automatic modulation classification exploiting hybrid

Research ArticleAutomatic Modulation Classification Exploiting HybridMachine Learning Network

FengWang Shanshan Huang HaoWang and Chenlu Yang

Array and Information Processing Laboratory College of Computer and Information Hohai University West Focheng Road No8Jiangning District Nanjing 211100 China

Correspondence should be addressed to FengWang jihonghopealiyuncom

Received 2 September 2018 Revised 17 October 2018 Accepted 25 November 2018 Published 4 December 2018

Academic Editor Ibrahim Zeid

Copyright copy 2018 Feng Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

It is a research hot spot in cognitive electronic warfare systems to classify the electromagnetic signals of a radar or communicationsystem according to their modulation characteristics We construct a multilayer hybrid machine learning network for theclassification of seven types of signals in different modulation We extract the signal modulation features exploiting a setof algorithms such as time-frequency analysis discrete Fourier transform and instantaneous autocorrelation and accomplishautomatic modulation classification using naive Bayesian and support vector machine in a hybrid manner The parameters in thenetwork for classification are determined automatically in the training process The numerical simulation results indicate that theproposed network accomplishes the classification accurately

1 Introduction

The automatic modulation classification (AMC) of the elec-tromagnetic signals of radar and communication systems isan important function in modern electronic warfare systems[1ndash4] The AMC process in a cognitive electronic warfaresystem for radar and communication signal surveillance isshown in Figure 1 The AMC mainly consists of featureextraction and modulation classification [5ndash7] Modulationfeature extraction is composed of a series of transform andanalysis algorithms in time domain frequency domain ortime-frequency domain such as time-frequency analysis [8]cyclic cumulant [9ndash12] and radar ambiguity function [13]and so on The classification processing consists of variouspattern recognition andmachine learning algorithms such assupport vector machine (SVM) [14] deep learning [15] andclustering algorithms [16]

Pattern recognition has made a lot of progress and gainedextensive applications in the field of computer vision whereSVM artificial neural network and deep learning are widelyused to realize image classification [17ndash19] The AMC ofthe communication and radar signals can be regarded asan important branch of pattern recognition A series ofresults have been reported in a range of open literatures

To recognize the radar emitter signal in [20] the feature isextracted by signal fuzzy function slice and singular valuedecomposition and modulation classification is obtained bythe utilization of a kind of fuzzy clustering classificationapproach In [21] a combination of the ldquoRihaczek distributionand Hough transformrdquo algorithms is introduced to extractthe features of the signals in time-frequency domain andthe AMC of radar signals in quadrature amplitude modu-lation (QAM) and phased shift keying (PSK) modulationis achieved In [22] wavelet transform and manifold learn-ing are employed to realize feature extraction and high-dimensional data dimensionality reduction respectively andthe nearest neighbor algorithm is adopted to realize clas-sification of five types of signals (binary amplitude shiftkeying (2ASK) binary frequency shift keying (2FSK) binaryphase shift keying (BPSK) linear frequency modulation(LFM) and Clock Pulse (CP) A type of feature extractionmethod using blind channel estimation and cumulant isproposed in [23] and classification of the modulated signalsis realized by a type of multiclassification algorithm based onmaximum likelihood [24] accomplishes feature extractionandmodulation classification using high-order cumulant andbinary tree based SVM and verifies its performance usingvarious signals such as 2ASK 4ASK quadrature phase shift

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 6152010 14 pageshttpsdoiorg10115520186152010

2 Mathematical Problems in Engineering

Received signals Signature of modulation Modulation classifier

Support vector machineDeep learning

Feature extraction

Time frequency analysisFourth order cumulant

Figure 1 The structure of an AMC system for radar and communication signal surveillance

keying (QPSK) 2FSK and 4-frequency shift keying (4FSK)[25] gives the modulation feature by the exploitation of atype of time-frequency image method based on local binarymode and identifies the radar signals by SVM algorithm In[26] genetic programming is carried out for extracting usefulfeatures and the nearest neighbor algorithm is selected forthe classification of certain types of radar signals

It can be seen from the above literatures and several otherrelated literatures [27ndash32] that there are several commonproblems in study of this field

(1) The articles usually focus on signals emitted fromeither radar or communication systems while electronicwarfare systems in application may receive signals from bothof these systems That is to say the current studied AMCalgorithms lack a universal study on the classification ofthe radar and communication signals simultaneously (2)The changes of the signal parameters are not considered inconstructing the data sample libraries for training and testthough it has been demonstrated that these changes have asignificant influence on the performance of the classificationalgorithms (3) Without exploring the different multifeaturesof the signal modulations the AMC approaches proposed inmany of the open literatures are based on only one featurewhich makes the classification more difficult to implement(4) Most studies overemphasize the use of advanced clas-sification algorithms while ignoring the study on signalfeature extraction techniques [33]The characteristics ofmosttypes of digital modulation used in modern communicationand radar systems have significant differences which can beobtained according to their definitions using certain featureextraction algorithms The lack of these features actuallyincreases the difficulties of the subsequent classificationalgorithms

Different from the above research works this paperemphasizes feature extraction and classification of the radarand communication signal simultaneously Multidimen-sional modulation features in time-frequency domain fre-quency domain and envelope domain and phase domain areextracted with the utilization of a set of feature extractionalgorithms so as to find the differences of signals in differentmodulation asmuch as possible It aims to reduce the pressureof the classification algorithm effectively and improve theclassification accuracy At the same time a multilayer hybrid

classification network is constructed for the classificationexploiting multiple features and its effectiveness to improvethe classification performance is tested by seven types of radarand communication signals commonly used in practicalsystems including BPSK QPSK 16-quadrature amplitudemodulation (16QAM) LFM single frequency (SF) 2FSK and4FSK

The rest of this paper is organized as follows Section 2gives the structure of the hybrid machine learning algorithmand describes the principle of the signal modulation featureextraction and classification network Section 3 analyzesthe feature extraction algorithms for the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK including time-frequency analysis instantaneous auto-correlation (IA) anddiscrete Fourier transform (DFT) Section 4 analyzes theidea of the dimension reduction of the modulation featureswhen using PCA and SVM for classification Performanceevaluation of the feature extraction and classification networkis discussed in Section 5 The Conclusions are drawn inSection 6

2 The Principle of the HybridClassification Network

Aiming at classifying the signal set BPSK QPSK 16QAMLFM SF 2FSK and 4FSK this paper proposes a hybridAMC network consisting of a variety of modulation featureextraction algorithms and machine learning classificationmethodsThe overall framework of the hybrid AMC networkis shown in Figure 2

(1) Classification of SF LFM and BPSK QPSK 16QAM2FSK and 4FSK According to Figure 2 short-time Fouriertransform (STFT) algorithm is used in the first-layer of thenetwork to extract the standard deviation of the first-orderdifference of the time-frequency spectrumpeaks (recorded as1205771) identifying SF LFM from BPSKQPSK 16QAM 2FSKand 4FSK

According to the signal definition of SF and LFM thefirst-order difference in time-frequency spectrum of thesetwo signals is a fixed constant Hence the values of 1205771for these two modulation types are approximately zeroeswhich is quite different from the large 1205771 values of the other

Mathematical Problems in Engineering 3

BPSK QPSK 16QAM LFM SF 2FSK 4FSK

Training set

Time-frequency analysis

SF LFM

Standard deviationof peak first-order

SF LFM BPSK QPSK 16QAM 2FSK 4FSK

Discrete Fourier transform

2FSKStandard deviation

BPSK QPSK 16QAM

4FSK

Instantaneous autocorrelation

Standard deviation of envelopeStandard deviation Zero-crossing ratio

PCA

Two dimensional feature construction

Test set reconfiguration

Projection matrix

Correct recognition rate

Test set



SVM Classifier

BPSK QPSK 16QAM


Positive class QPSK

ClassifierSVM1

ClassifierSVM2

No

Negative class BPSK

Negative class 16QAM

Naive Bayes

Naive Bayes


Second layer classification (left)

Second layer classification(right)

Third layer classification

First layer classification

Peak number3

difference1

3 = 2 3 = 4

2

lt

lt

gt

gt

Figure 2 Diagram of the classification network

signals According to the decision threshold 1205881 which canbe obtained through naive Bayes [34] during the trainingperiod the signal set SF LFM can be identified from theother signals

(2) Classification of SF and LFM The left branch of thesecond-layer of the network implements the classification ofthe signal set SF LFM According to the difference of SFand LFM the standard deviation feature based on the realpart of IA is extracted and recorded as 1205772 LFM and SF can

be classified in terms of the decision threshold 1205882 which canbe obtained by the naive Bayes training

(3) Classification of 2FSK 4FSK and BPSKQPSK16QAM The right branch of the second-layer implementsthe classification of the signal set BPSK QPSK 16QAM2FSK and 4FSK The frequency feature based on DFT isextracted for identification The numbers of frequency peaksof 2FSK and 4FSK are 2 and 4 respectively while the otherthree signals havemultiple frequency peaks in the bandwidth


The number of the frequency peaks is extracted and recordedas 1205773 According to the decision threshold 1205883 which can beobtained by training 2FSK4FSK can be identified from thesignal set BPSK QPSK and 16QAM(4) Classification of BPSK QPSK and 16QAM In thethird-layer of the network the remaining signal set BPSKQPSK 16QAM of the right branch is classified Threefeatures including standard deviation of envelope zero-crossing ratio and standard deviation of the real part of IAare extracted for classification By determining the principalcomponents with the contribution rate PCA algorithm isused to reduce the dimensionality of the features from 3-dimension to two-dimension making it suitable for theapplication of the one-to-one method of SVM RegardingQPSK as a positive class BPSK and 16QAM are sequentiallysubstituted into the SVM classifier as a negative class to findthe support vector Two optimal boundaries are determinedin light of the position of the support vector and theclassification of BPSK QPSK and 16QAM is accomplishedfinally

The classification structure can be regarded as a machinelearning network based on sample training and test It isnecessary to construct a large learning sample aggregate forextracting the modulation features of the above seven signalsand determine the multiple thresholds for the multilayerclassification during the training process In the test phasethe predetermined thresholds are used for different class andthe correct recognition rate of each class is achieved in theend

3 Feature Extraction Algorithms

The extracted modulation features are mainly based on thedifferences of radar and communication signals in time-frequency spectrum frequency spectrum and phase mod-ulation Different algorithms are used to extract differentfeatures for signals of different class The time-frequencyfeature is extracted by using STFT which identifies thesignal set SF LFM from the other signals SF and LFM arediscriminated by the feature of the real part of IA Accordingto the number of frequency peaks which obtained basedon DFT 2FSK and 4FSK are identified from the signal setBPSK QPSK and 16QAM The features based on the realpart of IA are used to distinguish between BPSK QPSKand 16QAM The following section will discuss the featureextraction algorithms including STFT IA and DFT

31 Feature Extraction Based on STFT Time-frequency fea-ture of the signals can be extracted by STFT For a discretesignal 119904(119899) at discrete time instant 119899 its STFT is given by

119878 (119898 119896) = 119873119904minus1sum119899=0

119904 (119899) ℎ (119899 minus 119898) 119890minus119895(2120587119873119904)119899119896119896 = 0 1 2 119873119904 minus 1

(1)

where 119896 represents the discrete frequency and 119873119904 is thetotal frequency number 119898 refers to time delay and ℎ(119899 minus

119898) denotes the Rectangular window function In (1) thenonstationary signal can be regarded as the superpositionof a series of short-time stationary signals which highlightsthe varying characteristics of the original signal frequencywith time delay The peak of the frequency along time delaydimension can be given by

119875 (119898) = max119896

|119878 (119898 119896)| 119898 = 0 1 2 119873 (2)

where119873 denotes the total number of windows and 119875(119898) rep-resents the maximum frequency peak corresponding to the119898th window The frequency peak of each time window canbe extractedThe difference of frequency peak correspondingto two adjacent time windows can be given by

