automatic modulation classification...
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AUTOMATIC MODULATION CLASSIFICATIONUSING FEATURE BASED APPROACH
A Thesis submitted in partial fulfillment of therequirements for the Degree of Doctor of Philosophy
By
Sajjad Ahmed Ghauri
0909-PDEE-004
Department of Electronic EngineeringSchool of Engineering & Applied Sciences (SEAS)
ISRA University, Islamabad CampusIslamabad, Pakistan
August 2015
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AUTOMATIC MODULATION CLASSIFICATIONUSING FEATURE BASED APPROACH
Submitted by
Sajjad Ahmed Ghauri
0909-PDEE-004
Dr. Ijaz Mansoor Qureshi (Supervisor)ProfessorDepartment of Electrical EngineeringAir University, Islamabad.
Dr. Tanweer Ahmad CheemaHODSchool of Engineering & Applied SciencesISRA University, Islamabad
Dr. Muhammad Sher (External Examiner)DeanFaculty of Basic & Applied Sciences,International Islamic University, Islamabad.
Dr. Ihsan ul Haq (External Examiner)Principal ICTFaculty of Engineering & Technology,International Islamic University, Islamabad.
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CERTIFICATE
It is certified that the research work contained in this thesis has
been carried out under the supervision of Dr. Ijaz Mansoor
Qureshi, at ISRA University, Islamabad Campus is original. It is
fully adequate, in scope and quality, as a thesis for the degree of
Doctor of Philosophy.
Signature: ___________________
SupervisorProf. Dr. Ijaz Mansoor Qureshi Department ofElectrical Engineering,Air University, Islamabad.
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DEDICATED TO
MY WORTHY FATHER
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ACKNOWLEDGEMENTS
I am grateful to The Almighty Allah, The Beneficent and The Merciful, Who
enabled me to complete this research work. I thank quite cordially to my supervisor
Dr. I. M. Qureshi, for his constant encouragements and bountiful enthusiasm. His
guidance in perusing for innovative ideas in wireless communications have always
inspired and motivated me to explore new horizons of research. He has always
treated me like his own child and has paid special attention to guide me about
studies and my research at all stages. He has not just benefitted me with a range of
solutions for wireless communication problems, but also skilled in research
conducting methodologies. Above all, I have learned to live a simple and pious life
from such a multi-dynamic and consummated individual. I pay tribute my teachers
Dr. A. N. Malik, Dr. T. A. Cheema and all other teachers who have taught me from
nursery to postgraduate classes.
My words are not enough to express the feeling of gratitude which I confide
in my heart about my parents. All what they have done for me is considerable effort
which projects their sublime love for knowledge in me. I have always found them
wishing good for me in their late night prayers. I cannot forget to thank rest of my
family members for their humble prayers and munificent assistance, especially my
beloved wife who has always inspired me, valued my ideas and encouraged me in
the arduous moments.
At last but not least, I appreciate my friend Mr. Hannan Adeel for their
sincere friendship. It is hard to forget those study sessions during our course work.
Lastly, I pray for all who have acquaintance with me.
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ABSTRACT
Automatic Modulation Classification (AMC) is a scheme to classify the
modulated signal by observing its received signal features. The received signal is
usually corrupted by influence of various sources, such as, white guassian noise
and fading, which degrades the signal quality. Automatic modulation classification
plays an important role in cognitive radio communication. Due to amassed usage of
digital signals in different technologies, such as, cognitive radios, scientists have
focused on recognizing these signal types. AMC is expected to be incorporated in
the upcoming cognitive communication. Generally, digital signal type classification
can be categorized into two major categories: decision theoretic (DT) methods and
pattern classification (PC) methods.
In this research we focused on PC methods which are based upon
features extraction. The feature extraction based modulation classification is
accomplished in two modules. The first module is the feature extraction and second
is classification process which gives decision based upon the features extracted.
The features extracted from the received signal are higher order moments, higher
order cummulants, spectral features, cyclo-stationary features and novel Gabor
features. The classification of digital modulation formats such as pulse amplitude
modulation (PAM), quadrature amplitude modulation (QAM) and phase shift keying
(PSK) and frequency shift keying (FSK) are considered throughout the research.
The performance of proposed classifier are analyzed on additive white guassian
noise channel (AWGN), Rayleigh flat fading channel, Rician flat fading channel and
log normal fading channel.
The proposed classifier algorithm for classification of different unknown
modulated signals is based on normalized higher even order cummulants features
and spectral features. The proposed classifiers are based on likelihood function,
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multilayer perceptron and linear discriminant analysis. The simulation results show
that the proposed algorithms have high classification accuracy even at low signal to
noise ratio (SNR). The proposed classifier algorithms perform efficiently as
compared to the existing classifiers.
A novel joint feature extraction and classification technique is proposed to
classify the digital modulated signals by adaptively tuning the parameters of Gabor
filter network. The Gabor atom parameters are tuned using delta rule and weights of
the Gabor filter using least mean square (LMS) algorithm. The proposed algorithm
classifies efficiently the PSK, FSK and QAM signals with 100% classification. The
Modified gabor filter network is proposed for classification of M-PAM signals.
The proposed HMM and Gabor filter network formulates an optimal classifier
structure. The proposed classifier use Baum-Welch algorithm and Genetic algorithm
(GA) to update the Gabor filter network and hidden markov model (HMM)
parameters. The fitness function for the genetic algorithm is probability of
observation sequence given the model. The objective is to maximize the probability
of observation sequence. To improve the classification accuracy, three parameters
of Gabor filters (GFs) network and one HMM parameter are adjusted simultaneously
such that the probability of observation sequence is maximized.
The proposed classifiers are compared with well-known techniques in the
literature and simulation results show the supremacy of the proposed schemes over
the contemporary techniques.
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ABBREVIATIONS
Abbreviation TermADMRA-------Analog and Digital Modulation Recognition Algorithm
ADMR----------------------Automatic Digital Modulation Classification
ALRT--------------------------------------- Average Likelihood Ratio Test
AMC--------------------------------- Automatic Modulation Classification
AMRA------------------------Analog Modulation Recognition Algorithm
ANN-------------------------------------------------Artificial Neural Network
AWGN------------------------------------ Additive White Gaussian Noise
BPA--------------------------------------------Back Propagation Algorithm
CDP-----------------------------------------------------Cyclic Domain Profile
COMINT---------------------------------------Communication Intelligence
CR ----------------------------------------------------------- Cognitive Radios
DCS----------------------------------------Digital Communication System
DMRA-------------------------Digital Modulation Recognition Algorithm
FBA------------------------------------------------ Feature Based Approach
FFBPA---------------------Feed Forward Back Propagation Algorithm
FFBPNN-----------Feed Forward Back Propagation Neural Network
FFT---------------------------------------------------Fast Fourier Transform
FSK-------------------------------------------------- Frequency Shift Keying
GA-----------------------------------------------------------Genetic Algorithm
GFN------------------------------------------------------Gabor Filter Network
GLRT---------------------------------- Generalized Likelihood Ratio Test
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GNN---------------------------------------------------Gabor Neural Network
GP-KNN-------------Genetic Programming with K-Nearest Neighbor
HLRT----------------------------------------- Hybrid Likelihood Ratio Test
HMM---------------------------------------------------Hidden Markov Model
HOC----------------------------------------------Higher Order Cummulants
HOS---------------------------------------------------Higher Order Statistics
HT------------------------------------------------------------Hough Transform
IB---------------------------------------------------Instantaneous Bandwidth
IF-----------------------------------------Instantaneous Carrier Frequency
LBA---------------------------------Likelihood Function Based Approach
LDA--------------------------------------------Linear Discriminant Analysis
LLF---------------------------------------------------------Likelihood Function
LMS-------------------------------------------------------Least Mean Square
LUT----------------------------------------------------------------Lookup Table
MC ------------------------------------------------- Modulation classification
MGFN---------------------------------------Modified Gabor Filter Network
MHD----------------------------------------------Margenau-Hill Distribution
ML--------------------------------------------------------Maximum Likelihood
MLP-----------------------------------------------------Multilayer Perceptron
MMSE----------------------------------------Minimum Mean Square Error
MSE--------------------------------------------------------Mean Square Error
ODST------------------------------Optimized Distribution Sampling Test
PAM--------------------------------------------Pulse Amplitude Modulation
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PCC-----------------------------------Probability of Correct Classification
PHC---------------------------------------------Phase-Histogram Classifier
PPDF---------------------------------Phase Probability Density Function
PRA-----------------------------------------Pattern Recognition Approach
PSD--------------------------------------------------Power Spectral Density
PSK ------------------------------------------------------- Phase Shift Keying
PSO--------------------------------------------Particle Swarm Optimization
QAM----------------------------------- Quadrature Amplitude Modulation
qLLR--------------------------------------------Quasi-Log-Likelihood Ratio
RBPA------------------------------Resilient Back Propagation Algorithm
RD---------------------------------------------------------Rihaczk Distribution
RLS--------------------------------------------------Recursive Least Square
SCF-------------------------------------------Spectral Coherence Function
SDR -------------------------------------------------Software Defined Radio
SLC-----------------------------------------------------Square Law Classifier
SNR-----------------------------------------------------Signal to Noise Ratio
STP--------------------------------------------Serial to Parallel Conversion
SUMC-----------------------------Single User Modulation Classification
SVD-----------------------------------------Singular Value Decomposition
SVM-------------------------------------------------Support Vector Machine
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TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS------------------------------------------------------------ ivABSTRACT------------------------------------------------------------------------------ vABBREVIATIONS --------------------------------------------------------------------- viiTABLE OF CONTENTS-------------------------------------------------------------- xLIST OF TABLES ---------------------------------------------------------------------- xiiiLIST OF FIGURES -------------------------------------------------------------------- xvi
CHAPTER I – INTRODUCTION --------------------------------------------------- 011.1 Introduction ------------------------------------------------------------------------- 011.2 Motivation and Problem Statement ------------------------------------------ 031.3 Contribution of the Thesis ------------------------------------------------------ 051.4 Organization of the Thesis ----------------------------------------------------- 06
CHAPTER II – LITERATURE REVIEW ------------------------------------------ 092.1 Introduction ------------------------------------------------------------------------- 092.2 Likelihood based Decision Theoretic Approach--------------------------- 10
2.2.1 Likelihood Ratio Test ------------------------------------------------------ 112.2.1.1 Average Likelihood Ratio Test ------------------------------------- 112.2.1.2 Generalized Likelihood Ratio Test -------------------------------- 112.2.1.3 Hybrid Likelihood Ratio Test --------------------------------------- 122.2.1.4 Quasi-Hybrid Likelihood Ratio Test ------------------------------ 122.2.1.5 Sequential Probability Ratio Test --------------------------------- 13
2.3 Features based Pattern Recognition Approach---------------------------- 152.3.1 Feature Extraction --------------------------------------------------------- 16
2.3.1.1 Statistical Features -------------------------------------------------- 162.3.1.2 Spectral Features --------------------------------------------------- 172.3.1.3 Cyclo-stationary Features ------------------------------------------ 172.3.1.4 Time Frequency Features ------------------------------------------ 18
2.3.2 Classification ---------------------------------------------------------------- 182.3.2.1 Nature Inspired Heuristic Techniques -------------------------- 192.3.2.2 Artificial Neural Network -------------------------------------------- 202.3.2.3 Fuzzy c-Means -------------------------------------------------------- 212.3.2.4 Hidden Markov Models -------------------------------------------- 22
2.4 Summary---------------------------------------------------------------------------- 25
CHAPTER III – AUTOMATIC MODULATION CLASSIFICATIONUSING FEATURE EXTRACTION TECHNIQUES----------------------------- 263.1 Generalized System Model ---------------------------------------------------- 263.2 Automatic Modulation Classification using Higher Order Statistics--- 29
