CuuDuongThanCong.com CuuDuongThanCong.com Automatic Modulation Classification CuuDuongThanCong.com CuuDuongThanCong.com Automatic Modulation Classification Principles, Algorithms and Applications Zhechen Zhu and Asoke K Nandi Brunel University London, UK CuuDuongThanCong.com This edition first published 2015 © 2015 John Wiley & Sons, Ltd Registered Office John Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, 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publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom If professional advice or other expert assistance is required, the services of a competent professional should be sought The advice and strategies contained herein may not be suitable for every situation In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions The fact that an organization or Website is referred to in this work as a citation and/or a potential source of further information does not mean that the author or the publisher endorses the information the organization or Website may provide or recommendations it may make Further, readers should be aware that Internet Websites listed in this work may have changed or disappeared between when this work was written and when it is read No warranty may be created or extended by any promotional statements for this work Neither the publisher nor the author shall be liable for any damages arising herefrom Library of Congress Cataloging-in-Publication Data Zhu, Zhechen Automatic modulation classification : principles, algorithms, and applications / Zhechen Zhu and Asoke K Nandi pages cm Includes bibliographical references and index ISBN 978-1-118-90649-1 (cloth) Modulation (Electronics) I Nandi, Asoke Kumar II Title TK5102.9.Z477 2015 621.38150 36–dc23 2014032270 A catalogue record for this book is available from the British Library Set in 10/12.5pt Palatino by SPi Publisher Services, Pondicherry, India 2015 CuuDuongThanCong.com To Xiaoyan and Qiaonan Zhu Marion, Robin, David, and Anita Nandi CuuDuongThanCong.com CuuDuongThanCong.com Contents About the Authors Preface xi xiii List of Abbreviations xv List of Symbols xix Introduction 1.1 Background 1.2 Applications of AMC 1.2.1 Military Applications 1.2.2 Civilian Applications 1.3 Field Overview and Book Scope 1.4 Modulation and Communication System Basics 1.4.1 Analogue Systems and Modulations 1.4.2 Digital Systems and Modulations 1.4.3 Received Signal with Channel Effects 1.5 Conclusion References 1 2 6 15 16 16 Signal Models for Modulation Classification 2.1 Introduction 2.2 Signal Model in AWGN Channel 2.2.1 Signal Distribution of I-Q Segments 2.2.2 Signal Distribution of Signal Phase 2.2.3 Signal Distribution of Signal Magnitude 2.3 Signal Models in Fading Channel 2.4 Signal Models in Non-Gaussian Channel 2.4.1 Middleton’s Class A Model 19 19 20 21 23 25 25 28 28 CuuDuongThanCong.com Contents viii 2.4.2 Symmetric Alpha Stable Model 2.4.3 Gaussian Mixture Model 2.5 Conclusion References 30 30 31 32 Likelihood-based Classifiers 3.1 Introduction 3.2 Maximum Likelihood Classifiers 3.2.1 Likelihood Function in AWGN Channels 3.2.2 Likelihood Function in Fading Channels 3.2.3 Likelihood Function in Non-Gaussian Noise Channels 3.2.4 Maximum Likelihood Classification Decision Making 3.3 Likelihood Ratio Test for Unknown Channel Parameters 3.3.1 Average Likelihood Ratio Test 3.3.2 Generalized Likelihood Ratio Test 3.3.3 Hybrid Likelihood Ratio Test 3.4 Complexity Reduction 3.4.1 Discrete Likelihood Ratio Test and Lookup Table 3.4.2 Minimum Distance Likelihood Function 3.4.3 Non-Parametric Likelihood Function 3.5 Conclusion References 35 35 36 36 38 40 40 41 43 44 44 45 45 45 46 Distribution Test-based Classifier 4.1 Introduction 4.2 Kolmogorov–Smirnov Test Classifier 4.2.1 The KS Test for Goodness of Fit 4.2.2 One-sample KS Test Classifier 4.2.3 Two-sample KS Test Classifier 4.2.4 Phase Difference Classifier 4.3 Cramer–Von Mises Test Classifier 4.4 Anderson–Darling Test Classifier 4.5 Optimized Distribution Sampling Test Classifier 4.5.1 Sampling Location Optimization 4.5.2 Distribution Sampling 4.5.3 Classification Decision Metrics 4.5.4 Modulation Classification Decision Making 4.6 Conclusion References 49 49 50 51 53 55 56 57 57 58 59 60 61 62 63 63 CuuDuongThanCong.com 39 39 160 Automatic Modulation Classification 10.4 Conclusion In this chapter we considered several modulation classification tasks that are unique to the military scenarios The detection of modulation type provides threat analysis and surveillance, as well