Automatic Modulation Classification
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Zhechen Zhu, Department of Electronic & Computer Engineering, Brunel University London, UK Zhechen 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, UK Prof. 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.
Content
About the Authors xi
Preface xiii
List of Abbreviations xv
List of Symbols xix
1 Introduction 1
1.1 Background 1
1.2 Applications of AMC 2
1.2.1 Military Applications 2
1.2.2 Civilian Applications 3
1.3 Field Overview and Book Scope 5
1.4 Modulation and Communication System Basics 6
1.4.1 Analogue Systems and Modulations 6
1.4.2 Digital Systems and Modulations 8
1.4.3 Received Signal with Channel Effects 15
1.5 Conclusion 16
References 16
2 Signal Models for Modulation Classification 19
2.1 Introduction 19
2.2 Signal Model in AWGN Channel 20
2.2.1 Signal Distribution of I-Q Segments 21
2.2.2 Signal Distribution of Signal Phase 23
2.2.3 Signal Distribution of Signal Magnitude 25
2.3 Signal Models in Fading Channel 25
2.4 Signal Models in Non-Gaussian Channel 28
2.4.1 Middleton's Class A Model 28
2.4.2 Symmetric Alpha Stable Model 30
2.4.3 Gaussian Mixture Model 30
2.5 Conclusion 31
References 32
3 Likelihood-based Classifiers 35
3.1 Introduction 35
3.2 Maximum Likelihood Classifiers 36
3.2.1 Likelihood Function in AWGN Channels 36
3.2.2 Likelihood Function in Fading Channels 38
3.2.3 Likelihood Function in Non-Gaussian Noise Channels 39
3.2.4 Maximum Likelihood Classification Decision Making 39
3.3 Likelihood Ratio Test for Unknown Channel Parameters 40
3.3.1 Average Likelihood Ratio Test 40
3.3.2 Generalized Likelihood Ratio Test 41
3.3.3 Hybrid Likelihood Ratio Test 43
3.4 Complexity Reduction 44
3.4.1 Discrete Likelihood Ratio Test and Lookup Table 44
3.4.2 Minimum Distance Likelihood Function 45
3.4.3 Non-Parametric Likelihood Function 45
3.5 Conclusion 45
References 46
4 Distribution Test-based Classifier 49
4.1 Introduction 49
4.2 Kolmogorov-Smirnov Test Classifier 50
4.2.1 The KS Test for Goodness of Fit 51
4.2.2 One-sample KS Test Classifier 53
4.2.3 Two-sample KS Test Classifier 55
4.2.4 Phase Difference Classifier 56
4.3 Cramer-Von Mises Test Classifier 57
4.4 Anderson-Darling Test Classifier 57
4.5 Optimized Distribution Sampling Test Classifier 58
4.5.1 Sampling Location Optimization 59
4.5.2 Distribution Sampling 60
4.5.3 Classification Decision Metrics 61
4.5.4 Modulation Classification Decision Making 62
4.6 Conclusion 63
References 63
5 Modulation Classification Features 65
5.1 Introduction 65
5.2 Signal Spectral-based Features 66
5.2.1 Signal Spectral-based Features 66
5.2.2 Spectral-based Features Specialities 69
5.2.3 Spectral-based Features Decision Making 70
5.2.4 Decision Threshold Optimization 70
5.3 Wavelet Transform-based Features 71
5.4 High-order Statistics-based Features 74
5.4.1 High-order Moment-based Features 74
5.4.2 High-order Cumulant-based Features 75
5.5 Cyclostationary Analysis-based Features 76
5.6 Conclusion 79
References 79
6 Machine Learning for Modulation Classification 81
6.1 Introduction 81
6.2 K-Nearest Neighbour Classifier 81
6.2.1 Reference Feature Space 82
6.2.2 Distance Definition 82
6.2.3 K-Nearest Neighbour Decision 83
6.3 Support Vector Machine Classifier 84
6.4 Logistic Regression for Feature Combination 86
6.5 Artificial Neural Network for Feature Combination 87
6.6 Genetic Algorithm for Feature Selection 89
6.7 Genetic Programming for Feature Selection and Combination 90
6.7.1 Tree-structured Solution 91
6.7.2 Genetic Operators 91
6.7.3 Fitness Evaluation 93
6.8 Conclusion 94
References 94
7 Blind Modulation Classification 97
7.1 Introduction 97
7.2 Expectation Maximization with Likelihood-based Classifier 98
7.2.1 Expectation Maximization Estimator 98
7.2.2 Maximum Likelihood Classifier 101
7.2.3 Minimum Likelihood Distance Classifier 102
7.3 Minimum Distance Centroid Estimation and Non-parametric Likelihood Classifier 103
7.3.1 Minimum Distance Centroid Estimation 103
7.3.2 Non-parametric Likelihood Function 105
7.4 Conclusion 107
References 107
8 Comparison of Modulation Classifiers 109
8.1 Introduction 109
8.2 System Requirements and Applicable Modulations 110
8.3 Classification Accuracy with Additive Noise 110
8.3.1 Benchmarking Classifiers 113
8.3.2 Performance Comparison in AWGN Channel 114
8.4 Classification Accuracy with Limited Signal Length 120
8.5 Classification Robustness against Phase Offset 126