3.2.1 Introduction------------------------------------------------------------------- 29
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3.2.2 Statistical Features -------------------------------------------------------- 303.2.3 Proposed Algorithm for AMC-------------------------------------------- 333.2.4 Simulation Results-------------------------------------------------------- 333.2.5 Summary--------------------------------------------------------------------- 40
3.3 Automatic Modulation Classification using Linear DiscriminantAnalysis (LDA)-------------------------------------------------------------------------- 40
3.3.1 Introduction------------------------------------------------------------------- 403.3.2 Higher Order Cummulants as Feature Set--------------------------- 413.3.3 Proposed Algorithm for AMC-------------------------------------------- 423.3.4 Simulation Results--------------------------------------------------------- 433.3.5 Summary------------------------------------------------------------------ 48
3.4 Automatic Modulation Classification using Spectral Features--------- 483.4.1 Introduction------------------------------------------------------------------- 483.4.2 Spectral Features---------------------------------------------------------- 483.4.3 Proposed Algorithm using MLP----------------------------------------- 513.4.4 Simulation Results--------------------------------------------------------- 543.4.5 Proposed Algorithm using SVM----------------------------------------- 573.4.6 Simulation Results--------------------------------------------------------- 613.4.7 Comparison with Existing Techniques ------------------------------- 623.4.8 Summary --------------------------------------------------------------------- 64
CHAPTER IV – AUTOMATIC MODULATION CLASSIFICATIONUSING GABOR FILTER NETWORK---------------------------------------------- 654.1 Introduction ------------------------------------------------------------------------- 654.2 System Model --------------------------------------------------------------------- 664.3 Gabor filter for Classification and Feature Extraction-------------------- 664.4 Training and Testing of Gabor filter network-------------------------------- 694.5 The Proposed Algorithm for Modulation Classification------------------- 744.6 Simulation Results ---------------------------------------------------------------- 764.7 Modified Gabor Filter Network for Classification of PAM signals------ 88
4.7.1 Modified Gabor Filter Network------------------------------------------ 894.7.2 Modified Proposed Algorithm for Modulation Classification----- 904.7.3 Simulation Results of Modified Gabor Filter Network ------------- 91
4.8 Comparison with Existing Techniques--------------------------------------- 984.9 Summary ---------------------------------------------------------------------------- 98
CHAPTER V – AUTOMATIC MODULATION CLASSIFCATION USINGHIDDEN MARKOV MODELS ------------------------------------------------------- 1015.1 Introduction ------------------------------------------------------------------------- 1015.2 System Model and Gabor Filter Network ----------------------------------- 1025.3 Genetic Algorithm ----------------------------------------------------------------- 1035.4 Hidden Markov Model ----------------------------------------------------------- 104
5.4.1 Baum Welch (BW) Algorithm ------------------------------------------- 1065.5 Proposed Classifier and its Training ----------------------------------------- 110
5.5.1 Training of Classifier ------------------------------------------------------ 112
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5.5.2 Testing of Classifier ------------------------------------------------------- 1135.6 Simulation Results ---------------------------------------------------------------- 1145.7 Comparison with Existing Techniques -------------------------------------- 1185.8 Summary ---------------------------------------------------------------------------- 121
CHAPTER VI –CONCLUSIONS AND FUTURE DIRECTIONS------------ 1226.1 Summary of Results ------------------------------------------------------------- 1226.2 Future Directions ------------------------------------------------------------------ 124
REFERENCES –----------------------------------------------------------------------- 126
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LIST OF TABLES
Table Page
II – 1 A Summary of Likelihood based Classifiers --------------------------------------13
II – 2 A Summary of Feature based Classifiers -----------------------------------------23
III – 1 Theoretical Normalized 4th, 6th & 8th order cummulants for variousModulation Constellations -------------------------------------------------------- 32
III – 2 Theoretical Values of Normalized cummulants of ConsideredModulation Types ------------------------------------------------------------------- 42
III – 3 Confusion Matrix for PSK modulation in AWGN channel (AveragePerformance 99.95%) ------------------------------------------------------------- 45
III – 4 Confusion Matrix for PSK modulation in AWGN+ Rician Flat FadingChannel (Average Performance 92.26%) ------------------------------------ 45
III – 5 Confusion Matrix for PSK modulation in AWGN + Rayleigh FlatFading Channel (Average Performance 91.38%)--------------------------- 45
III – 6 Confusion Matrix for FSK modulation in AWGN channel (AveragePerformance 99. 5%)-------------------------------------------------------------- 46
III – 7 Confusion Matrix for FSK modulation in AWGN+ Rician Flat FadingChannel (Average Performance 91%)----------------------------------------- 46
III – 8 Confusion Matrix for FSK modulation in AWGN + Rayleigh FlatFading Channel (Average Performance 88%)------------------------------- 46
III – 9 Confusion Matrix for QAM modulation in AWGN channel (AveragePerformance 99.95%)-------------------------------------------------------------- 47
III – 10 Confusion Matrix for QAM modulation in AWGN+ Rician Flat FadingChannel (Average Performance 81%)----------------------------------------- 47
III – 11 Confusion Matrix for QAM modulation in AWGN + Rayleigh FlatFading Channel (Average Performance 77.36%)--------------------------- 47
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III – 12 Specifications for the proposed classifier------------------------------------------53
III – 13 Percentage of correct classification on AWGN channel at 10dB ofSNR------------------------------------------------------------------------------------ 55
III – 14 Percentage of correct classification on Rician flat fading channel plusAWGN at 10dB of SNR ------------------------------------------------------------ 56
III – 15 Percentage of correct classification on Rayleigh flat fading channelplus AWGN at 10dB of SNR ---------------------------------------------------- 56
III – 16 Performance of Recognizer at SNR of 0 to 10 dB ------------------------------61
III – 17 Performance comparison of Spectral Features with existingtechniques----------------------------------------------------------------------------- 62
III – 18 Performance comparison of HOC features with existing techniques ------63
IV – 1 Updated Shift and Modulation Parameter for PSK modulation 2-64--------78
IV – 2 Updated Scale and weight Parameter for PSK modulation 2-64------------79
IV – 3 Updated Shift and Modulation Parameter for FSK modulation 2-64--------79
IV – 4 Updated Scale and weight Parameter for FSK modulation 2-64-------- 80
IV – 5 Updated Shift and Modulation Parameter for QAM modulation 2-64--- 81
IV – 6 Updated Scale and weight Parameter for QAM modulation 2-64------- 81
IV – 7 Training Performance of MGFN of M-PAM signal classificationwithout Noise------------------------------------------------------------------------- 93
IV – 8 Training Performance of MGFN of M-PAM signal classification onAWGN channel---------------------------------------------------------------------- 94
IV – 9 Testing Performance of MGFN of M-PAM signal classification onAWGN channel---------------------------------------------------------------------- 94
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IV – 10 Testing Performance of MGFN for M-PAM signal classification atSNR=10dB on AWGN channel--------------------------------------------------- 94
IV – 11 Testing Performance Comparison of MGFN on AWGN and Fadingchannels for the example of 8-PAM format--------------------------------- 97
IV – 12 Performance Comparison with the Existing Techniques-----------------------99
V – 1 Classification accuracy for the proposed classifier for different no. ofsamples and SNRs ---------------------------------------------------------------- 115
V – 2 Percentage Classification performance at different SNRs and 2048samples ------------------------------------------------------------------------------- 117
V – 3 Performance Comparison with the existing techniques -----------------------120
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LIST OF FIGURES
Figure Page
III – 1 The Generalized System Model ----------------------------------------------------- 28
III – 2 PCC on AWGN channel in scenario {BPSK, QPSK}, N=250----------------- 34
III – 3 PCC on AWGN channel in scenario {QAM 2 to 64}, N=3000----------------- 34
III – 4 PCC on AWGN channel in scenario {PAM 2 to 64}, N=3000----------------- 35
III – 5 PCC on Flat Fading channel in scenario {BPSK, QPSK}, N=250------------ 35
III – 6 PCC on Flat Fading channel in scenario {PAM 2 to 64}, N=2000----------- 36
III – 7 PCC on Flat Fading channel in scenario {QAM 2 to 64}, N=2000----------- 36
III – 8 PCC on Rayleigh Flat Fading channel in scenario {BPSK, QPSK},N=250--------------------------------------------------------------------------------------- 37
III – 9 PCC on Lognormal Fading channel in scenario {BPSK, QPSK}, N=250-- 37
III – 10 PCC on Rician Flat Fading channel in scenario {BPSK, QPSK}, N=250-- 38
III – 11 Performance of ADMC on Faded channel in scenario {BPSK, QPSK},N=250--------------------------------------------------------------------------------------- 38
III – 12 Performance of ADMC on Faded channel in scenario {QAM 2 to 64},N=3000-------------------------------------------------------------------------------------- 39
III – 13 Performance of ADMC on Faded channel in scenario {PAM 2 to 64},N=2500-------------------------------------------------------------------------------------- 39
III – 14 Flow Chart for Modulation Classification------------------------------------------- 42
III – 15 Proposed Architecture for classification of modulation formats--------------- 52
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III – 16 The FFBPN result for the proposed classifier {PSK 2 to 64} on AWGNchannel at SNR of 10dB.------------------------------------------------------------- 55
IV – 1 System Model for Modulation Classification--------------------------------------- 66
IV – 2 Gabor filter bank with input layer and output layer------------------------------- 67
IV – 3 Testing Scheme for Modulation Classification------------------------------------ 69
IV – 4 Training of gabor filter parameters and weights for modulationclassification in case of PSK modulation 2-64 for different number ofiterations at SNR=10dB---------------------------------------------------------------- 83
IV – 5 Training of gabor filter parameters and weights for modulationclassification in case of FSK modulation 2-64 for different number ofiterations at SNR=10dB---------------------------------------------------------------- 84
IV – 6 Training of gabor filter parameters and weights for modulationclassification in case of QAM modulation 2-64 for different number ofiterations at SNR=10dB--------------------------------------------------------------- 84
IV – 7 Training of gabor filter parameters and weights for modulationClassification in case of PSK modulation 2-64 at different SNRs andfixed number of iterations------------------------------------------------------------- 85
IV – 8 Training of gabor filter parameters and weights for modulationClassification in case of FSK modulation 2-64 at different SNRs andfixed number of iterations------------------------------------------------------------- 85
IV – 9 Training of gabor filter parameters and weights for modulationClassification in case of QAM 2-64 at different SNRs and fixed numberof iterations------------------------------------------------------------------------------- 86
IV – 10 Probability of correctness (PCC) versus Number of Iterations atSNR=10dB ------------------------------------------------------------------------------- 87
IV – 11 Probability of correctness (PCC) versus SNR for fixed Number ofIterations ---------------------------------------------------------------------------------- 88
IV – 12 Training of MGFN for the M-PAM formats under no Noise-------------------- 92
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IV – 13 Training of MGFN for the M-PAM formats on AWGN channel---------------- 93
IV – 14 Probability of Correctness curve for the example of PAM16------------------ 96
IV – 15 Probability of Correctness curve under AWGN channel for the exampleof PAM16--------------------------------------------------------------------------------- 97
V – 1 Flow chart of Genetic Algorithm ----------------------------------------------------- 103
V – 2 Proposed Classifier Structure -------------------------------------------------------- 111
V – 3 Structure of Proposed Classifier ----------------------------------------------------- 112
V – 4 Testing of Proposed Classifier ------------------------------------------------------- 114
V – 5 Classifier training for the case of PAM and QAM signals --------------------- 116
V – 6 Average classification performance for different number of sample-------- 116
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CHAPTER I
INTRODUCTION
1.1 Introduction
Generally in a communication system, there is mutual
cooperation/handshaking between transmitter and the receiver, so the receiver
has a priori knowledge of the modulation format of the transmitted signal. The
modulation format includes modulation type, modulation index and nominal
carrier frequency in analog communication systems. In digital communication
systems (DCS), the modulation format includes modulation type, alphabet size,
nominal carrier frequency, symbol constellation, frequency deviation (for
frequency modulated signals only) and the symbol rate. The system designer
generally focuses on making DCS reliable (Azzouz et al., 1996).