as the ability to handle a wide range of common modulation types The task of digital modulation classification is put in the challenge of lowprobability-of-detection signals Two different cases of LPD signal are considered, namely DSSS and FHSS For DSSS, different types of likelihood-based classifiers are selected for their high performance when the SNR is lower than dB In the case of FHSS, given the inevitable frequency offset, magnitude-based and phase differencebased classifiers are suggested for a robust classification of the FHSS signal, due to their inherent robustness against frequency offset References Pawula, R.F., Rice, S.O., and Roberts, J.H (1982) Distribution of the phase angle between two vectors perturbed by gaussian noise IEEE Transactions on Communications, 30 (8), 1828–1841 Poisel, A.R (2008) Introduction to Communication Electronic Warfare Systems, Artech House, Norwood, MA Wang, F., and Wang, X (2010) Fast and robust modulation classification via KolmogorovSmirnov test IEEE Transactions on Communications, 58 (8), 2324–2332 CuuDuongThanCong.com Index adaptive modulation and coding (AM&C), additive noise, 16 additive white Gaussian noise (AWGN) channel, 5, 20 analogue communication system, analogue modulation, AM, FM, 6, PM, 6, automatic modulation recognition, AWGN channel, 20 cumulant based feature, 74 cumulative distribution function (CDF), 50, 56–8 AWGN channel, 5, 20 cyclic cumulant based feature, 78 cyclic moment based feature, 75 cyclostationary process, 76 cyclic autocorrelation, 75 cyclic domain profile, 77 spectral coherence, 77 spectral correlation function, 77 back propagation, 88 blind modulation classifier, 97 broadband over power line (BPL), 141 digital communication system, 11 digital modulation, 6, 8–15 ASK, 8–9, 11 FSK, 8–9, 11 PAM, 11, 13 PSK, 11, 13 QAM, 13, 14 dimension reduction, 81 feature selection, 81 direct sequence spread sectrum (DSSS), 157 discrete signal, 16 distribution based classifier, 63 CvM test classifier, 57 distribution test Anderson–Darling test, 57–8 Cramer–von Mises test, 57 Kolmogorov–Smirnov test, 50–56 centroid parameter, 103 channel effect, 15–16 channel estimation, expectation maximization, 97–102, 147 expectation maximization estimation, 97 minimum centroid estimation, 98 channel gain, 15 channel state information (CSI), classification accuracy, computational complexity, 35 constellation, 14 continuous wavelet transform (CWT), 71 covariance matrix, 20 Automatic Modulation Classification: Principles, Algorithms and Applications, First Edition Zhechen Zhu and Asoke K Nandi © 2015 John Wiley & Sons, Ltd Published 2015 by John Wiley & Sons, Ltd CuuDuongThanCong.com Index 162 distribution test based classifier AD test classifier, 58 KS test classifier, 50–58, 63 ODST classifier, 59 phase difference classifier, 56 electronic support electronic attack, electronic warfare, 1, electronic attack, electronic protect, electronic support, empirical cumulative distribution function (ECDF), 50, 51 expectation maximization (EM), 97 expectation step, 99 maximization step, 99 update function, 100 expectation/condition maximization (ECM), 101 fading channel, 5, 20 attenuation, 20 fast fading, 25 frequency offset, 25, 28 offset, 25 phase offset, 15–16, 25, 26 slow fading, 25 feature based classifier, 19 cumulant based classifier, 50 cumulant based feature, 50, 74, 116–20, 123, 124, 128–30 moment based feature, 74, 75, 117, 123, 124, 128, 129, 132, 134 feature combination artificial neural network, 81 genetic programming, 81, 90–94 feature selection genetic algorithm, 62 genetic programming, 81, 90–94 logistic regression, 86–7 feature space, 81 Fisher’s criterion, 93 fitness, 90 evaluation, 90 function, 90 CuuDuongThanCong.com frequency-hopping spread spectrum (FHSS), 157 Gaussian Mixture Model, 28 Gaussian mixture model (GMM), 28 genetic algorithm, 62 genetic operator crossover, 89, 91 mutation, 89, 90 goodness of fit, 49 high order modulation, 43 I-Q, 14–15 in-phase component, 14–15 quadrature component, 14–15 impulsive noise, 5, 20 jamming, 1, K-means clustering, 99 k-nearest neighbour (KNN), 81 likelihood based classifier, 5, 26 likelihood ratio test, 40–43 maximum a posteriori, 144 maximum likelihood, 35–43, 45, 46 minimum distance likelihood, 45 minimum likelihood distance, 102 non-parametric likelihood, 45 likelihood function (LF), 35, 36 AWGN channel, 20 fading channel, non-Gaussian channel, 20 likelihood ratio test average likelihood ratio test, 35 generalized likelihood ratio test, 35 hybrid