Zhechen Zhu, Department of Electronic & Computer Engineering, Brunel University London, UKZhechen Zhu received his B.Eng. degree in the Department of Electrical Engineering and Electronics from the University of Liverpool in 2010.  His undergraduate project was awarded the Farnell Company Prize. He is currently pursuing his PhD degree at Brunel University conducting research on the subject of automatic modulation classification. His research interests include high order statistics, machine learning, statistical signal processing, blind signal processing, and their application in signal estimation and classification.Asoke K. Nandi, Department of Electronic & Computer Engineering, Brunel University London, UKProf. Nandi is Chair and Head of the Electronic and Computer Engineering Department at Brunel University London, UK. He leads the Signal Processing and Communications Research Group with interests in the areas of signal processing, machine learning, and communications research. He is a Finland Distinguished Professor at the University of Jyvaskyla, Finland. In 1983 Professor Nandi was a member of the UA1 team at CERN that discovered the three fundamental particles known as W+, W− and Z0, providing the evidence for the unification of the electromagnetic and weak forces, which was recognized by the Nobel Committee for Physics in 1984. He has authored or co-authored more than 190 journal papers, and 2 books. The Google Scholar h-index of his publications is 54. In 2010 he received the Glory of Bengal Award for his outstanding achievements in scientific research, and in 2012 was awarded the IEEE Heinrich Hertz Award. Prof. Nandi is a Fellow of the IEEE.

• About the Authors xiPreface xiiiList of Abbreviations xvList of Symbols xix1 Introduction 11.1 Background 11.2 Applications of AMC 21.2.1 Military Applications 21.2.2 Civilian Applications 31.3 Field Overview and Book Scope 51.4 Modulation and Communication System Basics 61.4.1 Analogue Systems and Modulations 61.4.2 Digital Systems and Modulations 81.4.3 Received Signal with Channel Effects 151.5 Conclusion 16References 162 Signal Models for Modulation Classification 192.1 Introduction 192.2 Signal Model in AWGN Channel 202.2.1 Signal Distribution of I-Q Segments 212.2.2 Signal Distribution of Signal Phase 232.2.3 Signal Distribution of Signal Magnitude 252.3 Signal Models in Fading Channel 252.4 Signal Models in Non-Gaussian Channel 282.4.1 Middleton’s Class A Model 282.4.2 Symmetric Alpha Stable Model 302.4.3 Gaussian Mixture Model 302.5 Conclusion 31References 323 Likelihood-based Classifiers 353.1 Introduction 353.2 Maximum Likelihood Classifiers 363.2.1 Likelihood Function in AWGN Channels 363.2.2 Likelihood Function in Fading Channels 383.2.3 Likelihood Function in Non-Gaussian Noise Channels 393.2.4 Maximum Likelihood Classification Decision Making 393.3 Likelihood Ratio Test for Unknown Channel Parameters 403.3.1 Average Likelihood Ratio Test 403.3.2 Generalized Likelihood Ratio Test 413.3.3 Hybrid Likelihood Ratio Test 433.4 Complexity Reduction 443.4.1 Discrete Likelihood Ratio Test and Lookup Table 443.4.2 Minimum Distance Likelihood Function 453.4.3 Non-Parametric Likelihood Function 453.5 Conclusion 45References 464 Distribution Test-based Classifier 494.1 Introduction 494.2 Kolmogorov–Smirnov Test Classifier 504.2.1 The KS Test for Goodness of Fit 514.2.2 One-sample KS Test Classifier 534.2.3 Two-sample KS Test Classifier 554.2.4 Phase Difference Classifier 564.3 Cramer–Von Mises Test Classifier 574.4 Anderson–Darling Test Classifier 574.5 Optimized Distribution Sampling Test Classifier 584.5.1 Sampling Location Optimization 594.5.2 Distribution Sampling 604.5.3 Classification Decision Metrics 614.5.4 Modulation Classification Decision Making 624.6 Conclusion 63References 635 Modulation Classification Features 655.1 Introduction 655.2 Signal Spectral-based Features 665.2.1 Signal Spectral-based Features 665.2.2 Spectral-based Features Specialities 695.2.3 Spectral-based Features Decision Making 705.2.4 Decision Threshold