In DCS, security is one of the fundamental requirements. Two users
do not want their communication to be known to any third user. So the
communication authorities might wish to detect the non-licensed transmitters.
The detection of non-licensed transmitters is to be done by recognizing or
classifying the modulation format. Some of the applications are interference
identification, spectrum management, surveillance, threat analysis, warning
and target acquisition (Azzouz et al., 1996a).
In communication intelligence (COMINT) systems, the classification of
modulation has been done manually. This is done by using the demodulator
banks where each of the demodulator banks is designed for one modulation
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type. Demodulator outputs give the modulation type of received signal which
is corrupted by noise and channel effects. The classification process requires
large signal duration, experienced analyzers and also requires intelligent
decision algorithm at the demodulator output. Implementation of such
classification process is complex, requiring excessive storage and unable to
guarantee reliable classification results. The modulation signals are
recognized and limited to the use of demodulator’s bank.
With the emergence of software-defined radios (SDRs), radio
frequency (RF) communication devices have the capability to transmit in low
power, change the transmitting frequency, and modify the modulation format
during transmission. Adaptive modulation varies the rate of data transmission
relative to the channel operating conditions. In an environment without
handshaking between the transmitter and receiver, RF signals need to be
recognized. Automatic Modulation Classification (AMC) is a widely used and
demanded feature on receiver side to adapt without handshaking between a
transmitter and relevant receiver pair.
Cognitive radio (CR) has become key research area in digital
communication. CR is promising technology that improves the spectrum
efficiency by opportunistically finding and utilizing the un-occupied frequency
bands. Automatic modulation classification has various applications in
Cognitive Radio (cooperative and non-cooperative communication), civilian
and military communication, electronic warfare and surveillance. In military
applications, there is no such information available about enemy signal. CR
needs to identify the modulation format employed in that signal. AMC is to
recognize the received signal modulation type, which has undergone through
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channel effects like fading, noise and interference etc. during transmission of
the signal. AMC is basically a non-cooperative communication which also
includes some aspects of cooperative communication, such as tracking and
identification of channel and estimation and detection of signal parameters.
1.2 Motivation and Problem Statement
Link adaptation which is also known as adaptive modulation and
coding, creates an adaptive modulation scheme where pool of multiple
modulations are employed by the same system. It enables the optimizing of
transmission reliability and data rate through adaptive selection of modulation
schemes according to channel conditions. While transmitter has freedom to
choose how signals are modulated. The receiver must have knowledge of the
modulation format to demodulate the signal. Easy way to achieve this is to add
modulation information in each frame, so that receiver would be notified about
any change in the modulation scheme. This will affect the spectrum efficiency
due to extra modulation information in each frame. The solution is automatic
modulation classification (Zhu 2014).
Existing approaches for AMC are based on decision theoretic
approach and pattern recognition approach. The likelihood approach is optimal
and pattern recognition approach is sub optimal. Both approaches provide
classification/recognition of modulation formats on fading channels. In this
research we will focus only on the feature based pattern classification
approach. The popular modulation formats are PAM, QAM, PSK and FSK of
order 2 to 64.
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The previously designed classifiers are capable to classify less
number of modulation formats by Cai et al., (2004), Dobre et al., (2007) and
Mustafa et al., (2004). The major problem in feature based pattern
classification is the extraction of the features. The most popular techniques
used for feature extraction in the literature are spectral features extraction,
cyclo-stationary property based feature extraction, higher order moments and
higher order cummulants (Azzouz et al., (1995); Poopola et al., (2011); Wong
et al., (2001); Nandi et al, (1998); Dobre et al., (2007); Dobre et al., (2010);
Ebrahimzadeh et al., (2012); He et al., (2008); Lanjun et al., (2010); Lopatka
et al., (2000); Ramkumar (2009)). The feature based approach is easy to
implement and computationally simple (Dobre et al., 2003).
The maximum number of modulation formats classified by the
previous methods are limited. The classification accuracy of the classifier are
mostly evaluated in the presence of additive white guassian noise (AWGN)
channel model. So classifying the maximum number of modulation formats
(PAM, QAM, PSK and FSK of order 2 to 64) is one of the problems which
needs to be addressed. The classification of modulation formats in the
presence of AWGN and also on fading channels (Rayleigh flat fading channel,
Rician flat fading channel and Log normal fading channel) is also an open issue
which needs to be addressed. In the effort to produce more efficient and
accurate classification performance, the feature based pattern recognition
approach is frequently used. The extraction of new features from the received
signal and devising an efficient classifier design has significantly improved the
performance of classifier. Thus problem statement is defined to
identify/classify the digital modulation formats from the noisy signal.
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1.3 Contribution of the Thesis
The objective of this thesis is to design an efficient classifier structure,
with improved performance as compared to state of art well known existing
techniques. The contribution is summarized as follows:-
1. The normalized higher order cummulants based modulation
classification is presented. Higher even-ordered normalized
cummulants are used, for the classification of modulation formats.
The main advantage of the proposed classifier based on maximum
likelihood and linear discriminant analysis is the improvement
being claimed as major contribution in the classification accuracy.
The performance of proposed classifier is also compared with the
well-known existing classifiers (Chen et al., (2008) & Orlic et al.,
(2009)).
2. The improved digital modulation classification scheme is
presented based on spectral features. The proposed classifier
uses feed-forward back propagation neural network (FFBPNN)
and support vector machine. The classification accuracy of the
proposed classifier shows better performance as compared to
existing techniques (Ghauri et al. (2014)).
3. The new features are extracted, named as Gabor features, which
to the best of our knowledge has not been utilized for the problem
of modulation classification. The proposed classifier parameters
and weights of the adaptive filter are adjusted until cost function is
minimized. The training and testing of proposed classifier shows
6
that proposed algorithm is capable of classifying the modulation
formats (PSK, FSK and QAM) of order 2 to 64 with high probability
of correctness.
4. The modified Gabor filter network for classification of M-PAM
signals is presented. Some changes are proposed to classify the
PAM signals as classification of M-PAM is difficult because of
increasing amplitude values as M varies from 2 to 64. The
proposed changes make the algorithm robust for the classification
of M-PAM modulation formats not only for AWGN channel but also
for use in fading channels.
5. The classifier based upon the hidden markov model (HMM) and
Gabor filter is presented. The parameters of the HMM and Gabor
filter network are updated to maximize the fitness function. The
proposed classifier structure is capable of efficiently classifying the
M-QAM and M-PAM signals. The proposed classifier is also
compared with the existing classifier.
1.4 Organization of the Thesis
Chapter II provides brief overview of automatic modulation
classification techniques in the literature over the past two decades. The
literature survey is divided into two subsections (decision theoretic approach
and pattern recognition approach). In the first section, an overview of existing
techniques based on decision theoretic approach is provided in which lookup
table (LUT), average likelihood ratio test (ALRT), hybrid likelihood ratio test
7
(HLRT), generalized likelihood ratio test (GLRT) and quasi-HLRT are
discussed. In second subsection, features based pattern recognition approach
is presented in which neural network based classifiers are briefly discussed.
The limitations and drawbacks of different types of classifiers are also
discussed.
In Chapter III, two features extraction techniques are given. In the first
technique, features extracted are higher order moments (HOM) and higher
order cummulants (HOC). The classifiers used are based on the maximum
likelihood and linear discriminant analysis. In the second technique, spectral
features are extracted from the received signal. The classifiers proposed are
based upon the FFBPNN and SVM. The quantitative analysis is presented to
compare the performance of the proposed classifier with the existing
classifiers.
In Chapter IV, two algorithms are presented to classify the digital
modulation formats (PSK, FSK, QAM and PAM). The new features are
extracted named as Gabor features. In these algorithms, Gabor filter network
and Modified Gabor filter network are used for joint feature extraction and
classification. The training and testing of Gabor filter network reveals that
proposed classifier provides better results as compared to the existing
techniques.
In Chapter V, classification of M-PAM and M-QAM signals are carried
out using Gabor filter bank and Hidden markov models. The Gabor filter bank
parameters and HMM parameters are updated using genetic algorithm and
Baum Welch algorithm. The objective is to maximize the fitness function. The
8
training and testing of proposed classifier demonstrates improved
classification accuracy over the state of art existing techniques.
Finally, Chapter VI summarizes and concludes the work and also gives
suggestions for future direction.
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CHAPTER IILITERATURE REVIEW
2.1 Introduction
A comprehensive review of literature regarding automatic modulation
techniques is presented. The automatic modulation classification (AMC) is an
intermediate step between detection of the information carried by the signal
and its demodulation. AMC is an approach which classifies the modulation
formats of the received signal on the receiver side. Automatic modulation
classification has found extensive importance in the field of electronic
surveillance, military sensitive areas, electronic counter measures, civilian
populated premises domain, software defined radios and lately in cognitive
radios (Dobre et al., (2010); Ye et al., (2007); Zeng et al., (2012); Zhou et al.,
(2010); Boutte et al., (2009); Avci et al.,(2007); Avci et al., (2008)). In military
domains it may be used for monitoring and interference recognition, whereas
in civil domain it includes interference confirmation, spectrum management
and signal confimation.