likelihood ratio test, 35 linear kernel, 84 link adaptation (LA), 1, log likelihood function, 99 logistic function, 86–7 logit function, 87 low probability of detection, 154 DSSS, 157 FHSS, 157 Index machine learning, 19 artificial neural network, 81 genetic algorithm, 81, 89–90 KNN classifier, 81–3 logistic regression, 86–7 support vector machine, 81 machine learning based classifier, 81 KNN classifier, 81 KNN classifier, 81–3, 86, 94 SVM classifier, 84 membership hard membership, 99 soft membership, 99 modulation accuracy, 5, 20 modulation candidate pool, modulation classification, 1, modulation hypothesis, 35 modulation identification, modulation recognition, moment based feature, 74 multi-layer perceptron (MLP), 87–8 multiple-input and multiple output (MIMO), non-Gaussian channel, 28–31 Gaussian mixture model, 28 Middleton’s Class A, 28 symmetric alpha stable, 28 non-linear kernel, 84–5 polynomial kernel, 85 non-parametric likelihood function (NPLF), 45 CuuDuongThanCong.com 163 pilot sample, 55 prior probability, 40 probability density function (PDF), 20 pulse shaping, 15–16 Rayleigh distribution, 106 Rayleigh fading channel, 145 Rice distribution, 25 semi-blind classifiers, 97 signal distribution AWGN channel, 5, 21–5 fading channel, 20, 25–7 non-Gaussian channel, 28–31 signal-to-centroid distance, 103 signal-to-noise ratio (SNR), 16 space-time coding (STC), 144 spatial multiplexing (SM), 144 spectral based feature, 65 surveillance, symbol mapping, 49 Symmetric Alpha Stable (SαS) model, 28 threat analysis, timing error, 16 von Mises distribution, 23 wavelet transform feature, 71–4 100 90 80 Classification accuracy (%) 70 60 50 2-PAM 4-PAM 40 8-PAM BPSK 30 QPSK 8-PSK 20 4-QAM 16-QAM 10 64-QAM –20 –15 –10 –5 10 15 20 SNR (dB) Figure 8.2 Classification accuracy of the ML classifier in AWGN channel Automatic Modulation Classification: Principles, Algorithms and Applications, First Edition Zhechen Zhu and Asoke K Nandi © 2015 John Wiley & Sons, Ltd Published 2015 by John Wiley & Sons, Ltd CuuDuongThanCong.com 100 90 80 Classification accuracy (%) 70 60 50 ML 40 KS 30 Moment Cumulant 20 GP-KNN 10 EM-ML –20 –15 –10 –5 10 15 SNR (dB) Figure 8.8 Average classification accuracy of all classifiers in AWGN channel CuuDuongThanCong.com 20 100 90 Classification accuracy (%) 80 70 60 2-PAM 50 4-PAM 40 8-PAM BPSK 30 QPSK 8-PSK 20 4-QAM 16-QAM 10 50 64-QAM 150 250 350 450 550 650 750 850 950 Signal length Figure 8.12 Classification accuracy of the cumulant-based classifier with different signal length CuuDuongThanCong.com 100 90 Classification accuracy (%) 80 70 60 ML 50 KS 40 Moment 30 Cumulant 20 GP-KNN 10 EM-ML 50 150 250 350 450 550 650 750 850 950 Signal length Figure 8.15 length Average classification accuracy of all classifiers with different signal CuuDuongThanCong.com 100 90 80 Classification accuracy (%) 70 2-PAM 60 4-PAM 8-PAM 50 BPSK 40 QPSK 30 8-PSK 4-QAM 20 16-QAM 10 64-QAM –1 –8 –6 –4 –2 10 Phase offset (°) Figure 8.18 offset Classification accuracy of the moment-based KNN classifier with phase CuuDuongThanCong.com 100 90 80 Classification accuracy (%) 70 60 ML 50 KS 40 Moment 30 Cumulant 20 GP-KNN 10 –10 –8 –6 –4 –2 EM-ML Phase offset (°) Figure 8.22 Average classification accuracy of all classifiers with phase offset CuuDuongThanCong.com 10 100 90 80 Classification accuracy (%) 2-PAM 70 4-PAM 8-PAM 60 BPSK QPSK 50 8-PSK 4-QAM 40 16-QAM 64-QAM 30 20 10 11 13 15 17 19 Frequency offset (×10–5) Figure 8.27 Classification accuracy of the GP-KNN classifier with frequency offset CuuDuongThanCong.com 100 ML Classification accuracy (%) 90 KS 80 Moment 70 Cumulant GP-KNN 60 EM-ML 50 40 30 20 10 11 Frequency Offset 13 15 17 19 (×10–5) Figure 8.29 Average classification accuracy of each classifier with frequency offset CuuDuongThanCong.com WILEY END USER LICENSE AGREEMENT Go to www.wiley.com/go/eula to access Wiley’s ebook EULA CuuDuongThanCong.com ... throughput, digital modulations of higher orders including M-ary ASK (M-ASK), M-ary FSK (M-FSK), M-ary PSK (M-PSK), M-ary PAM (M-PAM), and M-ary QAM (M-QAM) are often used The label “M” indicates the number... −1 0.5 16-QAM 1.5 Quadrature Quadrature 8-PSK 1.5 −1.5 −1.5 In-phase In-phase 0.5 1.5 −1.5 −1.5 In-phase −1 −0.5 In-phase Figure 1.11 Constellation plots of 2-PAM, QPSK, 8-PSK and 16-QAM coordinates... Wavelet Transform-based Features 5.4 High-order Statistics-based Features 5.4.1 High-order Moment-based Features 5.4.2 High-order Cumulant-based Features 5.5 Cyclostationary Analysis-based Features