

2

1

00 50 100 150 200 250


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n sq

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erro

rM

ean

squa

re er

ror

0 50 100 150 200 250


6

5

4

3

2

1

00 50 100 150 200 250


10

8

6

4

2

0

0 50 100 150 200 250


6

5

4

3

2

1

00 50 100 150 200 250


20

15

10

5

00 50 100 150 200 250


20

15

10

5

0

PSK2 PSK4 PSK8

PSK16 PSK32 PSK64


08

06

04

02

0

08

06

04

02

0

0 50 100 150 200 250


0 50 100 150 200 250



0 50 100 150 200 250



Mea

n sq

uare

erro

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ean

squa

re er

ror

0 50 100 150 200 250


1

08

06

04

02

0

2

15

1

05

0

1

08

06

04

02

0

2

15

1

05

0

FSK2 FSK4 FSK8

FSK16 FSK32 FSK64








10

8

6

4

2

0

8

6

4

2

0

8

6

4

2

0

30

25

20

15

10

5

0

25

20

15

10

5

0

8

6

4

2

00 50 100 150 200 250




0 50 100 150 200 250




Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64


04

03

02

01

0

08

06

04

02

0

25

2

15

1

05

0

5

4

3

2

1

0

10

8

6

4

2

0

15

10

5

0






FSK2 FSK4 FSK8


FSK16 FSK32 FSK64

Mea

n sq

uare

erro

rM

ean

squa

re er

ror







04

03

02

01

0Mea

n sq

uare

erro

rM

ean

squa

re er

ror







25

2

15

1

05

0

8

6

4

2

0

12

10

8

6

4

2

0

1

08

06

04

02

0

6

5

4

3

2

1

0

FSK2 FSK4 FSK8

FSK16 FSK32 FSK64


02

015

01

005

0

04

03

02

01

0

08

06

04

02

0

04

03

02

01

0

05

04

03

02

01

0

08

06

04

02

0







Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64


10908070605040302010

20 40 60 80 100 120 140 160 180 200


Prob

abili

ty o

f cor

rect

ness

(PCC




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)minus10 minus5 0 5 10 15 20

SNR (dB)



1

09

08

07

06

05

04

Prob

abili

ty o

f cor

rect

ness

(PCC

)

200 40 60 80 100 120 140 160 180 200




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)








6 Conclusion



1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)0 20 40 60 80 100 120 140 160 180 200






09

08

07

06

05

04

03

02Prob

abili

ty o

f cor

rect

ness

(PCC

)





References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










X

Min

Input signal

Gabor 1

Gabor 2

Gabor 3

Gabor P



119890119896= 119889119896 minus 119910119896 (7)







Δ120574119894 = minus120578120597119869 (119896)

120597120574119894 (8)



119869 (119896) = (119889 (119896) minus 119910 (119896))2 (9)


Δ119888119894 = 119888119894 (119899 + 1) minus 119888119894 (119899) (10)

= minus120578119888

2

120597119869 (119896)

120597119888119894

= minus120578119888

2[120597119869 (119896)

120597120593119894

120597120593119894

120597119888119894]

(11)

Δ120590119894 = 120590119894 (119899 + 1) minus 120590119894 (119899) (12)

= minus120578120590

2

120597119869 (119896)

120597120590119894

= minus120578120590

2[120597119869 (119896)

120597120593119894

120597120593119894

120597120590119894]

(13)

Δ119891119894= 119891119894 (119899 + 1) minus 119891119894 (119899) (14)

= minus120578119891

2

120597119869 (119896)

120597119891119894

= minus120578119891

2[120597119869 (119896)

120597120593119894

120597120593119894

120597119891119894]

(15)

From (9)

120597119869 (119896)

120597120593119894=

120597

120597120593119894[(119889 (119896) minus 119910 (119896))

2]

120597119869 (119896)

120597120593119894= 2 [119889 (119896) minus 119910 (119896)]

120597

120597120593119894(119889 (119896) minus 119910 (119896))