The most important applications in civil domain are intelligent
modems, software defined radios and cognitive radios (Dobre et al., 2006).
Due to incremental technologies such as cognitive radios, recent research has
been focused on identifying and then classifying these types of signal by Mitola
et al., (1999) and Mitola, (2000) and Haykin, (2005). In cognitive radios, the
secondary user use the spectrum of primary user with cooperation or by
10
sensing the primary user but with limitation of interference to primary user. For
this reason secondary user should have knowledge of modulation format of
the primary user signal as suggested by Ramkumar, (2011). In this chapter,
brief review of different techniques for classification of modulation formats is
presented.
2.2 Likelihood based Decision Theoretic Approach
As one of the automatic modulation techniques, the likelihood function
based (LB) decision theoretic approach is computationally complex but optimal
by Ghauri et al., (2014). The modulation classification in decision theoretic
approach has been viewed as multiple hypothesis test or may be sequence of
pair wise multiple hypothesis test. Once the likelihood function is set up,
likelihood ratio tests (LRT) are to be used to determine the modulation format
of the received signal by Wang et al., (2010). Due to phase errors, channel
effects, timing jitter and frequency offset, the decision theoretic approach is not
robust to model mismatch by Yucek et al., (2004).
The classifiers used in decision theoretic approach are based on
likelihood ratio test, log-likelihood ratio test, phased-based, phase histogram-
based and square-law based classifiers. Some of the test are average
likelihood ratio test (ALRT), generalized likelihood ratio test (GLRT), hybrid
likelihood ratio test (HLRT), quasi-HLRT, quasi-likelihood ratio (qLLR), log-
likelihood ratio test (LLRT) and sequential probability ratio test (SPRT) (Dobre
et al., 2005; Hameed et al., 2009; Dobre et al., 2006; Lin et al.,1997)
11
2.2.1 Likelihood Ratio Test (LRT)
The idea behind the likelihood based decision theoretic approach is
that the probability density function (PDF) of the observed waveform,
conditioned by the embedded modulated signal, contains all information for the
signal classification.
2.2.1.1 Average Likelihood Ratio Test (ALRT)
In average likelihood ratio test, the unknown quantities are treated as
random variables (RVs) with certain probability density function (PDF). The
PDF of the received signal is computed by averaging over each hypothesis.
The ALRT method gives maximum probability of classification, if the assumed
and actual distribution of the unknown quantities coincide. ALRT suffer from
the high computational complexity when number of unknown parameters are
increased (Huang et al., 1995; Long et al., 1994; Abdi et al., 2004; Sills, 1999;
Wei et al., 2000; Hong et al., 2003; Beidas et al., 1995). ALRT is optimal in a
Bayesian sense, if the chosen PDF is same as the true PDF (Beidas et al.,
1998).
2.2.1.2 Generalized Likelihood Ratio Test (GLRT)
Generalized likelihood ratio test (GLRT) treats the unknown quantities
as deterministic unknowns. These deterministic unknowns are estimated
under the hypothesis, after that unknown quantities are substituted by the
maximum likelihood estimate (MLE) obtained from the observed data to
perform the likelihood ratio test. When the length of observed data increased,
GLRT computational complexity increase exponentially (Panagiotou et al.,
12
2000). When the constellations are nested, the GLRT fails (Abdi et al., 2004;
Dobre et al., 2007). The remedy is to either avoid nested modulation schemes
or change the weighting probabilities.
2.2.1.3 Hybrid Likelihood Ratio Test (HLRT)
In hybrid likelihood ratio test, both ALRT and GLRT are combined in
which some of the unknown quantities are treated as random variable and
others are treated as deterministic known. In HLRT, the problem of nested
constellation is overcome by averaging the signal constellation points (Dobre
et al., 2007; Sills et al., 1999).
ALRT requires a multidimensional integration and GLRT requires a
multidimensional maximization. The ALRT is impractical because of
performing a multidimensional integration for a large number of unknown
quantities and also the need for knowing the prior PDFs. The GLRT requires
multidimensional maximization over the unknown data, which can lead to the
same value of the likelihood function for nested signal constellation, which
yields incorrect classification (Tress, 2001).
2.2.1.4 Quasi-Hybrid Likelihood Ratio Test (q-HLRT)
To reduce computational complexity in maximum likelihood estimation
of the HLRT, a sub-optimal algorithm namely quasi-HLRT is used. The ML
estimates obtain in q-HLRT from the conditional observation PDF instead of
un-conditional PDF in HLRT. The other parameters are estimated either using
the maximizing the PDF or the LFs. In q-HLRT, the likelihood function (LF)
under hypothesis is computed by using method of moments (MoM) estimates
13
of the unknown parameters and averaging over unknown constellation points.
The MoM estimates are computed based on second and fourth-order moments
of the received signal (Fahad et al., 2006).
2.2.1.5 Sequential Probability Ratio Test (SPRT)
In sequential test, random number of samples are used. For multiple
hypothesis, sequential test provides flexibility in controlling the error
probability. The maximum a posteriori (MAP) test have no control over the
individual error probability conditioned on hypothesis, while minimizes the total
error probability. The Neyman-Pearson maximizes the probability of correct
classification for the binary hypothesis but not in practice for the multiple
hypothesis. The sequential probability ratio test (SPRT) can be utilized for
binary as well as multi- hypothesis cases (Lin et al., 1997). It provides decision
error probability with least number of samples. The contributions of numerous
articles are summarized in compact form in Table II-1.
Table II-1: A Summary of Likelihood based Classifiers
Author(s) Classifier(s) Modulations Unknownparameter(s) Channel
Kim et al.,(1988) andHsue et al.,
(1989)
Quasi-ALRTBPSK, QPSK,BFSK, 4FSK,
8FSK
Carrier phaseθ AWGN
Long et al.,(1994) Quasi-ALRT 16PSK, 16QAM,
V29Carrier phase
θ AWGN
Beidas etal., (1995)
ALRT
Quasi-ALRT32FSK, 64FSK
Phase jitter
1
Kk k
AWGN
14
Nandi et al.,(1995)
Quasi-ALRTUW
BPSK, QPSK,8PSK, 16PSK
(12 Modulations)
Carrier phaseθ & timing
offsetAWGN
Chuggi etal., (1995) HLRT BPSK, QPSK,
OQPSK
Carrier phaseθ, signalpower &
PSD
AWGN
Ho et al.,(1995) HLRT MPSK, MFSK Angle of
arrival AWGN
Sapiano etal., (1996) ALRT UW BPSK, QPSK,
8PSK - AWGN
Beidas etal., (1996)and Beidas
et al.,(1998)
ALRT
Quasi-ALRT
32FSK, 64FSK Phase jitter& timing
offsetAWGN
Sills, (1999) ALRTBPSK, QPSK,
16QAM,V29,32QAM, 64QAM
Carrier phaseθ AWGN
Wei et al.,(2000) ALRT 16QAM, V29 - AWGN
Panagiaotou et al.,(2000)
GLRT
HLRT16PSK, 16QAM,
V29Carrier phase
θ AWGN
Hong et al.,(2003) ALRT BPSK, QPSK Signal level AWGN
Dobre et al.,(2004) HLRT
BPSK, QPSK,8PSK, 16PSK,
16QAM, 64QAM
Channelamplitude &
phase φ
FlatFading
Abdi et al.,(2004)
ALRT Quasi-HLRT
16QAM, 32QAM,64QAM
Channelamplitude a& phase φ
FlatFading
Li et al.,(2005) Quasi-HLRT 4QAM, 16QAM,
64QAMFrequencyoffset Δf AWGN
Dobre et al.,(2006)
HLRT
Quasi-HLRTBPSK, QPSK,8PSK, 16PSK
PSD N ,Channel
amplitude a& phase φ
FlatFading
15
Su et al.,(2008) ALRT, LUT 16-QAM, 32-QAM - AWGN
Hameed etal., (2009)
HLRT, q-HLRT
16QAM,BPSK,QPSK
Signalamplitude,Phase &
Noise power
Fading
Rvayuli etal., (2013) HML 16-QAM, 32-
QAM, 64-QAM - RayleighFading
Kebrya etal., (2013)
LLF,Weighted
SumAlgorithm
QPSK, 16QAM
Amplitude,Phase and
NoiseVariance
AWGN
Mohammadiet al.,(2013)
ExpectationMaximization
(EM)
BPSK, QPSK,16QAM, 64 QAM
Channelcoefficients,noise power
-
Sergienkoet al.,(2014)
LLF MPSK, 16QAM - -
Zhu et al.,(2014)
Non-parametric LF
BPSK, QPSK,8PSK, 4QAM,
16QAM, 64QAM
NoiseVariance Fading
2.3 Features based Pattern Recognition Approach
The feature based (FB) pattern recognition method is suboptimal
solution. In FB approach modulation recognition is carried out in two modules.
The first module is feature extraction subsystem, in which features are
extracted from the received signal. The second module is pattern recognizer
subsystem, in which input to the classifier structure are extracted features
which determines the modulation format. Due to robustness with respect to
model mismatches and low computational complexity, FB approach is used for
modulation recognition (Lanjun et al., 2011; Orlic et al., 2012; Wong et al.,
2001).
16
Feature based pattern recognition approach generally includes feature
extraction and classification. The most common features extracted from the
received signal are spectral features, statistical features, cyclo-stationary
features, time frequency features and wavelet features. The classifiers are
generally based on the nature inspired heuristic algorithms, artificial neural
networks, fuzzy logic and hidden markov models.
2.3.1 Feature Extraction
A feature provides an information, relevant to an application, required
for solving a computational task. Feature selection is dependent upon the
application area. In most of the applications, extraction of only one feature from
the received signal does not provide sufficient information about modulation
format hence instead of one, two or more different features are extracted.
Some of the features in the literature used are multi-fractal features, mean and
variance, empirical characteristics function (ECF), correlation function,
wavelets features, higher order correlation (He at al., 2008; Puengnim et al.,
2010; Dulek et al., 2014; Marey et al., 2014; Avci et al., 2007; Zeng et al., 2012;
Liu et al., 2014 and Beidas et al., 1995).
2.3.1.1 Statistical Features
The higher order statistics involves the moments and cummulants.
Cummulants are set of quantities that provides alternatives to the moments,
Cummulants are made up of moments. Cummulants may be of 2nd, 4th, 6th and
8th order. The higher order moments (HOM) and higher order cummulants
17
(HOC) are extracted from the received signal to discriminate the modulation
formats. The higher order cyclic cummulants are also used as feature set. The
HOC are utilized for the modulation classification by the Liu et al., (2014), Su,
(2013), Eldemerdash et al., (2013), Orlic et al., (2012), Sanderson et al.,
(2013), Zhou et al., (2010), Prakasam et al., (2008), Lopatka et al., (2000), Dai
et al., (2002), Cai et al., (2004) and Ebrahimzadeh et al., (2011).