8.6 Classification Robustness against Frequency Offset 132
8.7 Computational Complexity 137
8.8 Conclusion 138
References 139
9 Modulation Classification for Civilian Applications 141
9.1 Introduction 141
9.2 Modulation Classification for High-order Modulations 141
9.3 Modulation Classification for Link-adaptation Systems 143
9.4 Modulation Classification for MIMO Systems 144
9.5 Conclusion 150
References 150
10 Modulation Classifier Design for Military Applications 153
10.1 Introduction 153
10.2 Modulation Classifier with Unknown Modulation Pool 154
10.3 Modulation Classifier against Low Probability of Detection 157
10.3.1 Classification of DSSS Signals 157
10.3.2 Classification of FHSS Signals 158
10.4 Conclusion 160
References 160
Index 161
1
Introduction
1.1 Background
Automatic modulation classification (AMC) was first motivated by its application in military scenarios where electronic warfare, surveillance and threat analysis requires the recognition of signal modulations in order to identify adversary transmitting units, to prepare jamming signals, and to recover the intercepted signal. The term 'automatic' is used as opposed to the initial implementation of manual modulation classification where signals are processed by engineers with the aid of signal observation and processing equipment. Most modulation classifiers developed in the past 20 years are implemented through electronic processors. During the 1980s and 1990s there were considerable numbers of researchers in the field of signal processing and communications who dedicated their work to the problem of automatic modulation classification. This led to the publication of the first well received book on the subject by Azzouz and Nandi (1996). The interest in AMC for military purposes is sustained to this very day.
The beginning of twenty-first century saw a large number of innovations in communications technology. Among them are few that made essential contributions to the staggering increase of transmission throughput in various communication systems. Link adaptation (LA), also known as adaptive modulation and coding (AM&C), creates an adaptive modulation scheme where a pool of multiple modulations are employed by the same system (Goldsmith and Chua, 1998). It enables the optimization of the transmission reliability and data rate through the adaptive selection of modulation schemes according to channel conditions. While the transmitter has the freedom to choose how the signals are modulated, the receiver must have the knowledge of the modulation type to demodulation the signal so that the transmission can be successful. An easy way to achieve that is to include the modulation information in each signal frame so that the receivers would be notified about the change in modulation scheme, and react accordingly. However, this strategy affects the spectrum efficiency due to the extra modulation information in each signal frame. In the current situation where the wireless spectrum is extremely limited and valuable, the aforementioned strategy is simply not efficient enough. For this reason, AMC becomes an attractive solution to the problem. Thanks to the development in microprocessors, receivers nowadays are much enabled in terms of their computational power. Thus, the signal processing required by AMC algorithms becomes feasible. By automatically identifying the modulation type of the received signal, the receiver does not need to be notified about the modulation type and the demodulation can still be successfully achieved. In the end, spectrum efficiency is improved as no modulation information is needed in the transmitted signal frame. AMC has become an integral part of intelligent radio systems, including cognitive radio and software-defined radio.
Over the years, there have been many terms used to describe the same problem: modulation recognition, automatic modulation recognition, modulation identification, modulation classification, and automatic modulation classification. There are other names for the problem, such as PSK (phase-shift keying modulation) classification and M-QAM (M-ary quadrature amplitude modulation) classification that have a more specific target but which still operate under the same principle of automatic modulation classification. In this book, we have decided to use automatic modulation classification and AMC as a consistent reference to the same problem.