119882 (119898) = 119875 (119898 + 1) minus 119875 (119898) 119898 = 1 2 119873 minus 1 (3)

The standard deviation of the difference in (3) can begiven by

1205771 = radic 1119873 minus 1119873minus1sum119898=1

[119882 (119898) minus 119882]2 (4)

where 119882 refers to the mean of 119882 and 119882 = (1(119873 minus1)) sum119873minus1119898=1119882(119898) The STFT of the seven waveform types withSignal-to-Noise Ratio (SNR) equal to 20 dB are illustrated inFigure 3 As can be seen from Figure 3(a) the frequency ofSF is the same since it has only one frequency The differencebetween the adjacent frequencies for SF is constant so thestandard deviation is zero From Figure 3(b) we can see thatthe frequency of LFM changes linearly which leads to a con-stant difference between the two adjacent frequencies Hencethe standard deviation is also zero Figures 3(c) and 3(d) showthat the frequencies of 2FSK and 4FSK are variable whichmeans that the difference between the adjacent frequenciesis not constant Figures 3(e) 3(f) and 3(g) show that whenthere is a phase variation for BPSK QPSK or 16QAM signalthe instantaneous frequency has a large disturb which leadsto fluctuations between the adjacent frequencies Hence thestandard deviations of the signals such as BPSK QPSK16QAM 2FSK and 4FSK will be larger than those of the SFand LFM In this case SF and LFM can be identified from theother signals by setting the standard deviation threshold 120588132 Feature Extraction Using IA [35] Features based onIA can be extracted to distinguish between SF LFM andBPSK QPSK 16QAM respectively The IA of a discretesignal 119904(119899) is of the following form

119877 (119899 119898) = 119904 (119899) sdot 119904lowast (119899 minus 119898) (5)

where 119898 refers to time delay The difference between thedefinition of IA and auto-correlation function lies in thatthere is no time integration in the calculation of IA Theadvantage of using IA is that it retains the instantaneous phaseinformation of the signal The IA expressions of some of thesignals are analyzed below

(1) The signal of SF is of the following form

1199041 (119899) = 119860119890119895(21205871198910119899+1205930) (6)


minus5

0

5

x 107

05

1015

20minus40minus20

02040

Frequency (Hz)DelaySample point

Am

plitu

de (d

B)

(a) SF

minus50

5

x 107

02

46

810

minus40minus20

02040


Am

plitu

de (d

B)

(b) LFM

minus5

0

5

x 107

010

2030

40minus50

0

50


Am

plitu

de (d

B)

(c) 2FSK

minus5

0

5

x 107

010

2030

40minus50

0

50


Am

plitu

de (d

B)

(d) 4FSK

minus3 minus2 minus1 0 1 2 3

x 107

05

1015

20minus40minus20

02040


Am

plitu

de (d

B)

(e) BPSK


x 107

05

1015

20minus40minus20

02040


Am

plitu

de (d

B)

(f) QPSK

minus3 minus2 minus1 0 1 2 3x 107

05

1015

20minus40minus20

0204060


Am

plitu

de (d

B)

(g) 16QAM

Figure 3 Time-frequency spectrum using STFT

where 119860 is the amplitude of the signal 1198910 refers to the carrierfrequency and 1205930 represents the initial phase of the signalThe real part of IA of SF can be given by

119877 (119899 119898) = 1198602 cos (21205871198910119898) 119898 le 119899 le 119902 (7)

where 119902 is the number of samples of the signal It can be seenfrom (7) that if 119898 is certain the IA of SF is related only to thecarrier frequency which is a constant Hence the output ofthe real part of IA is a direct-current (DC) signal as shown inFigure 4(a)


(2) The signal of LFM is of the following form

1199042 (119899) = 1198601198901198952120587(1198910119899+(12)1205831198992) (8)

where 120583 is the slope of frequency modulation The real partof IA of LFM can be given by

119877 (119899 119898) = 1198602 cos (2120587 (1198910119898 minus 121205831198982 + 120583119898119899)) 119898 le 119899 le 119902 (9)

It can be seen from (9) that the output of the real part of IA isan alternating current (AC) signal of frequency 120583119898 which isshown in Figure 4(b)

(3) The expression of PSK can be given by

1199043 (119899) = 119860119890119895(21205871198910119899+120593119894) (10)

where 120593119894 denotes the discrete phase of a code group repre-senting BPSK or QPSK For BPSK the value of 120593119894 is 0 or 120587For QPSK the value of 120593119894 is 0 1205872 120587 or 31205872 The real partof IA of the PSK signal is of the following form

119877 (119899 119898) = 1198602 cos (21205871198910119898) 119894119901 + 119898 lt 119899 le (119894 + 1) 119901119877 (119899 119898) = 1198602 cos (21205871198910119898 + 120593119894+1 minus 120593119894)

(119894 + 1) 119901 lt 119899 le (119894 + 1) 119901 + 119898(11)

where119901 is the number of samples within one code and119898 lt 119901The real part of IA is DC within the same code period Indifferent code period it can be divided into two cases theadjacent code is the same (120593119894+1minus120593119894 = 0) or different (120593119894+1minus120593119894 =0) For BPSK shown in Figure 4(c) the real part of IA is atwo-value transition of which 120593119894+1 minus 120593119894 = 0 correspondsto a positive transitions and 120593119894+1 minus 120593119894 = plusmn120587 correspondsto a negative transition However there is a status of 120593119894+1 minus120593119894 = plusmn1205872 for QPSK for which the real part of IA is zero(the projection on the real axis) Therefore the real part ofIA for QPSK is a three-value output which is illustrated inFigure 4(d)

(4) The signal of 16QAMcan be expressed as

1199044 (119899) = 119860 119894119890119895(21205871198910119899+120593119894) (12)

where 119860 119894 refers to the amplitude of the code group The realpart of IA of 16QAM is of the following form

119877 (119899 119898) = 1198602 cos (21205871198910119898) 119894119901 + 119898 lt 119899 le (119894 + 1) 119901119877 (119899 119898) = 119860 119894+1119860 119894 cos (21205871198910119898 + 120593119894+1 minus 120593119894)

(119894 + 1) 119901 lt 119899 le (119894 + 1) 119901 + 119898(13)

From (13) we can see that when 119898 is constant the outputof IA is DC in the same code period However it causesa phase jump 120593119894+1 minus 120593119894 and amplitude transition 119860 119894+1 sdot 119860 119894between different code period Hence the output of the IAfor 16QAM is a multivalue transition see Figure 4(e)

Two features are extracted based on the real part of theIA

Feature 1 Define the standard deviation of IA as

1205772 = radic 1119873119904119873119904sum119894=1

(119886 (119894) minus 119886)2 (14)

where 119886(119894) is the value of the real part based on IA at timeinstant 119894 and 119886 = (1119873119904) sum119873119904119894=1 119886(119894) represents the mean of119886(119894) The standard deviation for SF signal will be small sincethe fluctuation of its IA is small However the IA of LFMfluctuates greatly ie the standard deviation is larger Underthis circumstance SF and LFM can be identified by settingthe standard deviation threshold 1205882 of the real part of IAFeature 2 Define zero-crossing ratio as

1205774 = Num 119886 (119894) isin 1205761 (15)

where Numsdot denotes a counter and 1205761 refers to a smallrange belonging to zero (such as minus0001 lt 1205761 lt 0001) Asshown in the Figure 4 a binary jump occurs for the IA ofBPSK meaning that there is no zero in the output Howeverthe IA of QPSK is of a three-value transition form with alarge number of zeroes in the output The IA of 16QAM issimilar to QPSK Therefore the difference of zero-crossingratio between BPSK and QPSK 16QAM signals can be usedas a classification feature

33 Feature Extraction Based on DFT For the remainingsignal set BPSKQPSK 16QAM 2FSK 4FSK the frequencyspectrum features of the signals are extracted using DFTAccording to the signal definitions the peaks of 2FSKand 4FSK are 2 and 4 within the bandwidth respectivelyHowever there are much more peaks for BPSK QPSK and16QAM

Since frequency peaks of the signal set BPSK QPSK16QAM 2FSK and 4FSK are different the number offrequency peaks based on DFT can be extracted as a typicalfeature For a discrete signal 119904(119899) its DFT can be given by

119891 (119896) = 119873119904minus1sum119899=0

119904 (119899) 119890minus119895(2120587119873119904)119899119896 119896 = 0 1 2 119873119904 minus 1 (16)

where 119896 represents the discrete frequency and 119873119904 is the totalfrequency number The number of peak can be defined as

1205773 = Num 1003816100381610038161003816119891 (119896)1003816100381610038161003816 gt 1205762 119896 = 0 1 2 119873119904 minus 1 (17)

where | sdot | refers to the modulo operation and 1205762 the thresholdof frequency peak taking 07 times of the maximum valueSince the number of peaks of 2FSK and 4FSK is smaller thanthe other three signals 2FSK and 4FSK can be identified fromother signals by setting the frequency peak threshold 1205883


0

02

04

06

08

1

12

14A

mpl

itude

1000 2000 3000 4000 50000Sample point

(a) SF

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(b) LFM

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(c) BPSK

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(d) QPSK

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Am

plitu

de

1000 2000 3000 4000 50000Sample point

(e) 16QAM

Figure 4 The real part of IA of the signals

34 Feature Extraction Based on Signal Envelope The mul-tilevel amplitude of the 16QAM signal is quite differentfrom the constant envelope BPSK and QPSK signal Henceenvelope features in time domain can be used to classifyBPSK QPSK and 16QAM For a discrete signal 119904(119899) the

standard deviation of the envelope can be defined as

1205775 = radic 1119873119904119873119878sum119899=1

|119904 (119899)| minus 119904]2 (18)


where 119904 = (1119873119904) sum119873119904119894=1 |119904(119894)| represents the mean of theinstantaneous envelope

4 Analysis of SVM Based on PCADimensionality Reduction

Three features are extracted for the classification of BPSKQPSK and 16QAM so as to ensure the classification accuracyunder various conditions Due to the large number offeatures the classification tends to be complicated If thethree features can be replaced by the two features SVM canbe used to classify the three modulated signals in the Two-dimensional (2D) feature space Therefore PCA algorithm isused to perform principal component analysis on the Three-dimensional (3D) features extracting principal componentsin features and reducing the dimension of features

41 PCA Algorithm The PCA algorithm transforms theoriginal data with possible correlation into a set of newdata with linear independence of each dimension throughlinear transformation and it can be used to extract theprincipal feature components of the data thereby achievingthe purpose of dimensionality reduction [36] The main ideais to map the 1198961 dimensional features to 1198962 dimension (1198962 lt1198961) which is a completely new orthogonal feature called theprincipal component It can be easily understood that PCAcan be used to find the most useful linear combination iethose new features with relatively large discrimination toachieve the purpose of reducing the dimension

There are two basic requirements for PCA dimensionalityreduction First of all the projections of the samples in theprincipal component direction are required to be as dispersedas possible The more dispersed projections the larger thevariance of the samples ie more useful information iscarried in the reduced dimension projections Secondly thedistances from the sample points to the principal componentdirection are required to be as small as possible ie the errorscan be reduced as much as possible The steps of the PCAdimensionality reduction algorithm [37] for 1198961-dimensionalmodulation feature samples are summarized as follows

(1) Arrange the modulation feature samples into matrixX of 119872 (sample numbers) rows and 1198961 columns

(2) Process the sample data recorded as 119883 includingzero-meanization and normalization

(3) For the processed sample data its covariance matrixcan be given by

119877119909 = 1119872 (119883119879119883) (19)

where [sdot]119879 refers to transposition operation(4) According to

119877119909119906 = 120582119906 (20)

calculate the eigenvalue 120582119894 and the eigenvector 119906119894of 119877119909 Arrange the eigenvalues from large to small