120597119869 (119896)

120597120593119894= minus 2 [119889 (119896) minus 119910 (119896)]

120597

120597120593119894(119910 (119896))

(16)

From (6)

120597

120597120593119894(119910 (119896)) =

120597

120597120593119894

[

[

119872

sum119895=1

120593119895119908119895]

]

120597

120597120593119894(119910 (119896)) =

119872

sum119895=1

120575119894119895119908119895

120597

120597120593119894(119910 (119896)) = 119908119894

(17)


120597119869 (119896)

120597120593119894= minus2(119889 (119896) minus 119910 (119896)) 119908

119894 (18)


From (11) (13) and (15)

Δ119888119894 = 120578119888(119889 (119896) minus 119910 (119896)) 119908119894120597120593119894

120597119888119894

Δ120590119894 = [120578120590(119889 (119896) minus 119910 (119896)) 119908119894]120597120593119894

120597120590119894

Δ119891119894= [120578119891(119889 (119896) minus 119910 (119896)) 119908119894]

120597120593119894

120597119891119894

119892119894 =1


119894)120590119894)2

cos (119891119894119905)

(19)

From (5)

120593119894 =

100381610038161003816100381610038161003816100381610038161003816119909119894

1


119894)120590119894)2

cos (119891119894119905)100381610038161003816100381610038161003816100381610038161003816 (20)



120597120593119894

120597119888119894=

120597

120597119888119894(119909119894119892119894)

=120597

120597119888119894[119909119894

1


119894)120590119894)2

cos (119891119894119905)]

=119909119894

radic120590119894cos (119891119894119905)


119894)120590119894)2


120590119894))(minus

1

120590119894)]

=119909119894

radic120590119894cos (119891119894119905) [119890

minus120587((119905minus119888119894)120590119894)2

(2120587(119905 minus 119888119894

1205901198942))]

=1199091198945radic120590119894


119894)120590119894)2

120597120593119894

120597120590119894=

120597

120597120590119894[119909119894

1


119894)120590119894)2

cos (119891119894119905)]

= 119909119894 cos (119891119894119905)

times [1


119894)120590119894)2


120590119894))


1205901198942

) + 119890minus120587((119905minus119888

119894)120590119894)2

times minus1

2120590119894minus32

]

=119909119894 cos (119891119894119905)


119894)120590119894)2

[2120587 (119905 minus 119888119894)

2

1205901198943

minus1

2120590119894]

120597120593119894

120597119891119894=

120597

120597119891119894[119909119894

1


119894)120590119894)2

cos (119891119894119905)]

= minus119905


119894)120590119894)2

sin (119891119894119905)

(21)


Δ119888119894 = 120578119888(119889 (119896) minus 119910 (119896)) 119908119894

times [1199091198945radic120590119894


119894)120590119894)2

] (22)

119888119894 (119899 + 1) = 119888119894 (119899) + 120578119888(119889 (119896) minus 119910 (119896)) 119908119894

times [1199091198945radic120590119894


119894)120590119894)2

] (23)

Δ120590119894 = [120578120590(119889 (119896) minus 119910 (119896)) 119908119894]

times 119909119894 cos (119891119894119905)


119894)120590119894)2

times [2120587 (119905 minus 119888119894)

2

1205901198943

minus1

2120590119894]

(24)

120590119894 (119899 + 1) = 120590119894 (119899) + [120578120590(119889 (119896) minus 119910 (119896)) 119908119894]

times 119909119894 cos (119891119894119905)


119894)120590119894)2

times [2120587 (119905 minus 119888119894)

2

1205901198943

minus1

2120590119894]

(25)

Δ119891119894= [120578119891(119889 (119896) minus 119910 (119896)) 119908119894]

times minus119905


119894)120590119894)2

sin (119891119894119905) (26)

119891119894 (119899 + 1) = 119891119894 (119899) + [120578119891(119889 (119896) minus 119910 (119896)) 119908119894]

times minus119905


119894)120590119894)2

sin (119891119894119905) (27)