1.2 Applications of AMC
Having discussed the possible use of AMC in both military and civilian scenarios, in this section we take a close look at how AMC is incorporated in different military and civilian systems.
1.2.1 Military Applications
AMC has an essential role in many military strategies. Modern electronic warfare (EW) consists of three major components: electronic support (ES), electronic attack (EA) and electronic protect (EP) (Poisel, 2008). In ES, the goal is to gather information from radio frequency emissions. This is often where AMC is employed after the signal detection is successfully achieved. The resulting modulation information could have several uses extending into all the components in EW. An illustration of how a modulation classifier is incorporated in the military EW systems is given in Figure 1.1.
Figure 1.1 Military signal intelligence system.
To further the process of ES, the modulation information can be used for demodulating the intercepted signal in order to recover the transmitted message among adversary units. This is of course completed with the aid of signal decryption and translation. Meanwhile, the modulation information alone can also provide vital information to the electronic mapping system where it could be used to identify the adversary units and their possible locations.
In EA, jamming is the primary measure to prevent the communication between adversary units. There are many jamming techniques available. However, the most common one relies on deploying jammers in the communication channel between adversary units and also transmitting noise signals or made-up signals using the matching modulation type. To override the adversary communication, the jamming signal must occupy the same frequency band as the adversary signal. This information is available from the signal detector. The power of the jamming signal must be significantly high, which is achieved by using an amplifier before transmitting the jamming signal. More importantly, the jamming signal must be modulated using the modulation scheme detected by the modulation classifier.
In EP, the objective is to protect friendly communications from adversary EA measures. As mentioned above, jammers transmit higher power signals to override adversary communication in the same frequency band. The key is to have the same signal modulation. An effective strategy to prevent friendly communication being jammed is to have awareness of the EA effort from adversary jammers and to dodge the jamming effort. More specifically, the friendly transmitter could monitor the jamming signal's modulation and switch the friendly unit to a different modulation scheme to avoid jamming.
1.2.2 Civilian Applications
In the civilian scene, AMC is most important for the application of LA. As demonstrated in Figure 1.2, the signal modulator in the LA transmitter is replaced by an adaptive modulation unit. The role of the adaptive modulator is to select the modulation from a predefined candidate pool and to complete the modulation process. The selection of modulation from the candidate pool is determined by the system specification and channel conditions. The lower-order and more robust modulations such as BPSK (binary phase-shift keying modulation) and QPSK (quadrature phase-shift keying modulation) are often selected when the channel is noisy and complex, given that the system requires high link reliability. The higher-order and more efficient modulations such as 16-QAM (16-quadrature amplitude modulation) and 64-QAM (64-quadrature amplitude modulation) are often selected to satisfy the demand for high-speed transmission in clear channels. The only communication between adaptive modulation module and the receiver is completed at system initialization where the information of the modulation candidate pool is notified to the receiver. During normal transmission the adaptive modulator embeds no extra information in the communication stream. At the receiving end of the LA system, channel estimation is performed prior to other tasks. If the channel is static, the estimation is only performed at the initial stage. If the channel is time variant, the channel state information (CSI) could be estimated regularly throughout the transmission. The estimated CSI and other information would then be fed back to the transmitter where the CSI will be used for the selection of modulation schemes. More importantly, the CSI is required to assist the modulation classifier. Depending on the AMC algorithm, different channel parameters are needed to complete the modulation classification. Normally, the accuracy of channel estimation has a significant impact on the performance of the modulation classifier. The resulting modulation classification decision is then fed to the reconfigurable signal demodulator for appropriate demodulation. If the modulation classification is accurate, the correct demodulation method would capture the message and complete the successful transmission. If the modulation classification is incorrect, the entire transmission fails as the message cannot be recovered from the demodulator. It is not difficult to see the importance of AMC in LA systems.
Figure 1.2 AMC in link adaptation system.
1.3 Field Overview and Book Scope
Given the importance of AMC in various military and civilian communication applications, there has been a large amount of research work dedicated to the problem of AMC in a wide variety of settings. The nature of the problem creates multiple dimensions in its solutions and inspires continuous contribution from generations of researchers.
First, the modulation classifier needs to be accurate. The accuracy is measured by the percentage of errors made in a number of signal frames being transmitted. The lower the error the better the classifier is perceived to be....