Positive classQPSK

ClassifierSVM1

ClassifierSVM2

Negative classBPSK

Negative class16QAM

QPSK BPSK QPSK 16QAM

Figure 5 Three-class classification of SVM based on one-to-onemethod

and the corresponding eigenvectors are also arrangedfrom large to small

(5) The contribution rate is defined as

120573 = sum1198962119894=1 120582119894sum1198961119894=1 120582119894 (21)

where 1198961 is the original sample data dimension and1198962 is the sample data dimension after dimensionalityreductionThe newmatrix 119861 (119861 = [1199061 sdot sdot sdot 1199061198962]) calledprojection matrix is composed of the feature vectorscorresponding to the first 1198962 eigenvalues

(6) Determine the projection data of the original featuredata in the projection matrix and then its principalcomponent can be given by

119909 = 119883119861 (22)

42 One-to-One Multiclassification Method Based on SVMSVM is originally an effective binary-class classificationmethod and its basic model is defined as a linear classifierwith largest interval in feature space For multiclassificationproblems SVM can also achieve classification in an one-to-many mode one-to-one mode etc In this paper the one-to-one mode of SVM is employed due to its simplicity Theflowchart for three-class classification using SVM based onone-to-one method is shown in Figure 5 and it will be usedto classify BPSK QPSK and 16QAM

The basic classification principle of SVM is summarizedbelow The discriminant function of implementing SVM isgiven by [38]

119892 (119909) = 119910119894 (119908119879119909 + 119887) (23)

where 119909 is the training sample input after dimensionalityreduction using PCA 119908 refers to a weight vector 119910119894(plusmn1)denotes a category label and 119887 is an offset Its interval is givenby

120575119894 = 119910119894 (119908119879119909 + 119887) = 10038161003816100381610038161003816119908119879119909 + 11988710038161003816100381610038161003816 = 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (24)


Its geometric interval is given by

119889 = 1119908 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (25)

The purpose of SVM is to find the optimal 1199080 and1198870 which is to maximize the geometric interval 119889 ie tominimize 119908 The problem can be transformed into

min119908

12 1199082119904119905 119910119894 [(119908119879119909119894 + 119887)] ge 1 119894 = 1 2 119872 (26)

where 119909119894 is a vector in 119909 = [11990911199092 119909119872]119879 ApplyingLagrange multiplication into (26) then we get

119871 (119908 119887 120572) = 12 (119908119879119908)minus 119872sum119894=1

120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)

where 119886119894 denotes a nonnegative Lagrange multiplier Calcu-late partial derivative of 119908 and 119887 respectively and make themequal to zero then we get

119908 = 119872sum119894=1

120572119894119910119894119909119894119872sum119894=1

120572119894119910119894 = 0(28)

Convert it to a dual problem and the target signal can be givenby

min120572

12119872sum119894=1

119872sum119895=1

120572119894120572119895119910119894119910119895119909119894119879119909119895 minus 119872sum119895=1

120572119895119904119905 119872sum

119895=1

120572119895119910119895 = 0120572119894 ge 0

(29)

According to (29) the optimal Lagrangemultiplier 1205720119894 can beobtained Then optimal weight 1199080 can be given by

1199080 = 119872sum119894=1

1205720119894119910119894119909119894 (30)

Furthermore according to 119892(119909) = 119908119879119909+ 119887 = ∓1 the optimalbias can be given by

1198870 = 119910119894 minus 119872sum119894=1

1205720119894119910119894119909119894119879119909 (31)

Finally the objective function of the optimal classification canbe given by

119892 (119909) = sign (119908119879119909 + 1198870)= sign(119872sum

119894=1

1205720119894119910119894119909119894119879119909 + 1198870) (32)

where sign(sdot) is a symbolic function It can be seen from theabove analysis that the determination of the optimal weightvector is determined only by the optimal Lagrange multiplierthe training samples and their categories The position ofthe support vector and the offset are determined throughtraining using the 2D feature data processed by PCA Finallythe optimal classification boundary is found to achieve thecorrect classification for the test samples

The objective of classifying BPSK QPSK and 16QAMcan be accomplished using the above classification process asdepicted in Figure 5 By specifying a signal as a positive classthe rest of the other two signals are treated as negative classesand finally the one-to-one method is used to classify themultiple signals Through the above feature analysis QPSKcan be designated as a positive class and BPSK and 16QAMare sequentially regarded as a negative class The basic SVMis used for twice to make the two optimal classificationboundaries which can accurately identify the three signalsto achieve the classification

5 Simulation Analysis

51 Performance Analysis without Fading Channel Effect

511 Simulation Setup In order to verify the performanceof the hybrid classifying network we did the followingsimulations including training phase and testing phaseAs known to all bandwidth code rate and SNR have amuch more significant influence on the signal features incomparison with sampling frequency and carrier frequencyHence the signal classes for training and testing are simulatedby changing BW CR and SNR instead of FS and FC forsimplicity In the training phase the SNRs of the seventypes of modulated signals are set to [10dB 20dB 30dB]respectively and the total number of samples is set to 5000The timing offset is 01120583s The parameters for different kindsof signals are shown in Table 1 where TW BW CR FCand FS stand for time-width bandwidth code rate carrierfrequency and sample frequency respectively There are 450data segments serving as sample data for each type of signalmodulation

512 Setting the resholds and Optimal Boundary Lines Inthe first-layer of the network the standard deviation featuresof the difference of the frequency peaks based on STFTare extracted and shown in Figure 6 Since SF has onlyone frequency the difference between adjacent frequenciesis approximately zero Hence the standard deviation arealso nearly zeros For LFM with linear frequency variationthe difference between the adjacent frequencies is constantleading to a zero value standard deviation For 2FSK and4FSK the difference between the adjacent frequencies leadsto large standard deviations For the remaining BPSK QPSKand 16QAM with phase jumps fluctuations in the differencebetween adjacent frequencies are the main reasons for largestandard deviations

Through training the standard deviation threshold 1205881isset as 04 according to the naive Bayesian algorithm [34] As


Table 1 Parameters for different types of modulated signals

Signal type TW120583s BWMHz CRMHz FCMHz FSMHzPSKs 25 1016204080 58102040 60 20016QAM 25 1016204080 58102040 60 200SF 50 002 - 10 100LFM 50 1020304050 - 10 1002FSK 50 1214182230 124610 1020 1004FSK 50 3234384250 124610 10203040 100

BPSKQPSK16QAM2FSK

4FSKSFLFM

0

2

4

6

8

10

12

14

16

18

20

Stan

dard

dev

iatio

n of

pea

k fre

quen

cy d

iffer

ence

500 1000 1500 2000 2500 3000 35000Sample number

Figure 6 Standard deviation of the difference of the STFT peak

shown in Figure 6 2FSK 4FSK BPSK QPSK and 16QAMis above the boundary line and SF LFM is below theboundary line

In the left-branch of the second-layer training standarddeviation characteristics based on the real part of IA areextracted to classify SF and LFMThe real part of IA of SF is aDC level whereas LFM corresponds to an AC signal Hencethe standard deviation between the two types of modulationis quite different as shown in Figure 7 Through training thethreshold 1205882 of standard deviation of the real part of IA canbe set to 052 according to the naive Bayesian algorithm Asshown in Figure 7 LFM is above the boundary line whereasSF is below the boundary line

In the right-branch of the second-layer the remainingsignal set BPSK QPSK 16QAM 2FSK and 4FSK is classi-fied by the features based on DFTBPSK QPSK and 16QAMhave multiple peaks within the bandwidth and the numberof peaks increases from 20 to 340 when the BW increasesas shown in Figure 8 However the peak numbers of 2FSKand 4FSK are distributed around 2 and 4 respectively whichmeans that the thresholds 1205883 can be set to 2 and 4 In this case2FSK and 4FSK can be identified from the signal set BPSKQPSK and QAM

SFLFM

0

01

02

03

04

05

06

07

08

Stan

dard

dev

iatio

n of

enve

lope

100 200 300 400 500 600 700 800 9000Sample number

Figure 7 Standard deviation of real part of IA of SF and LFM

2FSK4FSKBPSK

QPSK16QAM

0

50

100

150

200

250

300

350

Peak

num

ber

500 1000 1500 2000 25000Sample number

Figure 8 Peak numbers of the signal classes

In the third-layer of the network the signal set BPSKQPSK and 16QAM is trained by multiclassification methodof SVM based on PCA feature dimension reduction

The main features employed include standard deviationof the envelope zero-crossing ratio of the IA and standard


BPSKQPSK16QAM

QPSK 16QAM

BPSK

10dB

20dB

30dB

10dB10dB

20dB20dB

30dB

30dB0

005

01

015

02

025

03

035

04

045

05N

umbe

r rat

io o

ver z

ero

poin

t

200 400 600 800 1000 1200 14000Sample number

Figure 9 Zero-crossing ratio

BPSKQPSK16QAM

16QAM

BPSK

10dB

20dB

20dB

10dB

10dB

30dB

30dB 30dB

20dB

QPSK

01

02

03

04

05

06

07

08

09

Stan

dard

dev

iatio

n of

the r

eal p

art o

f IA

200 400 600 800 1000 1200 14000Sample number

Figure 10 Standard deviation of the real part of IA

deviation of the IA As can be seen from Figures 9ndash11 thedistinguishing characteristics of the signals are much moreobvious with the increase of the SNR The 3D features areanalyzed using PCA to make dimension degradation FromFigure 12 we can see that the contribution rate is still over97 after the dimensions reduces to 2D It indicates that thenew 2D features can reflect more than 97 of the original 3Dfeatures In other words the new 2D features can replace theoriginal 3D features with little loss

The new 2D feature data is used as the training setand the one-to-one method is substituted into the SVM forclassification The first step is to classify BPSK and QPSK IfQPSK is specified as a positive class then BPSK is used asa negative class The 2D new features of the two signals aresubstituted into the basic SVM for training The positions of

BPSKQPSK16QAM

16QAM

QPSK

20dB

10dB 10dB

10dB

20dB

20dB 30dB

30dB 30dB

BPSK

0

005

01

015

02

025

Stan

dard

dev

iatio

n of

enve

lope

200 400 600 800 1000 1200 14000Sample number

Figure 11 Standard deviation of envelope

0

02

04

06

08

1

12C

ontr

ibut

ion

rate

05 1 15 2 25 30Characteristic number

Figure 12 Characteristic of the contribution rate

the support vectors (the positions of the circles in Figure 13)are found thereby determining the optimal boundary 1According to the optimal boundary 1 the recognition ofBPSK and QPSK is attained The second step is to classifyQPSK and 16QAM If QPSK is specified as a positive classthen 16QAM is used as a negative class The 2D new featuresof the two signal classes are substituted into the basic SVMfor training The optimal boundary 2 is determined after thepositions of the support vectors are found According to theoptimal boundary 2 the recognition of QPSK and 16QAMare obtained The classification results are shown in Figure 13fromwhich we can see that BPSK QPSK and 16QAM can beaccurately identified by the two optimal boundary lines

513 Performance Analysis During the testing phase thecorrect recognition rates of the signal set BPSK QPSK16QAM LFM SF 2FSK and 4FSK at different SNRs areshown in Table 2 It can be seen from Table 2 that the correctrecognition rate of the signals improves with the increase of


Table 2 Correct recognition rate at different SNRs

Signal type SNR=10dB SNR=15dB SNR=20dB SNR=25dB SNR=30dBSF 9520 9782 9840 9920 9999LFM 9442 9580 9650 9760 98502FSK 9650 9820 9840 9950 99674FSK 9600 9750 9820 9867 9880BPSK 9430 9520 9623 9920 9947QPSK 9400 9478 9528 9726 986516QAM 9428 9512 9600 9830 9926

Table 3 Correct recognition rate at different SNRs with fading channel


the SNR Under the scenario of SNR=10dB the proposednetwork provides a correct recognition rate of over 94The results indicate that the classification performance of theproposed hybrid machine learning network is superior indiscriminating between the modulated signal candidates inthis paper