2.3.1.2 Spectral Features
The spectral features are obtained from three basic parameters i.e.
amplitude, phase and frequency. The amplitude, phase and frequency give the
hidden information contents in the modulated signal. These three parameters
are obtained by taking the Hilbert transform of the modulated signal. The
spectral features are the standard deviations of the centered instantaneous
amplitude, frequency and phase and power spectral density (PSD). The
spectral features exploited for the classification of limited number of the
modulation formats by Nandi et al., (1995), Popoola et al., (2011),
Ebrahmzadeh, (2011) and Valipour et al., (2012). The cyclic spectral features
which are extracted from the cyclo-stationary property are also used by Xianci
et al., (1995).
2.3.1.3 Cyclo-stationary Features
In practice, most of the modulated signals have some parameters
which change with time. In digital communication, these parameters may be
periodic keying of amplitude, frequency and phase. In previous decades, these
periodicities are not been used for extracting parameters from the received
18
signal. The most of the signals have the cyclo-stationary property which can
be exploited for classification of modulation formats. The features extracted
from the cyclo-stationary property are known as cyclo-stationary features.
These features are exploited for classification of limited number of modulations
by Ramkumar, (2009), Dobre et al., (2009), Like et al., (2009) and Sanderson
et al., (2013).
2.3.1.4 Time-Frequency Features
The Fourier transform (FT) mainly emphasises on the frequency
domain and cannot analyze the variations in time domain. To do the analysis
of frequency and time jointly, short time Fourier transform is used. Short Time
Fourier Transform (STFT), the simplest time-frequency representation, is a
two-dimensional representation created by computing the FT and using a
sliding temporal window. By using the STFT we can observe how the
frequency of the signal change with time. The features extracted from the time-
frequency analysis are used to classify the modulation formats. The Wigner-
Vile distribution and Margenau-Hill distribution are also used in time-frequency
analysis. The limited number of modulation formats classified by Ketterer et
al., (1999), Ye et al., (2007), Zhang et al., (1999) and Gandetto et al., (2014)
using time-frequency features.
2.3.2 Classification
In recent years, several classifiers have been proposed for the
purpose of classification of modulation formats. The features discussed in
19
section 2.3.1 are input to classifier structure which decides the modulation
format of received signal. The classifier structure includes the nature inspired
heuristic techniques, artificial neural networks, K-nearest neighbours (KNN),
support vector machine (SVM), fuzzy c-means and hidden markov models
(Ling et al., 2010; Puengnim et al., 2010; Avci et al., 2007 and Khaarbech et
al., 2014).
2.3.2.1 Nature Inspired Heuristic Techniques
The nature inspired heuristic techniques have been exploited for the
modulation classification in past several decades. The techniques involved are
genetic algorithm (GA), particle swarm optimization (PSO), ant colony
optimization (ACO), bee colony optimization (BCO) and ant bee colony
optimization (ABCO). The above listed algorithms are frequently used with the
neural networks for modulation classification.
Ling et al., (2010) uses particle swarm optimization (PSO) and
subtractive clustering. The features extracted from the PSO-SC are with the
best clustering radius. Zhu et al., (2014) used optimized distribution sampling
test (ODST) and GA to optimize the distance metrics. Ebrahimzadeh, (2011)
used spectral features and genetic algorithm (GA) based clustering for
modulation classification. Combination of spectral features, statistical features
and wavelet based features are used and performance of classifier is
optimized using PSO by Valipour et al., (2012). BCO is also used to improve
the overall performance of the proposed classifier by Ebrahimzadeh, (2012).
20
2.3.2.2 Artificial Neural Network
An artificial neural network (ANN) is a mathematical model that
resemble the interconnected neurons of human beings. It contains
interconnected processing elements in the form of layers. It acts as parallel
distributed processor which is capable of storing the information in training and
making it available for later use when required (Haykin (2008); Cheng et al.,
(2014); Gandetto et al., (2014); Guldemir et al., (2007)). Several neural
networks-based modulation classification schemes have been proposed by
the Wong et al., (2004), Cheng et al., (2014), Wong et al., (2001) and Yang et
al., (2001), Popoola et al., (2011), Zadeh et al., (2006), Yang et al., (2001),
Desimio et al., (1988), Luo et al., (2014).
In these techniques, discrete wavelet transform (DWT) and principal
component analysis (PCA) are used for feature extraction and reduction,
respectively. The ANN techniques used for classification of modulation formats
are back propagation neural network (BPNN), SVM, multi-layer perceptron
(MLP), radial basis function (RBF) and independent component analysis (ICA).
The back propagation neural network and its variants are used for
classification of modulation formats by Popoola (2014), Desimio et al. (1988),
Nandi et al. (1995), Azzouz et al. (1996), Azzouz et al. (1997a) and Azzouz et
al. (1997b), Park et al. (2006), Wong et al. (2004), Popoola et al. (2011), Cheng
et al. (2014) and Hassan et al. (2010).
One of the simplest classification technique is the KNN classifier.
Classification of an input feature vector is done by determining the k-closet
training vectors according to a suitable distance metric. This vector is then
21
assigned to that class to which the majority of those KNN belongs. KNN
classifiers are used with the neural network and evolutionary computing
techniques for modulation classification by Aslam et al., (2012). The fitness
function for genetic programming (GP) are evaluated by using KNN during
training phase.
The support vector machine is state of the art classification method
based on machine learning theory. Compared with other methods such as
ANN, decision tree and Bayesian network, SVMs have significant advantages
of higher accuracy, elegant mathematical tractability and direct geometric
interpretation. Besides, it does not need a large number of training samples to
avoid over-fitting. Original SVMs are the linear classifiers. The SVM and
multiclass SVM can be used for the modulation classification.
Ebrhimzadeh et al., (2010) used SVM and multi-class SVM as
classifier and performance of classifier is optimized using GA. Ebrahimzadeh,
(2012) used hierarchical support vector machine with BCO to improve the
overall performance of classifier. Ebrahimzadeh et al., (2011) used hybrid
neural network classifier for classification. Some of the related work carried out
using SVM by Valipour et al., (2012), Ebrahimzadeh et al., (2009), Mustafa et
al., (2004) and Park et al., (2006).
2.3.2.3 Fuzzy c-Means
Fuzzy c-means (FCM) method is a simple statistical feature
comparison that distinctively characterizes the object. FCM used an objective
function to allow cluster formation in multidimensional space. Each data point
in the space can belong to more than one cluster, with different membership
22
values. Avci et al., (2007) utilized the expert discrete wavelet adaptive network
based fuzzy inference system for modulation classification. The twenty
different feature sets are generated using daubenchies, coiflets, biorthogonal
and symlets wavelet families. Mobasseri, (1999) used a fuzzy c-means
clustering algorithm for recovery of constellation, after that recovered
constellations are modeled by binomial non-homogenous spatial random
fields. Lopatka et al., (2000) used mamdani fuzzy classifier for classification of
modulation formats.
2.3.2.4 Hidden Markov Model
In HMM, the main interest is to determine the posteriori probability of
the received signal. These probabilities are computed using Baum-Welch
algorithm. Puengnim et al., (2010) used BW algorithm for classifying the
modulation formats. The features extracted are the mean and variance for
classification, classifiers estimate the posteriori probabilities of the received
signal for each modulation type and plug them in to optimum Bayes decision
rule. Some of the related work using HMM by Puengnim et al., (2008) and
Puengnim et al., (2007). The automatic modulation classification (AMC)
algorithms are discussed in detail by Dobre et al., 2007, which rely on the
features extraction technique of the received signal. The contributions of
numerous articles are summarized in Table II-2.
23
Table II-2: A Summary of Feature Based Classifiers
Author(s) +Year Features Modulation
Formats Channel
Hsue et al.,(1990) andYang et al.,
(1991)
Variance of the zero-crossing intervalsequence, phase
difference and zero-crossing interval
histograms
UW, BPSK,QPSK,8PSK,BFSK, 4FSK,
8FSK
AWGN
Sapiano et al.,(1995) DFT of phase PDF UW, BPSK,
QPSK, 8PSK AWGN
Azzouz et al.,(1996)
Maximum PSD ofnormalized centeredamplitude, standard
deviations of normalizedcentered amplitude,phase and frequency
2ASK,4ASK,BPSK,QPSK,2FSK, 4FSK
AWGN
Martret et al.,(1997)
Fourth- and second-order moments of the
received signalQPSK, 16QAM AWGN
Yang et al.,(1997)andYang et al.,
(1998)
PDF of phase UW, BPSK,QPSK,8PSK AWGN
Marchand etal., (1998)
Fourth- and second-order cyclic cummulants
of the received signal
4QAM,16QAM,64QAM
AWGN
Hong, (1999)
Variance of HWTmagnitude and
normalized HWTmagnitude
QPSK, 4FSK,16QAM AWGN
Swami et al.,(2000)
Normalized fourth-ordercummulants of the
received signal and AMAcost function
BPSK, 4ASK,QPSK,16QAM,
V29,V32,64QAM
FrequencySelectiveChannel
Wei et al.,(2000)
Normalized fourth-ordercummulants of the
received signal
BPSK, 4ASK,16QAM,8PSK,V32, V29, V29c
AWGN,impulsivenoise, co-channel
interference
24
Hong et al.,(2002)
Variance of HWTmagnitude, HWT
magnitude and peakmagnitude histograms
BPSK, QPSK,8PSK,2FSK,
4FSK,8FSK,CP2FSK,CP4FSK,CP8F
SK, MSK
AWGN
Dobre et al.,(2003)
Eighth-order cycliccummulants of the
received signal
BPSK, QPSK,8PSK,ASK,
8ASK,16QAM,64QAM, 256QAM
AWGN
Yu et al.,(2003)
DFT of the receivedsignal
2FSK, 4FSK,8FSK,16FSK,
32FSKAWGN
Dobre et al.,(2004)
Eighth-, sixth-, andfourth- order cycliccummulants of the
received signal
4QAM, 16QAM AWGN,impulsive noise
.
Dobre et al.,(2005)
Eighth-order cycliccummulants of the
signal at the output of aselection combiner
4ASK,8ASK,BPSK,
QPSK,16QAM,32QAM,64QAM
Rayleigh &Rician Fading
Channels
Avci et al.,(2007)
Daubenchies, Coiflets,Biorthogonal andSymlets Wavelet
ASK8, FSK8,PSK8, QASK8 AWGN
He et al.,(2008)
Multi-fractalfeatures/dimensions
CW, BFSK,BPSK, 4ASK,
16QAMAWGN
Like et al.,(2009)
Hierarchical cyclo-stationary features
AM, BPSK,OFDM, CDMA,4ASK, 8ASK,
1-16PSK,16&64 QAM
Fading
Puengnim etal., (2010) Mean and Variance
QPSK,8PSK,16APSK,32APS
K
AWGN +Fading
Ling et al.,(2010)
Particle SwarmOptimization subtractive
clustering
(PSO-SC)
M-QAM AWGN
25
Ebrahimzadehet al., (2010) HOC & SVM BPSK, QPSK,
QAMMultipathFading
Hassan et al.,(2010)
HOM of continuouswavelet transform
M-ary ShiftKeying
AWGN +Fading
Ahmadi,(2011)
Constellation diagramand two threshold
algorithm
4QAM,16QAM,64QAM,256QAM
AWGN
Orlic et al.,(2012) 6th Order Cummulants QAM and PAM Multipath
Fading
Sanderson etal., (2013)
4th and 6th OrderCummulants &
Cyclostaionary Features
BPSK, QPSK,16-QAM
Fading +AWGN
Liu et al.,(2014)
Higher Order CyclicCummulants
BPSK, 4PAM,QPSK, 8PSK,
16-QAMAWGN
Marey et al.,(2014) Correlation function BPSK, QPSK,
8PSK,16QAM Fading
Cheng et al.,(2014) Spectral Features
2ASK, 4ASK,2FSK, 4FSK,
BPSK & QPSKAWGN
2.4 Summary
In this chapter, we focused only the features based pattern recognition
approach. The popular modulation formats considered for classification
purpose are PAM, QAM, PSK and FSK of order 2 to 64. The most popular
feature extraction techniques in the literature are spectral features, cyclo-
stationary features, higher-order moments and higher-order cummulants. A
detailed summary of algorithms based on decision theoretic approach and
pattern recognition approach are also given in tabular form.