Optimization 705.3 Wavelet Transform-based Features 715.4 High-order Statistics-based Features 745.4.1 High-order Moment-based Features 745.4.2 High-order Cumulant-based Features 755.5 Cyclostationary Analysis-based Features 765.6 Conclusion 79References 796 Machine Learning for Modulation Classification 816.1 Introduction 816.2 K-Nearest Neighbour Classifier 816.2.1 Reference Feature Space 826.2.2 Distance Definition 826.2.3 K-Nearest Neighbour Decision 836.3 Support Vector Machine Classifier 846.4 Logistic Regression for Feature Combination 866.5 Artificial Neural Network for Feature Combination 876.6 Genetic Algorithm for Feature Selection 896.7 Genetic Programming for Feature Selection and Combination 906.7.1 Tree-structured Solution 916.7.2 Genetic Operators 916.7.3 Fitness Evaluation 936.8 Conclusion 94References 947 Blind Modulation Classification 977.1 Introduction 977.2 Expectation Maximization with Likelihood-based Classifier 987.2.1 Expectation Maximization Estimator 987.2.2 Maximum Likelihood Classifier 1017.2.3 Minimum Likelihood Distance Classifier 1027.3 Minimum Distance Centroid Estimation and Non-parametric Likelihood Classifier 1037.3.1 Minimum Distance Centroid Estimation 1037.3.2 Non-parametric Likelihood Function 1057.4 Conclusion 107References 1078 Comparison of Modulation Classifiers 1098.1 Introduction 1098.2 System Requirements and Applicable Modulations 1108.3 Classification Accuracy with Additive Noise 1108.3.1 Benchmarking Classifiers 1138.3.2 Performance Comparison in AWGN Channel 1148.4 Classification Accuracy with Limited Signal Length 1208.5 Classification Robustness against Phase Offset 1268.6 Classification Robustness against Frequency Offset 1328.7 Computational Complexity 1378.8 Conclusion 138References 1399 Modulation Classification for Civilian Applications 1419.1 Introduction 1419.2 Modulation Classification for High-order Modulations 1419.3 Modulation Classification for Link-adaptation Systems 1439.4 Modulation Classification for MIMO Systems 1449.5 Conclusion 150References 15010 Modulation Classifier Design for Military Applications 15310.1 Introduction 15310.2 Modulation Classifier with Unknown Modulation Pool 15410.3 Modulation Classifier against Low Probability of Detection 15710.3.1 Classification of DSSS Signals 15710.3.2 Classification of FHSS Signals 15810.4 Conclusion 160References 160Index 161

Zhechen Zhu, Department of Electronic & Computer Engineering, Brunel University London, UKZhechen Zhu received his B.Eng. degree in the Department of Electrical Engineering and Electronics from the University of Liverpool in 2010.  His undergraduate project was awarded the Farnell Company Prize. He is currently pursuing his PhD degree at Brunel University conducting research on the subject of automatic modulation classification. His research interests include high order statistics, machine learning, statistical signal processing, blind signal processing, and their application in signal estimation and classification.Asoke K. Nandi, Department of Electronic & Computer Engineering, Brunel University London, UKProf. Nandi is Chair and Head of the Electronic and Computer Engineering Department at Brunel University London, UK. He leads the Signal Processing and Communications Research Group with interests in the areas of signal processing, machine learning, and communications research. He is a Finland Distinguished Professor at the University of Jyvaskyla, Finland. In 1983 Professor Nandi was a member of the UA1 team at CERN that discovered the three fundamental particles known as W+, W− and Z0, providing the evidence for the unification of the electromagnetic and weak forces, which was recognized by the Nobel Committee for Physics in 1984. He has authored or co-authored more than 190 journal papers, and 2 books. The Google Scholar h-index of his publications is 54. In 2010 he received the Glory of Bengal Award for his outstanding achievements in scientific research, and in 2012 was awarded the IEEE Heinrich Hertz Award. Prof. Nandi is a Fellow of the IEEE.