52 Performance Analysis under Fading Channel ConditionsMultipath effect of a channel usually leads to serious distor-tion on the received signal causing serious degradation onthe AMC algorithm A fading channel is taken into accountto analyze the performance of the proposed classificationnetwork in this simulation The received signal model in thefading channel circumstance can be written as

119911 (119899) = 119871minus1sum119896=0

ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)

where 119904(119899) is the transmitted signal 119903(119899) is the additive whiteGaussian noise and ℎ(119896) 119896 = 0 1 119871 minus 1 are the 119871fading channel coefficients The channel ℎ(119896) is considerednonrandom and assumed to be Rayleigh fading The channelcoefficients are randomly generated with variance 005 in thesimulation except for ℎ(0) = 1 Other simulation conditionsare the same as the above simulation

The correct recognition rates of the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK at different SNRsunder fading channel are shown in Table 3 Compared withTable 2 the correct recognition rate of each signal decreasesSF and LFM go down a bit just about 1 while 2FSKand 4FSK fall approximately 2 Especially the descendingvalue of BPSK QPSK and 16QAM can reach about 6 Theresult of the comparison indicates that the performance ofthe classification network in fading channel has a slighterdecrease than the scenarios without a fading channel

BPSKQPSK

16QAMSupport vector

16QAM

QPSK

BPSK

Optimum boundary 2

Support vector

Optimum boundary 1

minus2 minus1 0 1 2minus3First principal component characteristic

minus2

minus15

minus1

minus05

0

05

1

15

2

25

3

Seco

nd p

rinci

pal c

ompo

nent

char

acte

ristic

Figure 13 Three-class classification based on SVM

53 Performance Comparison with Algorithm in [9] Theclassification of QAM signal in the third layer is an importantpart in the proposed network whereas diversemethodologieshave been explored in how to classify the QAM signalclass The AMC algorithm based on high-order cyclosta-tionarity proposed in [9] is a classic algorithm for QAMsignal classification and has good classification effect andsuperior performance This paper applies the second-orderinstantaneous autocorrelation algorithm to realize AMC andits performance is compared with the one in [9]

The adopted signals include BPSK QPSK and 16QAMFigure 14 plots the total recognition performance of BPSKQPSK and 16QAM of the proposed algorithm and that of


Algorithm in [9]Proposed algorithm

075

08

085

09

095

1C

orre

ct re

cogn

ition

rate

5 10 15 20 250SNR (dB)

Figure 14 Comparison of correct recognition

the algorithm in [9] A comparison of these curves showsthat the two algorithms have similar performance in classi-fication The advantage of the instantaneous autocorrelationis less complexity in comparison with that of the high-ordercyclostationarity approach

6 Conclusion

This paper proposes an AMC network for the classifica-tion of radar and communication signals In general athree-layer classification network is employed consistingof a series of feature extraction and classification methodssuch as STFT DFT IA PCA SVM and naive Bayesianalgorithm Through the training of the large sample datathe setting of the classification thresholds of the machinelearning algorithms is automatically realized During thesample construction process the comprehensive coverage ofsignal samples is attained by changing the key parameterssuch as code rate and bandwidth The simulation resultsshow that the correct recognition rate of the seven typesof modulated signals can reach over 94 at SNR of 10dBand above if channel distortion is not considered For fadingchannel scenarios a degradation of the correct recognitionrate of about 6 is observed as a performance comparisonstudy

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was partially supported by the FundamentalResearch Funds for the Central Universities (Grant no2015B03014) and the Natural Science Foundation of JiangsuProvince (Grant no BK20151501)

References

[1] S Ayazgok C Erdem M T Ozturk A Orduyilmaz and MSerin ldquoAutomatic antenna scan type classification for next-generation electronic warfare receiversrdquo IET Radar Sonar ampNavigation vol 12 no 4 pp 466ndash474 2018

[2] C L Zhang and X N Yang ldquoResearch on the CognitiveElectronic Warfare and Cognitive Electronic Warfare SystemrdquoJournal of China Academy of Electronics amp Information Technol-ogy vol 9 no 6 pp 551ndash555 2014

[3] K Dabcevic M O Mughal L Marcenaro and C S RegazzonildquoCognitive Radio as the Facilitator for Advanced Communica-tions Electronic Warfare Solutionsrdquo Journal of Signal ProcessingSystems vol 83 no 1 pp 29ndash44 2016

[4] Z L Fan G S Zhu and H U Yuan-Kui ldquoAn Overview ofCognitive Electronic Warfarerdquo Electronic Information WarfareTechnology vol 30 no 1 pp 33ndash38 2015

[5] E E Azzouz and A K Nandi Automatic Modulation Recogni-tion of Communication Signals Springer US Boston MA 1996

[6] O A Dobre A Abdi Y Bar-Ness and W Su ldquoSurveyof automatic modulation classification techniques classicalapproaches and new trendsrdquo IET Communications vol 1 no2 pp 137ndash156 2007

[7] OADobre A Abdi Y Bar-Ness andW Su ldquoBlindmodulationclassification a concept whose time has comerdquo in Proceedings ofthe IEEESarnoff Symposium on Advances inWired andWirelessCommunication pp 223ndash228 April 2005

[8] D Zeng X Zeng G Lu and B Tang ldquoAutomatic modula-tion classification of radar signals using the generalised time-frequency representation of Zhao Atlas andMarksrdquo IET RadarSonar amp Navigation vol 5 no 4 pp 507ndash516 2011

[9] OADobreM Oner S Rajan andR Inkol ldquoCyclostationarity-based robust algorithms for QAM signal identificationrdquo IEEECommunications Letters vol 16 no 1 pp 12ndash15 2012

[10] HWang O ADobre C Li and R Inkol ldquoM-FSK signal recog-nition in fading channels for cognitive radiordquo in Proceedings ofthe 2012 6th IEEE Radio and Wireless Week RWW 2012 - 2012IEEE Radio and Wireless Symposium RWS 2012 pp 375ndash378USA January 2012

[11] H Wang O A Dobre C Li and D C Popescu ldquoBlindCyclostationarity-Based Symbol Period Estimation for FSKSignalsrdquo IEEE Communications Letters vol 19 no 7 pp 1149ndash1152 2015

[12] 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

[13] G Wannberg A Pellinen-Wannberg and A Westman ldquoAnambiguity-function-based method for analysis of Dopplerdecompressed radar signals applied to EISCAT measurementsof oblique UHF-VHFmeteor echoesrdquo Radio Science vol 31 no3 pp 497ndash518 1996

[14] Y LinX-CXu andZ-CWang ldquoNew individual identificationmethod of radiation source signal based on entropy feature and


SVMrdquo Journal of Harbin Institute of Technology (New Series)vol 21 no 1 pp 98ndash101 2014

[15] Z Luo L Liu J Yin Y Li and ZWu ldquoDeep learning of graphswith ngram convolutional neural networksrdquo IEEE Transactionson Knowledge and Data Engineering vol 29 no 10 pp 2125ndash2139 2017

[16] Z Jiang J Wang Q Song and Z Zhou ldquoA Refined Cluster-Analysis-Based Multibaseline Phase-Unwrapping AlgorithmrdquoIEEE Geoscience and Remote Sensing Letters vol 14 no 9 pp1565ndash1569 2017

[17] S HaoWWang Y Ye E Li and L Bruzzone ldquoADeepNetworkArchitecture for Super-Resolution-Aided Hyperspectral ImageClassification With Classwise Lossrdquo IEEE Transactions on Geo-science and Remote Sensing vol 56 no 8 pp 4650ndash4663 2018

[18] Y Wei W Xia M Lin et al ldquoHCP A flexible CNN frameworkfor multi-label image classificationrdquo IEEE Transactions onPattern Analysis and Machine Intelligence vol 38 no 9 pp1901ndash1907 2016

[19] J Pei Y Huang W Huo Y Zhang J Yang and T-S YeoldquoSAR automatic target recognition based on multiview deeplearning frameworkrdquo IEEE Transactions on Geoscience andRemote Sensing vol 56 no 4 pp 2196ndash2210 2018

[20] Q Guo P Nan X Zhang Y Zhao and J Wan ldquoRecognition ofradar emitter signals based on SVD and AF main ridge slicerdquoJournal of Communications and Networks vol 17 no 5 pp 491ndash498 2015

[21] D Zeng X Zeng H Cheng and B Tang ldquoAutomatic modu-lation classification of radar signals using the Rihaczek distri-bution and Hough transformrdquo IET Radar Sonar amp Navigationvol 6 no 5 pp 322ndash331 2012

[22] B Feng andY Lin ldquoRadar signal recognition based onmanifoldlearning methodrdquo International Journal of Control and Automa-tion vol 7 no 12 pp 399ndash406 2014

[23] S Huang Y Yao Z Wei Z Feng and P Zhang ldquoAutomaticModulation Classification of Overlapped Sources Using Multi-ple Cumulantsrdquo IEEETransactions on VehicularTechnology vol66 no 7 pp 6089ndash6101 2017

[24] L Wang and Y Ren ldquoRecognition of digital modulation signalsbased on high order cumulants and support vector machinesrdquoin Proceedings of the 2009 ISECS International Colloquiumon Computing Communication Control and Management(CCCM) pp 271ndash274 Sanya China August 2009

[25] H Bai Y-J Zhao and D-X Hu ldquoRadar signal recognitionbased on the local binary pattern feature of time-frequencyimagerdquo Yuhang XuebaoJournal of Astronautics vol 34 no 1pp 139ndash146 2013

[26] M W Aslam Z Zhu and A K Nandi ldquoAutomatic modulationclassification using combination of genetic programming andKNNrdquo IEEE Transactions on Wireless Communications vol 11no 8 pp 2742ndash2750 2012

[27] J Chorowski and J M Zurada ldquoLearning understandableneural networks with nonnegative weight constraintsrdquo IEEETransactions on Neural Networks and Learning Systems vol 26no 1 pp 62ndash69 2015

[28] J L Xu W Su and M Zhou ldquoLikelihood-ratio approaches toautomaticmodulation classificationrdquo IEEE Transactions on Sys-tems Man and Cybernetics Part C Applications and Reviewsvol 41 no 4 pp 455ndash469 2011

[29] X Yan G Liu H Wu and G Feng ldquoNew Automatic Modu-lation Classifier Using Cyclic-Spectrum Graphs With OptimalTraining Featuresrdquo IEEE Communications Letters vol 22 no 6pp 1204ndash1207 2018

[30] J L Xu W Su and M Zhou ldquoDistributed automatic modula-tion classification with multiple sensorsrdquo IEEE Sensors Journalvol 10 no 11 pp 1779ndash1785 2010

[31] H Abuella and M K Ozdemir ldquoAutomatic Modulation Classi-fication Based onKernelDensity EstimationrdquoCanadian Journalof Electrical and Computer Engineering vol 39 no 3 pp 203ndash209 2016

[32] F Wang O A Dobre C Chan and J Zhang ldquoFold-basedKolmogorov-Smirnov Modulation Classifierrdquo IEEE Signal Pro-cessing Letters vol 23 no 7 pp 1003ndash1007 2016

[33] 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

[34] M O Mughal and S Kim ldquoSignal Classification and JammingDetection in Wide-Band Radios Using Naıve Bayes ClassifierrdquoIEEE Communications Letters vol 22 no 7 pp 1398ndash1401 2018

[35] D X Liu and G Q Zhao ldquoAnalysis of Pulse ModulationSignalsrdquoModern Radar vol 25 no 11 pp 17ndash20 2003

[36] M S Muhlhaus M Oner O A Dobre and F K Jondral ldquoAlow complexity modulation classification algorithm for MIMOsystemsrdquo IEEE Communications Letters vol 17 no 10 pp 1881ndash1884 2013

[37] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010

[38] S Ertekin L Bottou and C L Giles ldquoNonconvex online sup-port vector machinesrdquo IEEE Transactions on Pattern Analysisand Machine Intelligence vol 33 no 2 pp 368ndash381 2011