Δ119908119894 = 119908119894 (119899 + 1) minus 119908119894 (119899) (28)

= minus120578119908

2

120597119869 (119896)

120597119908119894

= minus120578119908

2

120597

120597119908119894[(119889 (119896) minus 119910 (119896))

2]

=120578119908

22 (119889 (119896) minus 119910 (119896))

120597

120597119908119894119910 (119896)




119894)






119894)


119894 120590119894 119891119894) using (8) (23) (25) and (27)


119894)



119894)



119910119896=

119872

sum119894=1

120593119894119908119894



= 120578119908 (119889 (119896) minus 119910 (119896))120597

120597119908119894119910 (119896)

(29)

120597119910 (119896)

120597119908119894=

120597

120597119908119894

[

[

119872

sum119895=1

120593119895119908119895]

]

= 120593119894 (30)


Δ119908119894 = 120578119908 (119889 (119896) minus 119910 (119896)) 120593119894 (31)

From (28)

119908119894 (119899 + 1) = 119908119894 (119899) + 120578119908 (119889 (119896) minus 119910 (119896)) 120593119894 (32)




































4

3

2

1

00 50 100 150 200 250


Mea

n sq

uare

erro

rM

ean

squa

re er

ror

0 50 100 150 200 250


6

5

4

3

2

1

00 50 100 150 200 250


10

8

6

4

2

0

0 50 100 150 200 250


6

5

4

3

2

1

00 50 100 150 200 250


20

15

10

5

00 50 100 150 200 250


20

15

10

5

0

PSK2 PSK4 PSK8

PSK16 PSK32 PSK64


08

06

04

02

0

08

06

04

02

0

0 50 100 150 200 250


0 50 100 150 200 250



0 50 100 150 200 250



Mea

n sq

uare

erro

rM

ean

squa

re er

ror

0 50 100 150 200 250


1

08

06

04

02

0

2

15

1

05

0

1

08

06

04

02

0

2

15

1

05

0

FSK2 FSK4 FSK8

FSK16 FSK32 FSK64








10

8

6

4

2

0

8

6

4

2

0

8

6

4

2

0

30

25

20

15

10

5

0

25

20

15

10

5

0

8

6

4

2

00 50 100 150 200 250




0 50 100 150 200 250




Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64


04

03

02

01

0

08

06

04

02

0

25

2

15

1

05

0

5

4

3

2

1

0

10

8

6

4

2

0

15

10

5

0






FSK2 FSK4 FSK8


FSK16 FSK32 FSK64

Mea

n sq

uare

erro

rM

ean

squa

re er

ror







04

03

02

01

0Mea

n sq

uare

erro

rM

ean

squa

re er

ror







25

2

15

1

05

0

8

6

4

2

0

12

10

8

6

4

2

0

1

08

06

04

02

0

6

5

4

3

2

1

0

FSK2 FSK4 FSK8

FSK16 FSK32 FSK64


02

015

01

005

0

04

03

02

01

0

08

06

04

02

0

04

03

02

01

0

05

04

03

02

01

0

08

06

04

02

0







Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64


10908070605040302010

20 40 60 80 100 120 140 160 180 200


Prob

abili

ty o

f cor

rect

ness

(PCC




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)minus10 minus5 0 5 10 15 20

SNR (dB)



1

09

08

07

06

05

04

Prob

abili

ty o

f cor

rect

ness

(PCC

)

200 40 60 80 100 120 140 160 180 200




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)








6 Conclusion



1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)0 20 40 60 80 100 120 140 160 180 200






09

08

07

06

05

04

03

02Prob

abili

ty o

f cor

rect

ness

(PCC

)





References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










From (11) (13) and (15)

Δ119888119894 = 120578119888(119889 (119896) minus 119910 (119896)) 119908119894120597120593119894

120597119888119894

Δ120590119894 = [120578120590(119889 (119896) minus 119910 (119896)) 119908119894]120597120593119894