26
CHAPTER IIIAUTOMATIC MODULATION CLASSIFICATION USING
FEATURE EXTRACTION TECHNIQUES
In this chapter, the generalized system model for the classification of
digital modulation formats is presented. The features extracted from the
received signal are normalized higher order cummulants and spectral features.
The 8th order normalized cummulants are used for the classification of
modulation formats, where existing features are 4th and 6th order normalized
cummulants. The performance comparison with the existing techniques shows
that high classification accuracy is achieved using proposed features and also
classifier is capable to classify PSK, PAM and QAM efficiently. The classifier
performance is also evaluated on fading channels. The classifiers proposed in
this chapter are based on linear discriminant analysis, maximum likelihood,
feed forward back propagation neural network and support vector machine.
The classification accuracy of the proposed classifiers are much better at lower
SNRs and classifiers structure are capable to classify maximum number of
modulation formats. The classification performance is also compared with well-
known existing techniques in the literature.
3.1 Generalized System Model
In communication system, modulation format of the transmitted signal
is one of the important parameter. For non-cooperative communication
27
systems, identification of signal modulation format is one of the complex issue.
In practical communication system, signal modulation format has become
more diverse to improve its anti-interference ability. Modulation classification
(MC) is done before demodulation of the signal.
The generalized system model for the automatic modulation
classification (AMC) is shown in Figure III-1. The input symbols are modulated
by any of the modulation formats (PSK, FSK, PAM and QAM) of order 2 to 64.
The modulated symbols have undergone through the channel effects and as
well as channel noise. The generalized expression for the received signal is
represented in Eq.III.1.
( ) ( ; ) ( )ir t x t y t u (Eq.III.1)
where ( )y t is AWGN. The ( ; )ix t u is the noise free baseband complex
envelope of the received signal in its comprehensive form is given by
(2 )
1
; ))( ( 1j
Jj ft i
i i jj
x t a e e x h t j T
u (Eq.III.2)
where ia is unknown amplitude factor 2i
si
px
EaE
, where sE is
baseband signal energy, 2ix
is variance of ith signal constellation andpE is
transmitted pulse energy. f is carrier frequency offset, is carrier phase,
j is phase jitter (vary sample to sample), ijx is symbol sequence from ith
modulation format, is timing offset, (.)h is channel impulse response and T
is symbol period.
28
Figure III-1. The Generalized System Model
There are four basic types of modulation schemes; FSK, PSK, PAM
and QAM. Suppose we have a baseband (message) signal ( )m t and a carrier
signal:
( ) cos 2c c c cm t A f t (Eq.III.3)
where cA is the carrier amplitude and cf is the carrier frequency and
c is carrier phase angle. The transmitted signal is ( ) ( )* ( )cx t m t m t where
( )m t is the baseband signal and ( )cm t is the carrier signal. Modulated signals
for frequency shift keying (FSK) and phase shift keying (PSK) are defined by
( ) cos 2 ( )FSK cm t f t t (Eq.III.4)
(2 )PSK c im t Acos f t (Eq.III.5)
where 1, 2, 3...i M . In pulse amplitude modulation (PAM), the
samples of the baseband signal may vary with the amplitude of carrier in
proportion to the sampled values of baseband signal.
( ) ( )PAMn
m t m n p t nT (Eq.III.6)
29
where ( )m n are the pulse amplitude, T is the repetition of pulse
interval and 1/ T is the symbol rate. Quadrature amplitude modulation (QAM)
requires chang of amplitude and phase of signal and carrier. QAM can be
achieved by mixing two sine waves that are 90 degree out of phase with each
other. By varying only the amplitude of any signal will vary the phase and
amplitude of the mixed signal. Let 1( )m t and 2 ( )m t be the two signals such
that 1( ) ( )m t Acos and 2( ) ( )m t Asin . Modulated signal for QAM is
1 2( ) ( ) (2 ) ( ) (2 )QAM c cm t m t cos f t m t sin f t (Eq.III.7)
3.2 Automatic Modulation Classification usingHigher Order Statistics (HOS)
3.2.1 Introduction
In this section, AMC is presented using normalized 8th order
cummulants. The proposed algorithm considers the PAM 2 to 64, QAM 2 to
64, BPSK and QPSK for the classification. The proposed algorithm for
automatic digital modulation classification (ADMC) has significant
classification performance under the effect of AWGN. The classification
problem is divided into three scenarios of {BPSK, QPSK}, {PAM 2-64} and
{QAM 2-64}. The simulation results show that the proposed algorithm has high
classification accuracy at lower SNR. The performance is also compared with
6th order and 4th order normalized cummulants by Orlic et al., (2009) and Chen
et al., (2008).
30
3.2.2 Statistical Features
As cummulants are made up of moments, so various moments have
been used as features. For the complex valued stationary random processx(n), cummulants of 2nd, 4th, 6th and 8th order have the following definitions by
Ghauri et al., (2013).
220, E x n cumm x n , x nxC (Eq.III.8)
2 *21, E x n cumm x n , x nxC
(Eq.III.9)
240, 40 20M 3M
cumm x n , x n , x n , x n
xC
(Eq.III.10)
2
42, 42 20 21
* *
M M 2M
cumm x n , x n , x n , x n
xC
(Eq.III.11)
3
63, 63 21 42 21 20 43 22 41 20 21 22
* * *
M 9M M 12M 3M M 3M M 18M M M
cumm x n , x n , x n , x n , x n , x n
xC
(Eq.III.12)
2 2 2 484, 84 63 21 40 42 42 21 21
* * * *
M 16C C C 18C 72C C 24C
cumm x n , x n , x n , x n , x n , x n , x n , x n
xC
(Eq.III.13)
stands for moments of received signal and it is given by
* p q q
pqM E x k x k (Eq.III.14)
The normalized 8th order cummulants84 , xC by Ghauri et al. (2013):-
31
4
(84, )(84, )
(21, )
ˆ xx
x
CC
C (Eq.III.15)
In ADMC 84,ˆ
xC is the key feature. 84,ˆ
xC can also be estimated from the
received signal r t which is corrupted by AWGN noise and also from fading:
84,84, 2 4
21,
ˆ( )
rx
r g
CC
C
(Eq.III.16)
1 8
041 2
0
( )
( )
L
k
L
k
h k
h k
(Eq.III.17)
The normalized 6th order cummulants63 , xC by Orlic et al. (2009)
63,
63, 3
21,
ˆ xx
x
CC
C (Eq.III.18)
63,
63, 3221,
ˆ rx
r g
CC
C
(Eq.III.19)
1 6
031 2
0
( )
( )
L
k
L
k
h k
h k
(Eq.III.20)
The normalized 4th order cummulants42 , xC by Wu et al. (2008)
42,
42, 2
21,
ˆ xx
x
CC
C (Eq.III.21)
42,42, 2 2
21,
ˆ( )
rx
r g
CC
C
(Eq.III.22)
32
1 4
021 2
0
( )
( )
L
k
L
k
h k
h k
(Eq.III.23)
Table III-I, shows the theoretical values for normalized cummulants
84 , xC ,63 , xC and
42 , xC for the considered modulation scenarios.
Table III-1. Theoretical Normalized 4th, 6th & 8th order cummulants for variousModulation Constellations
42,ˆ
xC 63,ˆ
xC 84,ˆ
xC
BPSK -2 13 -163
QPSK -1 4 -34
PAM2 -2 13 -163
PAM 4 -1.3586 70.7 440.60
PAM 8 -1.2368 522.26 1292.9717
PAM 16 -1.2113 3636.415 36934.8038
PAM 32 -1.2039 23019.7704 931687.15872
PAM 64 -1.1988 15363.424446 2588813.3566
QAM 2 -2 13 -163
QAM 4 -1 1.96 13.6
QAM 8 -1.0011 0.0192 0.0637
QAM 16 -0.6778 2.08 -13.9808
QAM 32 -0.6876 1.9448 -12.005
QAM 64 -0.6167 1.7972 -11.5022
33
3.2.3 Proposed Algorithm for AMC
The algorithm for automatic digital modulation classification on fading
channel (Rayleigh Flat, Rician Flat and Log-normal) by Ghauri et al. (2014):-
Step 1. Calculate the normalized channel coefficients h(k).
Step 2. Calculate the β according to Eq. III-17, Eq.III-20 and Eq.III-23.
Step 3. Calculate the normalized even order cummulants according tothe Eq. III-15, Eq. III-18 and Eq. III-21.
Step 4. Compare the 84,ˆ
xC , 63,ˆ
xC and 42,ˆ
xC with the theoretical valueslisted in Table III-1 to determine the modulation type of thereceived signal.
3.2.4 Simulation Results
The performance of the proposed classifier is analyzed in this section.
The simulation results shows the probability of correct classification (PCC) in
the presence of AWGN channel, as well as on fading channels such as
Rayleigh flat, Rician flat and Lognormal fading channels. The results also
shows the comparison of utilizing the normalized eight-order 84,ˆ
xC , sixth-order
63,ˆ
xC & fourth-order 42,ˆ
xC cummulants. The correct rate of classification using 8th
order cummulants is much higher than that of using 6th and 4th order
cummulants.
34
Figure III-2. PCC on AWGN channel in scenario {BPSK, QPSK}, N=250
Figure III-2, shows the classifier performance using 8th order
cummulants using AWGN channel. The average PCC is approximately 0.99 at
SNR=2dB, where using 6th and 4th order cummulants, the average PCC is 0.91
and 0.82 respectively at the same SNR. Figure III-3, shows the PCC curve for
scenario {QAM 2 to 64} considering AWGN channel with N=3000. The 8th order
cummulants average PCC is approximately 0.9 at SNR=0dB, where using 6th
and 4th order cummulants the average PCC is 0.85 and 0.77 respectively, at
same SNR.