Hindawiwwwhindawicom Volume 2018

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Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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Dierential EquationsInternational Journal of

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Submit your manuscripts atwwwhindawicom


Received signals Signature of modulation Modulation classifier

Support vector machineDeep learning

Feature extraction

Time frequency analysisFourth order cumulant

Figure 1 The structure of an AMC system for radar and communication signal surveillance

keying (QPSK) 2FSK and 4-frequency shift keying (4FSK)[25] gives the modulation feature by the exploitation of atype of time-frequency image method based on local binarymode and identifies the radar signals by SVM algorithm In[26] genetic programming is carried out for extracting usefulfeatures and the nearest neighbor algorithm is selected forthe classification of certain types of radar signals

It can be seen from the above literatures and several otherrelated literatures [27ndash32] that there are several commonproblems in study of this field

(1) The articles usually focus on signals emitted fromeither radar or communication systems while electronicwarfare systems in application may receive signals from bothof these systems That is to say the current studied AMCalgorithms lack a universal study on the classification ofthe radar and communication signals simultaneously (2)The changes of the signal parameters are not considered inconstructing the data sample libraries for training and testthough it has been demonstrated that these changes have asignificant influence on the performance of the classificationalgorithms (3) Without exploring the different multifeaturesof the signal modulations the AMC approaches proposed inmany of the open literatures are based on only one featurewhich makes the classification more difficult to implement(4) Most studies overemphasize the use of advanced clas-sification algorithms while ignoring the study on signalfeature extraction techniques [33]The characteristics ofmosttypes of digital modulation used in modern communicationand radar systems have significant differences which can beobtained according to their definitions using certain featureextraction algorithms The lack of these features actuallyincreases the difficulties of the subsequent classificationalgorithms

Different from the above research works this paperemphasizes feature extraction and classification of the radarand communication signal simultaneously Multidimen-sional modulation features in time-frequency domain fre-quency domain and envelope domain and phase domain areextracted with the utilization of a set of feature extractionalgorithms so as to find the differences of signals in differentmodulation asmuch as possible It aims to reduce the pressureof the classification algorithm effectively and improve theclassification accuracy At the same time a multilayer hybrid

classification network is constructed for the classificationexploiting multiple features and its effectiveness to improvethe classification performance is tested by seven types of radarand communication signals commonly used in practicalsystems including BPSK QPSK 16-quadrature amplitudemodulation (16QAM) LFM single frequency (SF) 2FSK and4FSK

The rest of this paper is organized as follows Section 2gives the structure of the hybrid machine learning algorithmand describes the principle of the signal modulation featureextraction and classification network Section 3 analyzesthe feature extraction algorithms for the signal set BPSKQPSK 16QAM LFM SF 2FSK and 4FSK including time-frequency analysis instantaneous auto-correlation (IA) anddiscrete Fourier transform (DFT) Section 4 analyzes theidea of the dimension reduction of the modulation featureswhen using PCA and SVM for classification Performanceevaluation of the feature extraction and classification networkis discussed in Section 5 The Conclusions are drawn inSection 6

2 The Principle of the HybridClassification Network

Aiming at classifying the signal set BPSK QPSK 16QAMLFM SF 2FSK and 4FSK this paper proposes a hybridAMC network consisting of a variety of modulation featureextraction algorithms and machine learning classificationmethodsThe overall framework of the hybrid AMC networkis shown in Figure 2

(1) Classification of SF LFM and BPSK QPSK 16QAM2FSK and 4FSK According to Figure 2 short-time Fouriertransform (STFT) algorithm is used in the first-layer of thenetwork to extract the standard deviation of the first-orderdifference of the time-frequency spectrumpeaks (recorded as1205771) identifying SF LFM from BPSKQPSK 16QAM 2FSKand 4FSK

According to the signal definition of SF and LFM thefirst-order difference in time-frequency spectrum of thesetwo signals is a fixed constant Hence the values of 1205771for these two modulation types are approximately zeroeswhich is quite different from the large 1205771 values of the other



Training set


SF LFM





BPSK QPSK 16QAM

4FSK



PCA



Projection matrix


Test set



SVM Classifier

BPSK QPSK 16QAM


Positive class QPSK

ClassifierSVM1

ClassifierSVM2

No

Negative class BPSK


Naive Bayes

Naive Bayes






Peak number3

difference1

3 = 2 3 = 4

2

lt

lt

gt

gt












119878 (119898 119896) = 119873119904minus1sum119899=0


(1)



119875 (119898) = max119896

|119878 (119898 119896)| 119898 = 0 1 2 119873 (2)


119882 (119898) = 119875 (119898 + 1) minus 119875 (119898) 119898 = 1 2 119873 minus 1 (3)



[119882 (119898) minus 119882]2 (4)





1199041 (119899) = 119860119890119895(21205871198910119899+1205930) (6)


minus5

0

5

x 107

05

1015

20minus40minus20

02040


Am

plitu

de (d

B)

(a) SF

minus50

5

x 107

02

46

810

minus40minus20

02040


Am

plitu

de (d

B)

(b) LFM

minus5

0

5

x 107

010

2030

40minus50

0

50


Am

plitu

de (d

B)

(c) 2FSK

minus5

0

5

x 107

010

2030

40minus50

0

50


Am

plitu

de (d

B)

(d) 4FSK


x 107

05

1015

20minus40minus20

02040


Am

plitu

de (d

B)

(e) BPSK


x 107

05

1015

20minus40minus20

02040


Am

plitu

de (d

B)

(f) QPSK


05

1015

20minus40minus20

0204060


Am

plitu

de (d

B)

(g) 16QAM



119877 (119899 119898) = 1198602 cos (21205871198910119898) 119898 le 119899 le 119902 (7)




1199042 (119899) = 1198601198901198952120587(1198910119899+(12)1205831198992) (8)


119877 (119899 119898) = 1198602 cos (2120587 (1198910119898 minus 121205831198982 + 120583119898119899)) 119898 le 119899 le 119902 (9)



1199043 (119899) = 119860119890119895(21205871198910119899+120593119894) (10)



(119894 + 1) 119901 lt 119899 le (119894 + 1) 119901 + 119898(11)



1199044 (119899) = 119860 119894119890119895(21205871198910119899+120593119894) (12)



(119894 + 1) 119901 lt 119899 le (119894 + 1) 119901 + 119898(13)




1205772 = radic 1119873119904119873119904sum119894=1

(119886 (119894) minus 119886)2 (14)


1205774 = Num 119886 (119894) isin 1205761 (15)




119891 (119896) = 119873119904minus1sum119899=0

119904 (119899) 119890minus119895(2120587119873119904)119899119896 119896 = 0 1 2 119873119904 minus 1 (16)


1205773 = Num 1003816100381610038161003816119891 (119896)1003816100381610038161003816 gt 1205762 119896 = 0 1 2 119873119904 minus 1 (17)



0

02

04

06

08

1

12

14A

mpl

itude

1000 2000 3000 4000 50000Sample point

(a) SF

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(b) LFM

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(c) BPSK

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(d) QPSK

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Am

plitu

de

1000 2000 3000 4000 50000Sample point

(e) 16QAM




1205775 = radic 1119873119904119873119878sum119899=1

|119904 (119899)| minus 119904]2 (18)










119877119909 = 1119872 (119883119879119883) (19)


119877119909119906 = 120582119906 (20)


Positive classQPSK

ClassifierSVM1

ClassifierSVM2

Negative classBPSK

Negative class16QAM





120573 = sum1198962119894=1 120582119894sum1198961119894=1 120582119894 (21)



119909 = 119883119861 (22)



119892 (119909) = 119910119894 (119908119879119909 + 119887) (23)


120575119894 = 119910119894 (119908119879119909 + 119887) = 10038161003816100381610038161003816119908119879119909 + 11988710038161003816100381610038161003816 = 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (24)



119889 = 1119908 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (25)


min119908

12 1199082119904119905 119910119894 [(119908119879119909119894 + 119887)] ge 1 119894 = 1 2 119872 (26)


119871 (119908 119887 120572) = 12 (119908119879119908)minus 119872sum119894=1

120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)


119908 = 119872sum119894=1

120572119894119910119894119909119894119872sum119894=1

120572119894119910119894 = 0(28)


min120572

12119872sum119894=1

119872sum119895=1

120572119894120572119895119910119894119910119895119909119894119879119909119895 minus 119872sum119895=1

120572119895119904119905 119872sum

119895=1

120572119895119910119895 = 0120572119894 ge 0

(29)


1199080 = 119872sum119894=1

1205720119894119910119894119909119894 (30)


1198870 = 119910119894 minus 119872sum119894=1

1205720119894119910119894119909119894119879119909 (31)


119892 (119909) = sign (119908119879119909 + 1198870)= sign(119872sum

119894=1

1205720119894119910119894119909119894119879119909 + 1198870) (32)











BPSKQPSK16QAM2FSK

4FSKSFLFM

0

2

4

6

8

10

12

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16

18

20

Stan

dard

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ence

500 1000 1500 2000 2500 3000 35000Sample number





SFLFM

0

01

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08

Stan

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n of

enve

lope

100 200 300 400 500 600 700 800 9000Sample number


2FSK4FSKBPSK

QPSK16QAM

0

50

100

150

200

250

300

350

Peak

num

ber

500 1000 1500 2000 25000Sample number





BPSKQPSK16QAM

QPSK 16QAM

BPSK

10dB

20dB

30dB

10dB10dB

20dB20dB

30dB

30dB0

005

01

015

02

025

03

035

04

045

05N

umbe

r rat

io o

ver z

ero

poin

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BPSKQPSK16QAM

16QAM

BPSK

10dB

20dB

20dB

10dB

10dB

30dB

30dB 30dB

20dB

QPSK

01

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Stan

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BPSKQPSK16QAM

16QAM

QPSK

20dB

10dB 10dB

10dB

20dB

20dB 30dB

30dB 30dB

BPSK

0

005

01

015

02

025

Stan

dard

dev

iatio

n of

enve

lope

200 400 600 800 1000 1200 14000Sample number


0

02

04

06

08

1

12C

ontr

ibut

ion

rate












119911 (119899) = 119871minus1sum119896=0

ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)



BPSKQPSK

16QAMSupport vector

16QAM

QPSK

BPSK

Optimum boundary 2

Support vector

Optimum boundary 1


minus2

minus15

minus1

minus05

0

05

1

15

2

25

3

Seco

nd p

rinci

pal c

ompo

nent

char

acte

ristic






075

08

085

09

095

1C

orre

ct re

cogn

ition

rate

5 10 15 20 250SNR (dB)



6 Conclusion


Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018










Training set


SF LFM





BPSK QPSK 16QAM

4FSK



PCA



Projection matrix


Test set



SVM Classifier

BPSK QPSK 16QAM


Positive class QPSK

ClassifierSVM1

ClassifierSVM2

No

Negative class BPSK


Naive Bayes

Naive Bayes






Peak number3

difference1

3 = 2 3 = 4

2

lt

lt

gt

gt












119878 (119898 119896) = 119873119904minus1sum119899=0


(1)



119875 (119898) = max119896

|119878 (119898 119896)| 119898 = 0 1 2 119873 (2)


119882 (119898) = 119875 (119898 + 1) minus 119875 (119898) 119898 = 1 2 119873 minus 1 (3)



[119882 (119898) minus 119882]2 (4)





1199041 (119899) = 119860119890119895(21205871198910119899+1205930) (6)


minus5

0

5

x 107

05

1015

20minus40minus20

02040


Am

plitu

de (d

B)

(a) SF

minus50

5

x 107

02

46

810

minus40minus20

02040


Am

plitu

de (d

B)

(b) LFM

minus5

0

5

x 107

010

2030

40minus50

0

50


Am

plitu

de (d

B)