120597120590119894

Δ119891119894= [120578119891(119889 (119896) minus 119910 (119896)) 119908119894]

120597120593119894

120597119891119894

119892119894 =1


119894)120590119894)2

cos (119891119894119905)

(19)

From (5)

120593119894 =

100381610038161003816100381610038161003816100381610038161003816119909119894

1


119894)120590119894)2

cos (119891119894119905)100381610038161003816100381610038161003816100381610038161003816 (20)



120597120593119894

120597119888119894=

120597

120597119888119894(119909119894119892119894)

=120597

120597119888119894[119909119894

1


119894)120590119894)2

cos (119891119894119905)]

=119909119894

radic120590119894cos (119891119894119905)


119894)120590119894)2


120590119894))(minus

1

120590119894)]

=119909119894

radic120590119894cos (119891119894119905) [119890

minus120587((119905minus119888119894)120590119894)2

(2120587(119905 minus 119888119894

1205901198942))]

=1199091198945radic120590119894


119894)120590119894)2

120597120593119894

120597120590119894=

120597

120597120590119894[119909119894

1


119894)120590119894)2

cos (119891119894119905)]

= 119909119894 cos (119891119894119905)

times [1


119894)120590119894)2


120590119894))


1205901198942

) + 119890minus120587((119905minus119888

119894)120590119894)2

times minus1

2120590119894minus32

]

=119909119894 cos (119891119894119905)


119894)120590119894)2

[2120587 (119905 minus 119888119894)

2

1205901198943

minus1

2120590119894]

120597120593119894

120597119891119894=

120597

120597119891119894[119909119894

1


119894)120590119894)2

cos (119891119894119905)]

= minus119905


119894)120590119894)2

sin (119891119894119905)

(21)


Δ119888119894 = 120578119888(119889 (119896) minus 119910 (119896)) 119908119894

times [1199091198945radic120590119894


119894)120590119894)2

] (22)

119888119894 (119899 + 1) = 119888119894 (119899) + 120578119888(119889 (119896) minus 119910 (119896)) 119908119894

times [1199091198945radic120590119894


119894)120590119894)2

] (23)

Δ120590119894 = [120578120590(119889 (119896) minus 119910 (119896)) 119908119894]

times 119909119894 cos (119891119894119905)


119894)120590119894)2

times [2120587 (119905 minus 119888119894)

2

1205901198943

minus1

2120590119894]

(24)

120590119894 (119899 + 1) = 120590119894 (119899) + [120578120590(119889 (119896) minus 119910 (119896)) 119908119894]

times 119909119894 cos (119891119894119905)


119894)120590119894)2

times [2120587 (119905 minus 119888119894)

2

1205901198943

minus1

2120590119894]

(25)

Δ119891119894= [120578119891(119889 (119896) minus 119910 (119896)) 119908119894]

times minus119905


119894)120590119894)2

sin (119891119894119905) (26)

119891119894 (119899 + 1) = 119891119894 (119899) + [120578119891(119889 (119896) minus 119910 (119896)) 119908119894]

times minus119905


119894)120590119894)2

sin (119891119894119905) (27)



Δ119908119894 = 119908119894 (119899 + 1) minus 119908119894 (119899) (28)

= minus120578119908

2

120597119869 (119896)

120597119908119894

= minus120578119908

2

120597

120597119908119894[(119889 (119896) minus 119910 (119896))

2]

=120578119908

22 (119889 (119896) minus 119910 (119896))

120597

120597119908119894119910 (119896)




119894)






119894)


119894 120590119894 119891119894) using (8) (23) (25) and (27)


119894)



119894)



119910119896=

119872

sum119894=1

120593119894119908119894



= 120578119908 (119889 (119896) minus 119910 (119896))120597

120597119908119894119910 (119896)

(29)

120597119910 (119896)

120597119908119894=

120597

120597119908119894

[

[

119872

sum119895=1

120593119895119908119895]

]

= 120593119894 (30)


Δ119908119894 = 120578119908 (119889 (119896) minus 119910 (119896)) 120593119894 (31)