Figure III-3. PCC on AWGN channel in scenario {QAM 2 to 64}, N=3000
-10 -8 -6 -4 -2 0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR in dB
PC
C
8th Order Cummulants6th Order Cummulants4th Order Cummulants
-10 -8 -6 -4 -2 0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR in dB
PC
C
4th Order Cummulants
6th Order Cummulants
8th Order Cummulants
35
Figure III-4. PCC on AWGN channel in scenario {PAM 2 to 64}, N=3000
Figure III-4, shows the correction rate using 8th order cummulants is
reaching approximately 1 at SNR=2dB, where using 6th and 4th order
cummulants the average PCC is 0.96 and 0.84 respectively at the same SNR.
Figure III-5, III-6 & III-7 show the PCC curve for scenario {BPSK, QPSK}, {PAM
2 to 64} and {QAM 2 to 64} on fading channels having number of samples 250,
2000 & 2000 respectively.
Figure III-5. PCC on Flat Fading channel in scenario {BPSK, QPSK}, N=250
-10 -8 -6 -4 -2 0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR in dB
PC
C
4th Order Cummulants
6th Order Cummulants
8th Order Cummulants
-10 -8 -6 -4 -2 0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR in dB
PC
C
4th Order Cummulants
6th Order Cummulants
8th Order Cummulants
36
Figure III-6. PCC on Flat Fading channel in scenario {PAM 2 to 64}, N=2000
The curves show that using 8th order cummulants PCC is higher than
the 6th and 4th order cummulants in all three cases. The average PCC using
8th order cummulants for scenario {BPSK, QPSK} is 0.95, average PCC for
scenario {PAM 2 to 64} is 0.7 and average PCC for scenario {QAM 2 to 64} is
0.64 at SNR=0dB.
Figure III-7. PCC on Flat Fading channel in scenario {QAM 2 to 64}, N=2000
-10 -8 -6 -4 -2 0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR in dB
PC
C
4th Order Cummulants
6th Order Cummulants
8th Order Cummulants
-10 -8 -6 -4 -2 0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR in dB
PC
C
4th Order Cummulants6th Order Cummulants8th Order Cummulants
37
Figure III-8. PCC on Rayleigh Flat Fading channel in scenario {BPSK,QPSK}, N=250
Figure III-8, III-9 & III-10 shows the PCC curve for scenario {BPSK,
QPSK} on Rayleigh flat fading, lognormal fading and Rician flat fading channel
having N=250. The curve shows that using 8th order cummulants PCC is higher
on faded channels. The average PCC is 0.94 using 8th order cummulants while
average PCC is 0.8 using 4th cummulants.
Figure III-9. PCC on Lognormal Fading channel in scenario {BPSK, QPSK},N=250
-10 -8 -6 -4 -2 0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR in dB
PC
C
4th Order Cummulants
6th Order Cummulants
8th Order Cummulants
-10 -8 -6 -4 -2 0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR in dB
PC
C
4th Order Cummulants
6th Order Cummulants
8th Order Cummualnts
38
Figure III-10. PCC on Rician Flat Fading channel in scenario {BPSK, QPSK},N=250
Figure III-11, shows the performance evaluation of ADMC on faded
channel and AWGN channel for the scenario {BPSK, QPSK}. The 8th order
cummulants feature provides higher accuracy on all faded channel.
Figure III-11. Performance of ADMC on Faded channel in scenario {BPSK,QPSK}, N=250
-10 -8 -6 -4 -2 0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR in dB
PC
C
4th Order Cummulants6th Order Cummulants8th Order Cummulants
-10 -8 -6 -4 -2 0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR in dB
PC
C
8th Order Cumulants AWGN channel8th Order Cumulants Flat Fading channel8th Order Cumulants Rayleigh Flat Fading channel8th Order Cumulants Log Normal Faing channel8th Order Cumulants Rician Fading channel6th Order Cumulants AWGN channel6th Order Cumulants Flat Fading channel6th Order Cumulants Rayleigh Flat Fading channel6th Order Cumulants Log Normal Faing channel6th Order Cumulants Rician Fading channel4th Order Cumulants AWGN channel4th Order Cumulants Flat Fading channel4th Order Cumulants Rayleigh Flat Fading channel4th Order Cumulants Log Normal Faing channel4th Order Cumulants Rician Fading channel
39
Figure III-12. Performance of ADMC on Faded channel in scenario {QAM 2 to64}, N=3000.
The PCC for scenario {QAM 2 to 64} on Rayleigh flat, Rician flat and
lognormal fading channel is shown in Figure III-12. The usage of 8th order
cummulants shows the better classification rate than that of 6th & 4th order
cummulants. For example average PCC is 0.57 at SNR= -2dB on lognormal
fading channel, while using 6th & 4th order cummulants the average PCC is
0.51, 0.45, respectively, at same SNR.
Figure III-13. Performance of ADMC on Faded channel in scenario {PAM 2 to64}, N=2500
-10 -8 -6 -4 -2 0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR in dB
PC
C
8th Order Cumulants AWGN channel8th Order Cumulants Flat Fading channel8th Order Cumulants Rayleigh Flat Fading channel8th Order Cumulants Log Normal Faing channel8th Order Cumulants Rician Fading channel6th Order Cumulants AWGN channel6th Order Cumulants Flat Fading channel6th Order Cumulants Rayleigh Flat Fading channel6th Order Cumulants Log Normal Faing channel6th Order Cumulants Rician Fading channel4th Order Cumulants AWGN channel4th Order Cumulants Flat Fading channel4th Order Cumulants Rayleigh Flat Fading channel4th Order Cumulants Log Normal Faing channel4th Order Cumulants Rician Fading channel
-10 -8 -6 -4 -2 0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR in dB
PC
C
8th Order Cumulants AWGN channel8th Order Cumulants Flat Fading channel8th Order Cumulants Rayleigh Flat Fading channel8th Order Cumulants Log Normal Faing channel8th Order Cumulants Rician Fading channel6th Order Cumulants AWGN channel6th Order Cumulants Flat Fading channel6th Order Cumulants Rayleigh Flat Fading channel6th Order Cumulants Log Normal Faing channel6th Order Cumulants Rician Fading channel4th Order Cumulants AWGN channel4th Order Cumulants Flat Fading channel4th Order Cumulants Rayleigh Flat Fading channel4th Order Cumulants Log Normal Faing channel4th Order Cumulants Rician Fading channel
40
The PCC for scenario {PAM 2 to 64} on Rayleigh flat, Rician flat and
lognormal fading channel is shown in Figure III-13. The performance of
classifier using 8th order cummulants feature is much better than 6th & 4th order
cummulants. For example average PCC is 0.6 at SNR= 0dB on Rician fading
channel, while using 6th & 4th order cummulants the average PCC is 0.57, 0.51,
respectively, at same SNR.
3.2.5 Summary
The performance of using normalized 8th order cummulants with
normalized 6th and 4th order cummulants are shown and it is found that the
probability of correct classification using 8th order cummulants is much better
than the 6th and 4th order cummulants at lower SNRs.
3.3 Automatic Modulation Classification usingLinear Discriminant Analysis (LDA)
3.3.1 Introduction
In this section, modulation classification has been carried out using
linear discriminant analysis (LDA) on fading channels. The features used for
the classification are higher order cummulants and normalized higher order
cummulants. The LDA classify the received signal into set of different classes.
The performance metric is minimum distance criterion which discriminates the
received signal data set into different classes. The performance of the
41
proposed algorithm shows substantial organization of different digital
modulated signals on faded channels.
3.3.2 Higher Order Cummulants as Feature Set
For classification of modulation signals higher order moments and
higher order cummulants are used. The HOC and HOM are defined in Eq. III-
8 to Eq. III-14. The 4th, 6th and 8th order cummulants are defined by Ghauri et
al., (2013):-
41 40 20 21
*
C M 3M M
cumm x n , x n , x n , x n
(Eq.III.24)
3
60 60 20 40 20C M 15M M 30M
cumm x n , x n , x n , x n , x n , x n
(Eq.III.25)
261 61 21 40 20 41 20 21
*
C M 5M M 10M M 30M M
cumm{x(n),x(n),x(n),x(n),x(n),x (n)}
(Eq.III.26)
2 2
62 62 20 42 21 41 22 40 20 22 21 22
* *
C M 6M M 8M M M M 6M M 24M M
cumm x n , x n , x n , x n , x n , x n
(Eq.III.27)
2 2 4
80 80 40 60 20 40 20 20C M 35M 28M M 420M M 630M
cumm x n , x n , x n , x n , x n , x n , x n , x n
(Eq.III.28)
The normalized 4th order cummulants and 6th order cummulants
values for {FSK2 to 64} modulation formats are given in Table III-2. The values
given in Table III-2 for considered modulation formats are theoretical values.
42
Table III-2. Theoretical Values of Normalized cummulants of ConsideredModulation Types
42,ˆ
xC 63,ˆ
xC
FSK2 -2 13
FSK 4 -1.3586 7.07
FSK 8 -1.2368 5.22
FSK 16 -1.2113 3.63
FSK 32 -1.2039 2.30
FSK 64 -1.1988 1.536
3.3.3 Proposed Algorithm for AMC
The proposed algorithm based on LDA is presented by Ghauri et al.
(2014). LDA works by projecting data into a feature space using a linear
mapping and then comparing the result to a centroid for each class. The flow
chart for classification of the modulation schemes is given below:
Figure III-14: Flow Chart for Modulation Classification
Signal Received
Apply Projection Matrix
Spectrum Analysis
Calculate Statistics
Calculate Distance
43
Proposed Algorithm for Modulation Classification using LDA:
Step 1. Create the two data sets i.e. classes c1 & c2
Step 2. Calculate the mean of each data μ1 & μ2
Step 3. Calculate the weighted mean μ=p1*μ1+ μ2*p2
Step 4. Calculate the covariance matrix Si of data set and mean of dataset.
Step 5. class independent case
inverse(Sw)*SB, where Sw and SB are within class scatter matrixand the between class scatter matrix
1 1
, ( )N N
Tw i B i i
i i
S S S n m m m m
Step 6. Find the projection matrix W
Step 7. Find the optimum weight vector.
Step 8. Find the transformed data set Ty W x
Step 9. Find the minimum distance between transformed data set andtest data.
3.3.4 Simulation Results
First, 30 training signals of 10,000 symbols are generated for the
(PSK2, PSK4, PSK8, PSK16, PSK32, PSK64, FSK2, FSK4, FSK8, FSK16,
FSK32, FSK64, QAM2, QAM4, QAM8, QAM16, QAM32, QAM64) modulation
formats and higher order moments & cummulants are also calculated for each
training signal. After that these parameters are passed to a training function
that determines a projection matrix and class centroids. The spectrum of each
signal is analyzed by calculating the fast fourier transform (FFT) of first 4096
samples. After that, normalized cummulants are calculated and projected into
feature space using the projection matrix. The projected features are
44
compared to class centroids and closet one is chosen as the modulation
format. From Table III-3 to III-5, the classification performance in form of
confusion matrix for PSK modulations on AWGN, Rayleigh flat fading channel
and Rician flat fading channel are shown at SNR of 10dB. The average
classifier performance in case of AWGN channel is 99.95%, where in case of
Rayleigh channel the performance is 91.3% at SNR of 10dB.