(c) 2FSK

minus5

0

5

x 107

010

2030

40minus50

0

50


Am

plitu

de (d

B)

(d) 4FSK


x 107

05

1015

20minus40minus20

02040


Am

plitu

de (d

B)

(e) BPSK


x 107

05

1015

20minus40minus20

02040


Am

plitu

de (d

B)

(f) QPSK


05

1015

20minus40minus20

0204060


Am

plitu

de (d

B)

(g) 16QAM



119877 (119899 119898) = 1198602 cos (21205871198910119898) 119898 le 119899 le 119902 (7)




1199042 (119899) = 1198601198901198952120587(1198910119899+(12)1205831198992) (8)


119877 (119899 119898) = 1198602 cos (2120587 (1198910119898 minus 121205831198982 + 120583119898119899)) 119898 le 119899 le 119902 (9)



1199043 (119899) = 119860119890119895(21205871198910119899+120593119894) (10)



(119894 + 1) 119901 lt 119899 le (119894 + 1) 119901 + 119898(11)



1199044 (119899) = 119860 119894119890119895(21205871198910119899+120593119894) (12)



(119894 + 1) 119901 lt 119899 le (119894 + 1) 119901 + 119898(13)




1205772 = radic 1119873119904119873119904sum119894=1

(119886 (119894) minus 119886)2 (14)


1205774 = Num 119886 (119894) isin 1205761 (15)




119891 (119896) = 119873119904minus1sum119899=0

119904 (119899) 119890minus119895(2120587119873119904)119899119896 119896 = 0 1 2 119873119904 minus 1 (16)


1205773 = Num 1003816100381610038161003816119891 (119896)1003816100381610038161003816 gt 1205762 119896 = 0 1 2 119873119904 minus 1 (17)



0

02

04

06

08

1

12

14A

mpl

itude

1000 2000 3000 4000 50000Sample point

(a) SF

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(b) LFM

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(c) BPSK

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(d) QPSK

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Am

plitu

de

1000 2000 3000 4000 50000Sample point

(e) 16QAM




1205775 = radic 1119873119904119873119878sum119899=1

|119904 (119899)| minus 119904]2 (18)










119877119909 = 1119872 (119883119879119883) (19)


119877119909119906 = 120582119906 (20)


Positive classQPSK

ClassifierSVM1

ClassifierSVM2

Negative classBPSK

Negative class16QAM





120573 = sum1198962119894=1 120582119894sum1198961119894=1 120582119894 (21)



119909 = 119883119861 (22)



119892 (119909) = 119910119894 (119908119879119909 + 119887) (23)


120575119894 = 119910119894 (119908119879119909 + 119887) = 10038161003816100381610038161003816119908119879119909 + 11988710038161003816100381610038161003816 = 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (24)



119889 = 1119908 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (25)


min119908

12 1199082119904119905 119910119894 [(119908119879119909119894 + 119887)] ge 1 119894 = 1 2 119872 (26)


119871 (119908 119887 120572) = 12 (119908119879119908)minus 119872sum119894=1

120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)


119908 = 119872sum119894=1

120572119894119910119894119909119894119872sum119894=1

120572119894119910119894 = 0(28)


min120572

12119872sum119894=1

119872sum119895=1

120572119894120572119895119910119894119910119895119909119894119879119909119895 minus 119872sum119895=1

120572119895119904119905 119872sum

119895=1

120572119895119910119895 = 0120572119894 ge 0

(29)


1199080 = 119872sum119894=1

1205720119894119910119894119909119894 (30)


1198870 = 119910119894 minus 119872sum119894=1

1205720119894119910119894119909119894119879119909 (31)


119892 (119909) = sign (119908119879119909 + 1198870)= sign(119872sum

119894=1

1205720119894119910119894119909119894119879119909 + 1198870) (32)











BPSKQPSK16QAM2FSK

4FSKSFLFM

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500 1000 1500 2000 2500 3000 35000Sample number





SFLFM

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n of

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lope

100 200 300 400 500 600 700 800 9000Sample number


2FSK4FSKBPSK

QPSK16QAM

0

50

100

150

200

250

300

350

Peak

num

ber

500 1000 1500 2000 25000Sample number





BPSKQPSK16QAM

QPSK 16QAM

BPSK

10dB

20dB

30dB

10dB10dB

20dB20dB

30dB

30dB0

005

01

015

02

025

03

035

04

045

05N

umbe

r rat

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ver z

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poin

t

200 400 600 800 1000 1200 14000Sample number


BPSKQPSK16QAM

16QAM

BPSK

10dB

20dB

20dB

10dB

10dB

30dB

30dB 30dB

20dB

QPSK

01

02

03

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09

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the r

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f IA

200 400 600 800 1000 1200 14000Sample number




BPSKQPSK16QAM

16QAM

QPSK

20dB

10dB 10dB

10dB

20dB

20dB 30dB

30dB 30dB

BPSK

0

005

01

015

02

025

Stan

dard

dev

iatio

n of

enve

lope

200 400 600 800 1000 1200 14000Sample number


0

02

04

06

08

1

12C

ontr

ibut

ion

rate












119911 (119899) = 119871minus1sum119896=0

ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)



BPSKQPSK

16QAMSupport vector

16QAM

QPSK

BPSK

Optimum boundary 2

Support vector

Optimum boundary 1


minus2

minus15

minus1

minus05

0

05

1

15

2

25

3

Seco

nd p

rinci

pal c

ompo

nent

char

acte

ristic






075

08

085

09

095

1C

orre

ct re

cogn

ition

rate

5 10 15 20 250SNR (dB)



6 Conclusion


Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018














119878 (119898 119896) = 119873119904minus1sum119899=0


(1)



119875 (119898) = max119896

|119878 (119898 119896)| 119898 = 0 1 2 119873 (2)


119882 (119898) = 119875 (119898 + 1) minus 119875 (119898) 119898 = 1 2 119873 minus 1 (3)



[119882 (119898) minus 119882]2 (4)





1199041 (119899) = 119860119890119895(21205871198910119899+1205930) (6)


minus5

0

5

x 107

05

1015

20minus40minus20

02040


Am

plitu

de (d

B)

(a) SF

minus50

5

x 107

02

46

810

minus40minus20

02040


Am

plitu

de (d

B)

(b) LFM

minus5

0

5

x 107

010

2030

40minus50

0

50


Am

plitu

de (d

B)

(c) 2FSK

minus5

0

5

x 107

010

2030

40minus50

0

50


Am

plitu

de (d

B)

(d) 4FSK


x 107

05

1015

20minus40minus20

02040


Am

plitu

de (d

B)

(e) BPSK


x 107

05

1015

20minus40minus20

02040


Am

plitu

de (d

B)

(f) QPSK


05

1015

20minus40minus20

0204060


Am

plitu

de (d

B)

(g) 16QAM



119877 (119899 119898) = 1198602 cos (21205871198910119898) 119898 le 119899 le 119902 (7)




1199042 (119899) = 1198601198901198952120587(1198910119899+(12)1205831198992) (8)


119877 (119899 119898) = 1198602 cos (2120587 (1198910119898 minus 121205831198982 + 120583119898119899)) 119898 le 119899 le 119902 (9)



1199043 (119899) = 119860119890119895(21205871198910119899+120593119894) (10)



(119894 + 1) 119901 lt 119899 le (119894 + 1) 119901 + 119898(11)



1199044 (119899) = 119860 119894119890119895(21205871198910119899+120593119894) (12)



(119894 + 1) 119901 lt 119899 le (119894 + 1) 119901 + 119898(13)




1205772 = radic 1119873119904119873119904sum119894=1

(119886 (119894) minus 119886)2 (14)


1205774 = Num 119886 (119894) isin 1205761 (15)




119891 (119896) = 119873119904minus1sum119899=0

119904 (119899) 119890minus119895(2120587119873119904)119899119896 119896 = 0 1 2 119873119904 minus 1 (16)


1205773 = Num 1003816100381610038161003816119891 (119896)1003816100381610038161003816 gt 1205762 119896 = 0 1 2 119873119904 minus 1 (17)



0

02

04

06

08

1

12

14A

mpl

itude

1000 2000 3000 4000 50000Sample point

(a) SF

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(b) LFM

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(c) BPSK

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(d) QPSK

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Am

plitu

de

1000 2000 3000 4000 50000Sample point

(e) 16QAM




1205775 = radic 1119873119904119873119878sum119899=1

|119904 (119899)| minus 119904]2 (18)










119877119909 = 1119872 (119883119879119883) (19)


119877119909119906 = 120582119906 (20)


Positive classQPSK

ClassifierSVM1

ClassifierSVM2

Negative classBPSK

Negative class16QAM





120573 = sum1198962119894=1 120582119894sum1198961119894=1 120582119894 (21)



119909 = 119883119861 (22)



119892 (119909) = 119910119894 (119908119879119909 + 119887) (23)


120575119894 = 119910119894 (119908119879119909 + 119887) = 10038161003816100381610038161003816119908119879119909 + 11988710038161003816100381610038161003816 = 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (24)



119889 = 1119908 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (25)


min119908

12 1199082119904119905 119910119894 [(119908119879119909119894 + 119887)] ge 1 119894 = 1 2 119872 (26)


119871 (119908 119887 120572) = 12 (119908119879119908)minus 119872sum119894=1

120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)


119908 = 119872sum119894=1

120572119894119910119894119909119894119872sum119894=1

120572119894119910119894 = 0(28)


min120572

12119872sum119894=1

119872sum119895=1

120572119894120572119895119910119894119910119895119909119894119879119909119895 minus 119872sum119895=1

120572119895119904119905 119872sum

119895=1

120572119895119910119895 = 0120572119894 ge 0

(29)


1199080 = 119872sum119894=1

1205720119894119910119894119909119894 (30)


1198870 = 119910119894 minus 119872sum119894=1

1205720119894119910119894119909119894119879119909 (31)


119892 (119909) = sign (119908119879119909 + 1198870)= sign(119872sum

119894=1

1205720119894119910119894119909119894119879119909 + 1198870) (32)











BPSKQPSK16QAM2FSK

4FSKSFLFM

0

2

4

6

8

10

12

14

16

18

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Stan

dard

dev

iatio

n of

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quen

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ence

500 1000 1500 2000 2500 3000 35000Sample number





SFLFM

0

01

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07

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Stan

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dev

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n of

enve

lope

100 200 300 400 500 600 700 800 9000Sample number


2FSK4FSKBPSK

QPSK16QAM

0

50

100

150

200

250

300

350

Peak

num

ber

500 1000 1500 2000 25000Sample number





BPSKQPSK16QAM

QPSK 16QAM

BPSK

10dB

20dB

30dB

10dB10dB

20dB20dB

30dB

30dB0

005

01

015

02

025

03

035

04

045

05N

umbe

r rat

io o

ver z

ero

poin

t

200 400 600 800 1000 1200 14000Sample number


BPSKQPSK16QAM

16QAM

BPSK

10dB

20dB

20dB

10dB

10dB

30dB

30dB 30dB

20dB

QPSK

01

02

03

04

05

06

07

08

09

Stan

dard

dev

iatio

n of

the r

eal p

art o

f IA

200 400 600 800 1000 1200 14000Sample number




BPSKQPSK16QAM

16QAM

QPSK

20dB

10dB 10dB

10dB

20dB

20dB 30dB

30dB 30dB

BPSK

0

005

01

015

02

025

Stan

dard

dev

iatio

n of

enve

lope

200 400 600 800 1000 1200 14000Sample number


0

02

04

06

08

1

12C

ontr

ibut

ion

rate












119911 (119899) = 119871minus1sum119896=0

ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)



BPSKQPSK

16QAMSupport vector

16QAM

QPSK

BPSK

Optimum boundary 2

Support vector

Optimum boundary 1


minus2

minus15

minus1

minus05

0

05

1

15

2

25

3

Seco

nd p

rinci

pal c

ompo

nent

char

acte

ristic






075

08

085

09

095

1C

orre

ct re

cogn

ition

rate

5 10 15 20 250SNR (dB)