From (28)

119908119894 (119899 + 1) = 119908119894 (119899) + 120578119908 (119889 (119896) minus 119910 (119896)) 120593119894 (32)




































4

3

2

1

00 50 100 150 200 250


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squa

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ror

0 50 100 150 200 250


6

5

4

3

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1

00 50 100 150 200 250


10

8

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0

0 50 100 150 200 250


6

5

4

3

2

1

00 50 100 150 200 250


20

15

10

5

00 50 100 150 200 250


20

15

10

5

0

PSK2 PSK4 PSK8

PSK16 PSK32 PSK64


08

06

04

02

0

08

06

04

02

0

0 50 100 150 200 250


0 50 100 150 200 250



0 50 100 150 200 250



Mea

n sq

uare

erro

rM

ean

squa

re er

ror

0 50 100 150 200 250


1

08

06

04

02

0

2

15

1

05

0

1

08

06

04

02

0

2

15

1

05

0

FSK2 FSK4 FSK8

FSK16 FSK32 FSK64








10

8

6

4

2

0

8

6

4

2

0

8

6

4

2

0

30

25

20

15

10

5

0

25

20

15

10

5

0

8

6

4

2

00 50 100 150 200 250




0 50 100 150 200 250




Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64


04

03

02

01

0

08

06

04

02

0

25

2

15

1

05

0

5

4

3

2

1

0

10

8

6

4

2

0

15

10

5

0






FSK2 FSK4 FSK8


FSK16 FSK32 FSK64

Mea

n sq

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ean

squa

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ror







04

03

02

01

0Mea

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rM

ean

squa

re er

ror







25

2

15

1

05

0

8

6

4

2

0

12

10

8

6

4

2

0

1

08

06

04

02

0

6

5

4

3

2

1

0

FSK2 FSK4 FSK8

FSK16 FSK32 FSK64


02

015

01

005

0

04

03

02

01

0

08

06

04

02

0

04

03

02

01

0

05

04

03

02

01

0

08

06

04

02

0







Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64


10908070605040302010

20 40 60 80 100 120 140 160 180 200


Prob

abili

ty o

f cor

rect

ness

(PCC




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)minus10 minus5 0 5 10 15 20

SNR (dB)



1

09

08

07

06

05

04

Prob

abili

ty o

f cor

rect

ness

(PCC

)

200 40 60 80 100 120 140 160 180 200




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)








6 Conclusion



1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)0 20 40 60 80 100 120 140 160 180 200






09

08

07

06

05

04

03

02Prob

abili

ty o

f cor

rect

ness

(PCC

)





References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119894)






119894)


119894 120590119894 119891119894) using (8) (23) (25) and (27)


119894)



119894)



119910119896=

119872

sum119894=1

120593119894119908119894



= 120578119908 (119889 (119896) minus 119910 (119896))120597

120597119908119894119910 (119896)

(29)

120597119910 (119896)

120597119908119894=

120597

120597119908119894

[

[

119872

sum119895=1

120593119895119908119895]

]

= 120593119894 (30)


Δ119908119894 = 120578119908 (119889 (119896) minus 119910 (119896)) 120593119894 (31)

From (28)

119908119894 (119899 + 1) = 119908119894 (119899) + 120578119908 (119889 (119896) minus 119910 (119896)) 120593119894 (32)




