• About the Authors xiPreface xiiiList of Abbreviations xvList of Symbols xix1 Introduction 11.1 Background 11.2 Applications of AMC 21.2.1 Military Applications 21.2.2 Civilian Applications 31.3 Field Overview and Book Scope 51.4 Modulation and Communication System Basics 61.4.1 Analogue Systems and Modulations 61.4.2 Digital Systems and Modulations 81.4.3 Received Signal with Channel Effects 151.5 Conclusion 16References 162 Signal Models for Modulation Classification 192.1 Introduction 192.2 Signal Model in AWGN Channel 202.2.1 Signal Distribution of I-Q Segments 212.2.2 Signal Distribution of Signal Phase 232.2.3 Signal Distribution of Signal Magnitude 252.3 Signal Models in Fading Channel 252.4 Signal Models in Non-Gaussian Channel 282.4.1 Middleton’s Class A Model 282.4.2 Symmetric Alpha Stable Model 302.4.3 Gaussian Mixture Model 302.5 Conclusion 31References 323 Likelihood-based Classifiers 353.1 Introduction 353.2 Maximum Likelihood Classifiers 363.2.1 Likelihood Function in AWGN Channels 363.2.2 Likelihood Function in Fading Channels 383.2.3 Likelihood Function in Non-Gaussian Noise Channels 393.2.4 Maximum Likelihood Classification Decision Making 393.3 Likelihood Ratio Test for Unknown Channel Parameters 403.3.1 Average Likelihood Ratio Test 403.3.2 Generalized Likelihood Ratio Test 413.3.3 Hybrid Likelihood Ratio Test 433.4 Complexity Reduction 443.4.1 Discrete Likelihood Ratio Test and Lookup Table 443.4.2 Minimum Distance Likelihood Function 453.4.3 Non-Parametric Likelihood Function 453.5 Conclusion 45References 464 Distribution Test-based Classifier 494.1 Introduction 494.2 Kolmogorov–Smirnov Test Classifier 504.2.1 The KS Test for Goodness of Fit 514.2.2 One-sample KS Test Classifier 534.2.3 Two-sample KS Test Classifier 554.2.4 Phase Difference Classifier 564.3 Cramer–Von Mises Test Classifier 574.4 Anderson–Darling Test Classifier 574.5 Optimized Distribution Sampling Test Classifier 584.5.1 Sampling Location Optimization 594.5.2 Distribution Sampling 604.5.3 Classification Decision Metrics 614.5.4 Modulation Classification Decision Making 624.6 Conclusion 63References 635 Modulation Classification Features 655.1 Introduction 655.2 Signal Spectral-based Features 665.2.1 Signal Spectral-based Features 665.2.2 Spectral-based Features Specialities 695.2.3 Spectral-based Features Decision Making 705.2.4 Decision Threshold Optimization 705.3 Wavelet Transform-based Features 715.4 High-order Statistics-based Features 745.4.1 High-order Moment-based Features 745.4.2 High-order Cumulant-based Features 755.5 Cyclostationary Analysis-based Features 765.6 Conclusion 79References 796 Machine Learning for Modulation Classification 816.1 Introduction 816.2 K-Nearest Neighbour Classifier 816.2.1 Reference Feature Space 826.2.2 Distance Definition 826.2.3 K-Nearest Neighbour Decision 836.3 Support Vector Machine Classifier 846.4 Logistic Regression for Feature Combination 866.5 Artificial Neural Network for Feature Combination 876.6 Genetic Algorithm for Feature Selection 896.7 Genetic Programming for Feature Selection and Combination 906.7.1 Tree-structured Solution 916.7.2 Genetic Operators 916.7.3 Fitness Evaluation 936.8 Conclusion 94References 947 Blind Modulation Classification 977.1 Introduction 977.2 Expectation Maximization with Likelihood-based Classifier 987.2.1 Expectation Maximization Estimator 987.2.2 Maximum Likelihood Classifier 1017.2.3 Minimum Likelihood Distance Classifier 1027.3 Minimum Distance Centroid Estimation and Non-parametric Likelihood Classifier 1037.3.1 Minimum Distance Centroid Estimation 1037.3.2 Non-parametric Likelihood Function 1057.4 Conclusion 107References 1078 Comparison of Modulation Classifiers 1098.1 Introduction 1098.2 System Requirements and Applicable Modulations 1108.3 Classification Accuracy with Additive Noise 1108.3.1 Benchmarking Classifiers 1138.3.2 Performance Comparison in AWGN Channel 1148.4 Classification Accuracy with Limited Signal Length 1208.5 Classification Robustness against Phase Offset 1268.6 Classification Robustness against Frequency Offset 1328.7 Computational Complexity 1378.8 Conclusion 138References 1399 Modulation Classification for Civilian Applications 1419.1 Introduction 1419.2 Modulation Classification for High-order Modulations 1419.3 Modulation Classification for Link-adaptation Systems 1439.4 Modulation Classification for MIMO Systems 1449.5 Conclusion 150References 15010 Modulation Classifier Design for Military Applications 15310.1 Introduction 15310.2 Modulation Classifier with Unknown Modulation Pool 15410.3 Modulation Classifier against Low Probability of Detection 15710.3.1 Classification of DSSS Signals 15710.3.2 Classification of FHSS Signals 15810.4 Conclusion 160References 160Index 161