6 Conclusion


Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018









minus5

0

5

x 107

05

1015

20minus40minus20

02040


Am

plitu

de (d

B)

(a) SF

minus50

5

x 107

02

46

810

minus40minus20

02040


Am

plitu

de (d

B)

(b) LFM

minus5

0

5

x 107

010

2030

40minus50

0

50


Am

plitu

de (d

B)

(c) 2FSK

minus5

0

5

x 107

010

2030

40minus50

0

50


Am

plitu

de (d

B)

(d) 4FSK


x 107

05

1015

20minus40minus20

02040


Am

plitu

de (d

B)

(e) BPSK


x 107

05

1015

20minus40minus20

02040


Am

plitu

de (d

B)

(f) QPSK


05

1015

20minus40minus20

0204060


Am

plitu

de (d

B)

(g) 16QAM



119877 (119899 119898) = 1198602 cos (21205871198910119898) 119898 le 119899 le 119902 (7)




1199042 (119899) = 1198601198901198952120587(1198910119899+(12)1205831198992) (8)


119877 (119899 119898) = 1198602 cos (2120587 (1198910119898 minus 121205831198982 + 120583119898119899)) 119898 le 119899 le 119902 (9)



1199043 (119899) = 119860119890119895(21205871198910119899+120593119894) (10)



(119894 + 1) 119901 lt 119899 le (119894 + 1) 119901 + 119898(11)



1199044 (119899) = 119860 119894119890119895(21205871198910119899+120593119894) (12)



(119894 + 1) 119901 lt 119899 le (119894 + 1) 119901 + 119898(13)




1205772 = radic 1119873119904119873119904sum119894=1

(119886 (119894) minus 119886)2 (14)


1205774 = Num 119886 (119894) isin 1205761 (15)




119891 (119896) = 119873119904minus1sum119899=0

119904 (119899) 119890minus119895(2120587119873119904)119899119896 119896 = 0 1 2 119873119904 minus 1 (16)


1205773 = Num 1003816100381610038161003816119891 (119896)1003816100381610038161003816 gt 1205762 119896 = 0 1 2 119873119904 minus 1 (17)



0

02

04

06

08

1

12

14A

mpl

itude

1000 2000 3000 4000 50000Sample point

(a) SF

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(b) LFM

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(c) BPSK

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

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(d) QPSK

minus08

minus06

minus04

minus02

0

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04

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1

Am

plitu

de

1000 2000 3000 4000 50000Sample point

(e) 16QAM




1205775 = radic 1119873119904119873119878sum119899=1

|119904 (119899)| minus 119904]2 (18)










119877119909 = 1119872 (119883119879119883) (19)


119877119909119906 = 120582119906 (20)


Positive classQPSK

ClassifierSVM1

ClassifierSVM2

Negative classBPSK

Negative class16QAM





120573 = sum1198962119894=1 120582119894sum1198961119894=1 120582119894 (21)



119909 = 119883119861 (22)



119892 (119909) = 119910119894 (119908119879119909 + 119887) (23)


120575119894 = 119910119894 (119908119879119909 + 119887) = 10038161003816100381610038161003816119908119879119909 + 11988710038161003816100381610038161003816 = 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (24)



119889 = 1119908 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (25)


min119908

12 1199082119904119905 119910119894 [(119908119879119909119894 + 119887)] ge 1 119894 = 1 2 119872 (26)


119871 (119908 119887 120572) = 12 (119908119879119908)minus 119872sum119894=1

120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)


119908 = 119872sum119894=1

120572119894119910119894119909119894119872sum119894=1

120572119894119910119894 = 0(28)


min120572

12119872sum119894=1

119872sum119895=1

120572119894120572119895119910119894119910119895119909119894119879119909119895 minus 119872sum119895=1

120572119895119904119905 119872sum

119895=1

120572119895119910119895 = 0120572119894 ge 0

(29)


1199080 = 119872sum119894=1

1205720119894119910119894119909119894 (30)


1198870 = 119910119894 minus 119872sum119894=1

1205720119894119910119894119909119894119879119909 (31)


119892 (119909) = sign (119908119879119909 + 1198870)= sign(119872sum

119894=1

1205720119894119910119894119909119894119879119909 + 1198870) (32)











BPSKQPSK16QAM2FSK

4FSKSFLFM

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2FSK4FSKBPSK

QPSK16QAM

0

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Peak

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ber

500 1000 1500 2000 25000Sample number





BPSKQPSK16QAM

QPSK 16QAM

BPSK

10dB

20dB

30dB

10dB10dB

20dB20dB

30dB

30dB0

005

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BPSKQPSK16QAM

16QAM

BPSK

10dB

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20dB

10dB

10dB

30dB

30dB 30dB

20dB

QPSK

01

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BPSKQPSK16QAM

16QAM

QPSK

20dB

10dB 10dB

10dB

20dB

20dB 30dB

30dB 30dB

BPSK

0

005

01

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200 400 600 800 1000 1200 14000Sample number


0

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1

12C

ontr

ibut

ion

rate












119911 (119899) = 119871minus1sum119896=0

ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)



BPSKQPSK

16QAMSupport vector

16QAM

QPSK

BPSK

Optimum boundary 2

Support vector

Optimum boundary 1


minus2

minus15

minus1

minus05

0

05

1

15

2

25

3

Seco

nd p

rinci

pal c

ompo

nent

char

acte

ristic






075

08

085

09

095

1C

orre

ct re

cogn

ition

rate

5 10 15 20 250SNR (dB)



6 Conclusion


Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018










1199042 (119899) = 1198601198901198952120587(1198910119899+(12)1205831198992) (8)


119877 (119899 119898) = 1198602 cos (2120587 (1198910119898 minus 121205831198982 + 120583119898119899)) 119898 le 119899 le 119902 (9)



1199043 (119899) = 119860119890119895(21205871198910119899+120593119894) (10)



(119894 + 1) 119901 lt 119899 le (119894 + 1) 119901 + 119898(11)



1199044 (119899) = 119860 119894119890119895(21205871198910119899+120593119894) (12)



(119894 + 1) 119901 lt 119899 le (119894 + 1) 119901 + 119898(13)




1205772 = radic 1119873119904119873119904sum119894=1

(119886 (119894) minus 119886)2 (14)


1205774 = Num 119886 (119894) isin 1205761 (15)




119891 (119896) = 119873119904minus1sum119899=0

119904 (119899) 119890minus119895(2120587119873119904)119899119896 119896 = 0 1 2 119873119904 minus 1 (16)


1205773 = Num 1003816100381610038161003816119891 (119896)1003816100381610038161003816 gt 1205762 119896 = 0 1 2 119873119904 minus 1 (17)



0

02

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1

12

14A

mpl

itude

1000 2000 3000 4000 50000Sample point

(a) SF

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(b) LFM

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(c) BPSK

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(d) QPSK

minus08

minus06

minus04

minus02

0

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04

06

08

1

Am

plitu

de

1000 2000 3000 4000 50000Sample point

(e) 16QAM




1205775 = radic 1119873119904119873119878sum119899=1

|119904 (119899)| minus 119904]2 (18)










119877119909 = 1119872 (119883119879119883) (19)


119877119909119906 = 120582119906 (20)


Positive classQPSK

ClassifierSVM1

ClassifierSVM2

Negative classBPSK

Negative class16QAM





120573 = sum1198962119894=1 120582119894sum1198961119894=1 120582119894 (21)



119909 = 119883119861 (22)



119892 (119909) = 119910119894 (119908119879119909 + 119887) (23)


120575119894 = 119910119894 (119908119879119909 + 119887) = 10038161003816100381610038161003816119908119879119909 + 11988710038161003816100381610038161003816 = 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (24)



119889 = 1119908 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (25)


min119908

12 1199082119904119905 119910119894 [(119908119879119909119894 + 119887)] ge 1 119894 = 1 2 119872 (26)


119871 (119908 119887 120572) = 12 (119908119879119908)minus 119872sum119894=1

120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)


119908 = 119872sum119894=1

120572119894119910119894119909119894119872sum119894=1

120572119894119910119894 = 0(28)


min120572

12119872sum119894=1

119872sum119895=1

120572119894120572119895119910119894119910119895119909119894119879119909119895 minus 119872sum119895=1

120572119895119904119905 119872sum

119895=1

120572119895119910119895 = 0120572119894 ge 0

(29)


1199080 = 119872sum119894=1

1205720119894119910119894119909119894 (30)


1198870 = 119910119894 minus 119872sum119894=1

1205720119894119910119894119909119894119879119909 (31)


119892 (119909) = sign (119908119879119909 + 1198870)= sign(119872sum

119894=1

1205720119894119910119894119909119894119879119909 + 1198870) (32)











BPSKQPSK16QAM2FSK

4FSKSFLFM

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SFLFM

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2FSK4FSKBPSK

QPSK16QAM

0

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Peak

num

ber

500 1000 1500 2000 25000Sample number





BPSKQPSK16QAM

QPSK 16QAM

BPSK

10dB

20dB

30dB

10dB10dB

20dB20dB

30dB

30dB0

005

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03

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BPSKQPSK16QAM

16QAM

BPSK

10dB

20dB

20dB

10dB

10dB

30dB

30dB 30dB

20dB

QPSK

01

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BPSKQPSK16QAM

16QAM

QPSK

20dB

10dB 10dB

10dB

20dB

20dB 30dB

30dB 30dB

BPSK

0

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0

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rate












119911 (119899) = 119871minus1sum119896=0

ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)



BPSKQPSK

16QAMSupport vector

16QAM

QPSK

BPSK

Optimum boundary 2

Support vector

Optimum boundary 1


minus2

minus15

minus1

minus05

0

05

1

15

2

25

3

Seco

nd p

rinci

pal c

ompo

nent

char

acte

ristic






075

08

085

09

095

1C

orre

ct re

cogn

ition

rate

5 10 15 20 250SNR (dB)



6 Conclusion


Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018









0

02

04

06

08

1

12

14A

mpl

itude

1000 2000 3000 4000 50000Sample point

(a) SF

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(b) LFM

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

1

15

Am

plitu

de

(c) BPSK

1000 2000 3000 4000 50000Sample point

minus15

minus1

minus05

0

05

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Am

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(d) QPSK

minus08

minus06

minus04

minus02

0

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06

08

1

Am

plitu

de

1000 2000 3000 4000 50000Sample point

(e) 16QAM




1205775 = radic 1119873119904119873119878sum119899=1

|119904 (119899)| minus 119904]2 (18)










119877119909 = 1119872 (119883119879119883) (19)


119877119909119906 = 120582119906 (20)


Positive classQPSK

ClassifierSVM1

ClassifierSVM2

Negative classBPSK

Negative class16QAM





120573 = sum1198962119894=1 120582119894sum1198961119894=1 120582119894 (21)



119909 = 119883119861 (22)



119892 (119909) = 119910119894 (119908119879119909 + 119887) (23)


120575119894 = 119910119894 (119908119879119909 + 119887) = 10038161003816100381610038161003816119908119879119909 + 11988710038161003816100381610038161003816 = 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (24)



119889 = 1119908 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (25)


min119908

12 1199082119904119905 119910119894 [(119908119879119909119894 + 119887)] ge 1 119894 = 1 2 119872 (26)


119871 (119908 119887 120572) = 12 (119908119879119908)minus 119872sum119894=1

120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)


119908 = 119872sum119894=1

120572119894119910119894119909119894119872sum119894=1

120572119894119910119894 = 0(28)


min120572

12119872sum119894=1

119872sum119895=1

120572119894120572119895119910119894119910119895119909119894119879119909119895 minus 119872sum119895=1

120572119895119904119905 119872sum

119895=1

120572119895119910119895 = 0120572119894 ge 0

(29)


1199080 = 119872sum119894=1

1205720119894119910119894119909119894 (30)