4

3

2

1

00 50 100 150 200 250


Mea

n sq

uare

erro

rM

ean

squa

re er

ror

0 50 100 150 200 250


6

5

4

3

2

1

00 50 100 150 200 250


10

8

6

4

2

0

0 50 100 150 200 250


6

5

4

3

2

1

00 50 100 150 200 250


20

15

10

5

00 50 100 150 200 250


20

15

10

5

0

PSK2 PSK4 PSK8

PSK16 PSK32 PSK64


08

06

04

02

0

08

06

04

02

0

0 50 100 150 200 250


0 50 100 150 200 250



0 50 100 150 200 250



Mea

n sq

uare

erro

rM

ean

squa

re er

ror

0 50 100 150 200 250


1

08

06

04

02

0

2

15

1

05

0

1

08

06

04

02

0

2

15

1

05

0

FSK2 FSK4 FSK8

FSK16 FSK32 FSK64








10

8

6

4

2

0

8

6

4

2

0

8

6

4

2

0

30

25

20

15

10

5

0

25

20

15

10

5

0

8

6

4

2

00 50 100 150 200 250




0 50 100 150 200 250




Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64


04

03

02

01

0

08

06

04

02

0

25

2

15

1

05

0

5

4

3

2

1

0

10

8

6

4

2

0

15

10

5

0






FSK2 FSK4 FSK8


FSK16 FSK32 FSK64

Mea

n sq

uare

erro

rM

ean

squa

re er

ror







04

03

02

01

0Mea

n sq

uare

erro

rM

ean

squa

re er

ror







25

2

15

1

05

0

8

6

4

2

0

12

10

8

6

4

2

0

1

08

06

04

02

0

6

5

4

3

2

1

0

FSK2 FSK4 FSK8

FSK16 FSK32 FSK64


02

015

01

005

0

04

03

02

01

0

08

06

04

02

0

04

03

02

01

0

05

04

03

02

01

0

08

06

04

02

0







Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64


10908070605040302010

20 40 60 80 100 120 140 160 180 200


Prob

abili

ty o

f cor

rect

ness

(PCC




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)minus10 minus5 0 5 10 15 20

SNR (dB)



1

09

08

07

06

05

04

Prob

abili

ty o

f cor

rect

ness

(PCC

)

200 40 60 80 100 120 140 160 180 200




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)








6 Conclusion



1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)0 20 40 60 80 100 120 140 160 180 200






09

08

07

06

05

04

03

02Prob

abili

ty o

f cor

rect

ness

(PCC

)





References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





































4

3

2

1

00 50 100 150 200 250


Mea

n sq

uare

erro

rM

ean

squa

re er

ror

0 50 100 150 200 250


6

5

4

3

2

1

00 50 100 150 200 250


10

8

6

4

2

0

0 50 100 150 200 250


6

5

4

3

2

1

00 50 100 150 200 250


20

15

10

5

00 50 100 150 200 250


20

15

10

5

0

PSK2 PSK4 PSK8

PSK16 PSK32 PSK64


08

06

04

02

0

08

06

04

02

0

0 50 100 150 200 250


0 50 100 150 200 250



0 50 100 150 200 250



Mea

n sq

uare

erro

rM

ean

squa

re er

ror

0 50 100 150 200 250


1

08

06

04

02

0

2

15

1

05

0

1

08

06

04

02

0

2

15

1

05

0

FSK2 FSK4 FSK8

FSK16 FSK32 FSK64








10

8

6

4

2

0

8

6

4

2

0

8

6

4

2

0

30

25

20

15

10

5

0

25

20

15

10

5

0

8

6

4

2

00 50 100 150 200 250




0 50 100 150 200 250




Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64


04

03

02

01

0

08

06

04

02

0

25

2

15

1

05

0

5

4

3

2

1

0

10

8

6

4

2

0

15

10

5

0






FSK2 FSK4 FSK8


FSK16 FSK32 FSK64

Mea

n sq

uare

erro

rM

ean

squa

re er

ror







04

03

02

01

0Mea

n sq

uare

erro

rM

ean

squa

re er

ror







25

2

15

1

05

0

8

6

4

2

0

12

10

8

6

4

2

0

1

08

06

04

02

0

6

5

4

3

2

1

0

FSK2 FSK4 FSK8

FSK16 FSK32 FSK64


02

015

01

005

0

04

03

02

01

0

08

06

04

02

0

04

03

02

01

0

05

04

03

02

01

0

08

06

04

02

0







Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64


10908070605040302010

20 40 60 80 100 120 140 160 180 200


Prob

abili

ty o

f cor

rect

ness

(PCC




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)minus10 minus5 0 5 10 15 20

SNR (dB)



1

09

08

07

06

05

04

Prob

abili

ty o

f cor

rect

ness

(PCC

)

200 40 60 80 100 120 140 160 180 200




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)








6 Conclusion



1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)0 20 40 60 80 100 120 140 160 180 200






09

08

07

06

05

04

03

02Prob

abili

ty o

f cor

rect

ness

(PCC

)





References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










10

8

6

4

2

0

8

6

4

2

0

8

6

4

2

0

30

25

20

15

10

5

0

25

20

15

10

5

0

8

6

4

2

00 50 100 150 200 250




0 50 100 150 200 250




Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64


04

03

02

01

0

08

06

04

02

0

25

2

15

1

05

0

5

4

3

2

1

0

10

8

6

4

2

0

15

10

5

0






FSK2 FSK4 FSK8


FSK16 FSK32 FSK64

Mea

n sq

uare

erro

rM

ean

squa

re er

ror







04

03

02

01

0Mea

n sq

uare

erro

rM

ean

squa

re er

ror







25

2

15

1

05

0

8

6

4

2

0

12

10

8

6

4

2

0

1

08

06

04

02

0

6

5

4

3

2

1

0

FSK2 FSK4 FSK8

FSK16 FSK32 FSK64


02

015

01

005

0

04

03

02

01

0

08

06

04

02

0

04

03

02

01

0

05

04

03

02

01

0

08

06

04

02

0







Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64


10908070605040302010

20 40 60 80 100 120 140 160 180 200


Prob

abili

ty o

f cor

rect

ness

(PCC




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)minus10 minus5 0 5 10 15 20

SNR (dB)



1

09

08

07

06

05

04

Prob

abili

ty o

f cor

rect

ness

(PCC

)

200 40 60 80 100 120 140 160 180 200




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)








6 Conclusion



1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)0 20 40 60 80 100 120 140 160 180 200






09

08

07

06

05

04

03

02Prob

abili

ty o

f cor

rect

ness

(PCC

)





References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










04

03

02

01

0Mea

n sq

uare

erro

rM

ean

squa

re er

ror







25

2

15

1

05

0

8

6

4

2

0

12

10

8

6

4

2

0

1

08

06

04

02

0

6

5

4

3

2

1

0

FSK2 FSK4 FSK8

FSK16 FSK32 FSK64


02

015

01

005

0

04

03

02

01

0

08

06

04

02

0

04

03

02

01

0

05

04

03

02

01

0

08

06

04

02

0







Mea

n sq

uare

erro

rM

ean

squa

re er

ror

QAM2 QAM4 QAM8

QAM16 QAM32 QAM64


10908070605040302010

20 40 60 80 100 120 140 160 180 200


Prob

abili

ty o

f cor

rect

ness

(PCC




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)minus10 minus5 0 5 10 15 20

SNR (dB)



1

09

08

07

06

05

04

Prob

abili

ty o

f cor

rect

ness

(PCC

)

200 40 60 80 100 120 140 160 180 200




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)








6 Conclusion



1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)0 20 40 60 80 100 120 140 160 180 200






09

08

07

06

05

04

03

02Prob

abili

ty o

f cor

rect

ness

(PCC

)





References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)minus10 minus5 0 5 10 15 20

SNR (dB)



1

09

08

07

06

05

04

Prob

abili

ty o

f cor

rect

ness

(PCC

)

200 40 60 80 100 120 140 160 180 200




1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)








6 Conclusion



1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)0 20 40 60 80 100 120 140 160 180 200






09

08

07

06

05

04

03

02Prob

abili

ty o

f cor

rect

ness

(PCC

)





References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1

09

08

07

06

05

04

03

02

01

0Prob

abili

ty o

f cor

rect

ness

(PCC

)0 20 40 60 80 100 120 140 160 180 200






09

08

07

06

05

04

03

02Prob

abili

ty o

f cor

rect

ness

(PCC

)





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 novel modulation classification...

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