1198870 = 119910119894 minus 119872sum119894=1

1205720119894119910119894119909119894119879119909 (31)


119892 (119909) = sign (119908119879119909 + 1198870)= sign(119872sum

119894=1

1205720119894119910119894119909119894119879119909 + 1198870) (32)











BPSKQPSK16QAM2FSK

4FSKSFLFM

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SFLFM

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2FSK4FSKBPSK

QPSK16QAM

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ber

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BPSKQPSK16QAM

QPSK 16QAM

BPSK

10dB

20dB

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10dB10dB

20dB20dB

30dB

30dB0

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BPSKQPSK16QAM

16QAM

BPSK

10dB

20dB

20dB

10dB

10dB

30dB

30dB 30dB

20dB

QPSK

01

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BPSKQPSK16QAM

16QAM

QPSK

20dB

10dB 10dB

10dB

20dB

20dB 30dB

30dB 30dB

BPSK

0

005

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0

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119911 (119899) = 119871minus1sum119896=0

ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)



BPSKQPSK

16QAMSupport vector

16QAM

QPSK

BPSK

Optimum boundary 2

Support vector

Optimum boundary 1


minus2

minus15

minus1

minus05

0

05

1

15

2

25

3

Seco

nd p

rinci

pal c

ompo

nent

char

acte

ristic






075

08

085

09

095

1C

orre

ct re

cogn

ition

rate

5 10 15 20 250SNR (dB)



6 Conclusion


Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018

















119877119909 = 1119872 (119883119879119883) (19)


119877119909119906 = 120582119906 (20)


Positive classQPSK

ClassifierSVM1

ClassifierSVM2

Negative classBPSK

Negative class16QAM





120573 = sum1198962119894=1 120582119894sum1198961119894=1 120582119894 (21)



119909 = 119883119861 (22)



119892 (119909) = 119910119894 (119908119879119909 + 119887) (23)


120575119894 = 119910119894 (119908119879119909 + 119887) = 10038161003816100381610038161003816119908119879119909 + 11988710038161003816100381610038161003816 = 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (24)



119889 = 1119908 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (25)


min119908

12 1199082119904119905 119910119894 [(119908119879119909119894 + 119887)] ge 1 119894 = 1 2 119872 (26)


119871 (119908 119887 120572) = 12 (119908119879119908)minus 119872sum119894=1

120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)


119908 = 119872sum119894=1

120572119894119910119894119909119894119872sum119894=1

120572119894119910119894 = 0(28)


min120572

12119872sum119894=1

119872sum119895=1

120572119894120572119895119910119894119910119895119909119894119879119909119895 minus 119872sum119895=1

120572119895119904119905 119872sum

119895=1

120572119895119910119895 = 0120572119894 ge 0

(29)


1199080 = 119872sum119894=1

1205720119894119910119894119909119894 (30)


1198870 = 119910119894 minus 119872sum119894=1

1205720119894119910119894119909119894119879119909 (31)


119892 (119909) = sign (119908119879119909 + 1198870)= sign(119872sum

119894=1

1205720119894119910119894119909119894119879119909 + 1198870) (32)











BPSKQPSK16QAM2FSK

4FSKSFLFM

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SFLFM

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2FSK4FSKBPSK

QPSK16QAM

0

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ber

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BPSKQPSK16QAM

QPSK 16QAM

BPSK

10dB

20dB

30dB

10dB10dB

20dB20dB

30dB

30dB0

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BPSKQPSK16QAM

16QAM

BPSK

10dB

20dB

20dB

10dB

10dB

30dB

30dB 30dB

20dB

QPSK

01

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BPSKQPSK16QAM

16QAM

QPSK

20dB

10dB 10dB

10dB

20dB

20dB 30dB

30dB 30dB

BPSK

0

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119911 (119899) = 119871minus1sum119896=0

ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)



BPSKQPSK

16QAMSupport vector

16QAM

QPSK

BPSK

Optimum boundary 2

Support vector

Optimum boundary 1


minus2

minus15

minus1

minus05

0

05

1

15

2

25

3

Seco

nd p

rinci

pal c

ompo

nent

char

acte

ristic






075

08

085

09

095

1C

orre

ct re

cogn

ition

rate

5 10 15 20 250SNR (dB)



6 Conclusion


Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018










119889 = 1119908 1003816100381610038161003816119892 (119909)1003816100381610038161003816 (25)


min119908

12 1199082119904119905 119910119894 [(119908119879119909119894 + 119887)] ge 1 119894 = 1 2 119872 (26)


119871 (119908 119887 120572) = 12 (119908119879119908)minus 119872sum119894=1

120572119894 119910119894 [(119908119879119909119894 + 119887)] minus 1 (27)


119908 = 119872sum119894=1

120572119894119910119894119909119894119872sum119894=1

120572119894119910119894 = 0(28)


min120572

12119872sum119894=1

119872sum119895=1

120572119894120572119895119910119894119910119895119909119894119879119909119895 minus 119872sum119895=1

120572119895119904119905 119872sum

119895=1

120572119895119910119895 = 0120572119894 ge 0

(29)


1199080 = 119872sum119894=1

1205720119894119910119894119909119894 (30)


1198870 = 119910119894 minus 119872sum119894=1

1205720119894119910119894119909119894119879119909 (31)


119892 (119909) = sign (119908119879119909 + 1198870)= sign(119872sum

119894=1

1205720119894119910119894119909119894119879119909 + 1198870) (32)











BPSKQPSK16QAM2FSK

4FSKSFLFM

0

2

4

6

8

10

12

14

16

18

20

Stan

dard

dev

iatio

n of

pea

k fre

quen

cy d

iffer

ence

500 1000 1500 2000 2500 3000 35000Sample number





SFLFM

0

01

02

03

04

05

06

07

08

Stan

dard

dev

iatio

n of

enve

lope

100 200 300 400 500 600 700 800 9000Sample number


2FSK4FSKBPSK

QPSK16QAM

0

50

100

150

200

250

300

350

Peak

num

ber

500 1000 1500 2000 25000Sample number





BPSKQPSK16QAM

QPSK 16QAM

BPSK

10dB

20dB

30dB

10dB10dB

20dB20dB

30dB

30dB0

005

01

015

02

025

03

035

04

045

05N

umbe

r rat

io o

ver z

ero

poin

t

200 400 600 800 1000 1200 14000Sample number


BPSKQPSK16QAM

16QAM

BPSK

10dB

20dB

20dB

10dB

10dB

30dB

30dB 30dB

20dB

QPSK

01

02

03

04

05

06

07

08

09

Stan

dard

dev

iatio

n of

the r

eal p

art o

f IA

200 400 600 800 1000 1200 14000Sample number




BPSKQPSK16QAM

16QAM

QPSK

20dB

10dB 10dB

10dB

20dB

20dB 30dB

30dB 30dB

BPSK

0

005

01

015

02

025

Stan

dard

dev

iatio

n of

enve

lope

200 400 600 800 1000 1200 14000Sample number


0

02

04

06

08

1

12C

ontr

ibut

ion

rate












119911 (119899) = 119871minus1sum119896=0

ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)



BPSKQPSK

16QAMSupport vector

16QAM

QPSK

BPSK

Optimum boundary 2

Support vector

Optimum boundary 1


minus2

minus15

minus1

minus05

0

05

1

15

2

25

3

Seco

nd p

rinci

pal c

ompo

nent

char

acte

ristic






075

08

085

09

095

1C

orre

ct re

cogn

ition

rate

5 10 15 20 250SNR (dB)



6 Conclusion


Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018











BPSKQPSK16QAM2FSK

4FSKSFLFM

0

2

4

6

8

10

12

14

16

18

20

Stan

dard

dev

iatio

n of

pea

k fre

quen

cy d

iffer

ence

500 1000 1500 2000 2500 3000 35000Sample number





SFLFM

0

01

02

03

04

05

06

07

08

Stan

dard

dev

iatio

n of

enve

lope

100 200 300 400 500 600 700 800 9000Sample number


2FSK4FSKBPSK

QPSK16QAM

0

50

100

150

200

250

300

350

Peak

num

ber

500 1000 1500 2000 25000Sample number





BPSKQPSK16QAM

QPSK 16QAM

BPSK

10dB

20dB

30dB

10dB10dB

20dB20dB

30dB

30dB0

005

01

015

02

025

03

035

04

045

05N

umbe

r rat

io o

ver z

ero

poin

t

200 400 600 800 1000 1200 14000Sample number


BPSKQPSK16QAM

16QAM

BPSK

10dB

20dB

20dB

10dB

10dB

30dB

30dB 30dB

20dB

QPSK

01

02

03

04

05

06

07

08

09

Stan

dard

dev

iatio

n of

the r

eal p

art o

f IA

200 400 600 800 1000 1200 14000Sample number




BPSKQPSK16QAM

16QAM

QPSK

20dB

10dB 10dB

10dB

20dB

20dB 30dB

30dB 30dB

BPSK

0

005

01

015

02

025

Stan

dard

dev

iatio

n of

enve

lope

200 400 600 800 1000 1200 14000Sample number


0

02

04

06

08

1

12C

ontr

ibut

ion

rate












119911 (119899) = 119871minus1sum119896=0

ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)



BPSKQPSK

16QAMSupport vector

16QAM

QPSK

BPSK

Optimum boundary 2

Support vector

Optimum boundary 1


minus2

minus15

minus1

minus05

0

05

1

15

2

25

3

Seco

nd p

rinci

pal c

ompo

nent

char

acte

ristic






075

08

085

09

095

1C

orre

ct re

cogn

ition

rate

5 10 15 20 250SNR (dB)



6 Conclusion


Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018









BPSKQPSK16QAM

QPSK 16QAM

BPSK

10dB

20dB

30dB

10dB10dB

20dB20dB

30dB

30dB0

005

01

015

02

025

03

035

04

045

05N

umbe

r rat

io o

ver z

ero

poin

t

200 400 600 800 1000 1200 14000Sample number


BPSKQPSK16QAM

16QAM

BPSK

10dB

20dB

20dB

10dB

10dB

30dB

30dB 30dB

20dB

QPSK

01

02

03

04

05

06

07

08

09

Stan

dard

dev

iatio

n of

the r

eal p

art o

f IA

200 400 600 800 1000 1200 14000Sample number




BPSKQPSK16QAM

16QAM

QPSK

20dB

10dB 10dB

10dB

20dB

20dB 30dB

30dB 30dB

BPSK

0

005

01

015

02

025

Stan

dard

dev

iatio

n of

enve

lope

200 400 600 800 1000 1200 14000Sample number


0

02

04

06

08

1

12C

ontr

ibut

ion

rate












119911 (119899) = 119871minus1sum119896=0

ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)



BPSKQPSK

16QAMSupport vector

16QAM

QPSK

BPSK

Optimum boundary 2

Support vector

Optimum boundary 1


minus2

minus15

minus1

minus05

0

05

1

15

2

25

3

Seco

nd p

rinci

pal c

ompo

nent

char

acte

ristic






075

08

085

09

095

1C

orre

ct re

cogn

ition

rate

5 10 15 20 250SNR (dB)



6 Conclusion


Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018















119911 (119899) = 119871minus1sum119896=0

ℎ (119896) 119904 (119899 minus 119896) + 119903 (119899) (33)



BPSKQPSK

16QAMSupport vector

16QAM

QPSK

BPSK

Optimum boundary 2

Support vector

Optimum boundary 1


minus2

minus15

minus1

minus05

0

05

1

15

2

25

3

Seco

nd p

rinci

pal c

ompo

nent

char

acte

ristic






075

08

085

09

095

1C

orre

ct re

cogn

ition

rate

5 10 15 20 250SNR (dB)



6 Conclusion


Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018










075

08

085

09

095

1C

orre

ct re

cogn

ition

rate

5 10 15 20 250SNR (dB)



6 Conclusion


Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018









































Journal of












Journal of







Volume 2018






Volume 2018








automatic modulation classification exploiting hybrid

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