From Table III-6 to III-8, the classification performance in form of
confusion matrix for FSK modulations on AWGN, Rayleigh flat fading and
Rician flat fading channel are shown at SNR of 10dB. The average classifier
performance in case of AWGN channel is 99.5 %, where in case of Rayleigh
channel the performance is 88% and in case of Rician channel the
performance is 91% at SNR of 10dB. The performance is better in case of
Rician channel when comparing with Rayleigh channel, because it has one
line of sight component which preserves the spectral component of FSK
signals, resulting in high accuracy of classification.
From Table III-9 to III-11, the confusion matrix for QAM modulations
on AWGN channel, Rayleigh flat fading channel and Rician flat fading channel
are shown at SNR of 10dB. The average classifier performance in case of
AWGN channel is 99.95 %, where in case of Rayleigh channel the
performance is 77.36% and in case of Rician channel the performance is 81%
at SNR of 10dB.
45
Table III-3. Confusion Matrix for PSK modulation in AWGN channel (AveragePerformance 99.95%)
10 dB 2PSK 4PSK 8PSK 16PSK 32PSK 64PSK
2PSK 10000 0 0 0 0 0
4PSK 0 10000 0 0 0 0
8PSK 0 0 10000 0 0 0
16PSK 0 0 3 9992 5 0
32PSK 0 0 0 10 9985 5
64PSK 0 0 0 0 10 9990
Table III-4. Confusion Matrix for PSK modulation in AWGN+ Rician FlatFading Channel (Average Performance 92.26%)
10dB 2PSK 4PSK 8PSK 16PSK 32PSK 64PSK
2PSK 9793 207 0 0 0 0
4PSK 295 9395 290 40 0 0
8PSK 0 111 9639 250 0 0
16PSK 0 190 413 8967 430 0
32PSK 0 0 174 309 9091 426
64PSK 0 0 110 390 1038 8462
Table III-5. Confusion Matrix for PSK modulation in AWGN + Rayleigh FlatFading Channel (Average Performance 91.38%)
10dB 2PSK 4PSK 8PSK 16PSK 32PSK 64PSK
2PSK 9793 207 0 0 0 0
4PSK 496 9304 200 0 0 0
8PSK 0 185 9625 190 0 0
16PSK 0 9 895 8925 171 0
32PSK 0 0 48 931 8920 101
64PSK 0 0 0 681 994 8325
46
Table III-6. Confusion Matrix for FSK modulation in AWGN channel (AveragePerformance 99. 5%)
10dB 2FSK 4FSK 8FSK 16FSK 32FSK 64FSK
2FSK 10000 0 0 0 0 0
4FSK 0 10000 0 0 0 0
8FSK 0 4 9996 0 0 0
16FSK 0 8 31 9961 0 0
32FSK 0 11 22 34 9921 12
64FSK 0 2 11 27 133 9827
Table III-7. Confusion Matrix for FSK modulation in AWGN+ Rician FlatFading Channel (Average Performance 91%)
10dB 2FSK 4FSK 8FSK 16FSK 32FSK 64FSK
2FSK 10000 0 0 0 0 0
4FSK 416 9584 0 0 0 0
8FSK 0 421 9196 383 0 0
16FSK 0 0 921 8942 137 0
32FSK 0 0 0 876 8425 699
64FSK 0 0 0 713 893 8394
Table III-8. Confusion Matrix for FSK modulation in AWGN + Rayleigh FlatFading Channel (Average Performance 88%)
10dB 2FSK 4FSK 8FSK 16FSK 32FSK 64FSK
2FSK 10000 0 0 0 0 0
4FSK 632 9179 189 0 0 0
8FSK 0 645 8924 431 0 0
16FSK 0 0 1116 8795 89 0
32FSK 0 0 69 1721 8210 0
64FSK 0 0 18 381 1891 7710
47
Table III-9. Confusion Matrix for QAM modulation in AWGN channel(Average Performance 99.95%)
10dB 2QAM 4QAM 8QAM 16QAM 32QAM 64QAM
2QAM 10000 0 0 0 0 0
4QAM 0 10000 0 0 0 0
8QAM 0 0 9996 0 0 0
16QAM 0 0 0 9995 3 2
32QAM 0 0 4 4 9990 2
64QAM 0 0 0 6 8 9986
Table III-10. Confusion Matrix for QAM modulation in AWGN+ Rician FlatFading Channel (Average Performance 81%)
10dB 2QAM 4QAM 8QAM 16QAM 32QAM 64QAM
2QAM 10000 0 0 0 0 0
4QAM 639 9158 203 0 0 0
8QAM 0 793 8854 353 0 0
16QAM 0 0 1432 7698 870 0
32QAM 0 0 0 1834 6825 1341
64QAM 0 0 0 999 2921 6080
Table III-11. Confusion Matrix for QAM modulation in AWGN + Rayleigh FlatFading Channel (Average Performance 77.36%)
10dB 2QAM 4QAM 8QAM 16QAM 32QAM 64QAM
2QAM 10000 0 0 0 0 0
4QAM 686 8925 389 0 0 0
8QAM 0 813 8456 731 0 0
16QAM 0 0 1392 7121 1487 0
32QAM 0 0 0 2031 6489 1480
64QAM 0 0 0 1486 3089 5425
48
3.3.5 Summary
The linear classifiers proposed here are very effective on fading
channels. The simulation shows that the classifier performance is
approximately 99.9% at SNR of 10 dB. The average performance of classifier
for PSK modulated signals in the presence of AWGN channel is 99.95% at
SNR of 10dB, while the performance of classifier in Rayleigh flat fading and
Rician flat fading channel are approximately 91.38% and 92.26% respectively.
3.4 Automatic Modulation Classification usingSpectral Features
3.4.1 Introduction
In this section we have used spectral features for classification of PSK,
PAM, QAM and FSK modulation formats. The proposed classifier is multilayer
perceptron (MLP) which is also referred to as feed forward back propagation
neural network (FFBPNN) and support vector machine (SVM). The
performance comparison with the existing techniques shows the supremacy of
proposed classifiers.
3.4.2 Spectral Features
A common method is to use the information contents in the
instantaneous amplitude, frequency and phase of the modulated signal. We
49
have used standard deviation of normalized signal frequency, phase and
amplitude derived from instantaneous amplitude, phase and frequency of the
considered (FSK, PSK, PAM, QAM) modulated signals by Dobre et al., (2005),
Nandi et al., (1998), Ghauri et al., (2013) and Ghauri et al., (2014).
Let a signal with sampling rate of sf =4000 is generated and digitally
modulated using Eq. III-1. After modulation, Hilbert transform is used for
calculating amplitude, frequency and phase. Then these three parameters
(amplitude, phase and frequency) are used for extraction of the features
ap dp , aa fa fn max(σ , σ σ σ , σ , γ ).
A. ap : Standard deviation of absolute value of the centered non-linear
components of instantaneous phase
2
2
1 1 ( ) | |ap NL NL
s s
i iN N
(Eq.III.29)
where Ns are number of samples in NLφ (i) at instants
it f
Nonlinear component of centered instantaneous phase
NL oφ i φ(i) φ andNs
oi 1s
1φ φ(i) N
, ap is used to discriminate the
modulation formats which have absolute phase information.
B. dp : Standard deviation of direct value of the centered non-linear
components of instantaneous phase
2
2
1 1 ( ) ( )dp NL NL
s s
i iN N
(Eq.III.30)
50
dp is used to discriminate the modulation formats which have direct
information and no direct information.
C. aa : Standard deviation of absolute value of the normalized centered
instantaneous amplitude
2
2
1 1 ( ) | | aa cn cn
s s
A i A iN N
(Eq.III.31)
cnA i is normalized centered instantaneous amplitude at time instant
s
it f , 1cn nA i A i and ( ) /n aA i A i m , am is average value of
instantaneous amplitude over one frame. 1
1 sN
ais
m A iN
. This feature
is used to distinguish the modulation formats which have absolute
amplitude information and no absolute amplitude information.
D.fa : Standard deviation of absolute value of the normalized centered
instantaneous frequency
2
21 1 ( ) | |fa n n
s s
f i f iN N
(Eq.III.32)
Normalized centered instantaneous frequency cn
s
f if i r , sr is the
symbol rate, c i ff i f m andN
fi 1s
1m f (i)
N
where sN is symbol
rate.fa is used to discriminate the modulation formats that have no
absolute frequency information and direct frequency information.
51
E. fn : Standard deviation of direct value of the normalized centered
instantaneous frequency
2
2
1 1 ( ) ( )fn n nf i f i
Ns Ns
(Eq.III.33)
F. max : Maximum value of the power spectral density of the normalized
centered instantaneous amplitude
2
1maxmax cnDFT A i
Ns (Eq.III.34)
DFT is the Discrete Fourier transform of the modulated signal, max uses
to discriminate the modulation formats which has amplitude information
from that which has no amplitude information (PSD=0).
3.4.3 Proposed Algorithm using MLP
The proposed FFBPNN have three layers; input layer, hidden layer and output
layer. At input layer neurons are only used for distribution of extracted features
to the hidden layer neurons which are used for the computations. The output
of the hidden layer is input to the output layer. Six neurons are used in input
layer as analogous to the number of features extracted from the received
signal. Hidden layer carries ten neurons, while six neurons in output layer
corresponding to the number of outputs/ modulation formats. The proposed
classifier architecture for the classification of considered modulation formats is
shown in Figure III-15 by Ghauri et al. (2014).
52
Figure III-15: Proposed Architecture for classification of modulation formats
Training of Algorithm: The input data set and target data set are
used to train the proposed classifier for considered modulation formats. The
difference between the output value and target value is known as error value,
which is back propagated to hidden layer. The feed forward back propagation
algorithm is used which involves forward and backward path. In forward path,
weights are initialized for training the feed forward network, while in this path
weights values are fixed. The error signal is given by
j j je t y (Eq.III.35)
wherejt is the target response of jth input and is the output of the
network. In second path weights are updated, till the error is minimized in a
statistical sense using mean square error criterion.
53
N2
j jj 0
1Cost function J (t y )
N
(Eq.III.36)
The training of proposed classifier for the classification is as follows:
Step-1. The input and target vectors are concatenated to represent the datamatrix
Step-2. Generated data are normalized and randomly sorted
Step-3. The 50% of normalized data are used for the training the neuralnetwork.
20% of normalized data are used to validation.
Step-4. While for testing the network, 30% of the normalized data are used.
Step-5. Feed forward back propagation neural network is created. Theactivation function used are tang-sigmoid (tanh) and (logistic) log-sigmoid.
Testing of proposed algorithm: For testing the FFBPNN, net lab
toolbox is used. The 30% of the normalized data are used to test the
performance of classifier for different values of SNR.
Table III-12: Specifications for the proposed classifier
S. No. Parameters Value
1. neural network architecture Feed-forward
2. input layer neurons 6
3. hidden layer neurons 10
4. output layer neurons 6
5. weight-decay Coefficient 0.001
6. hidden & output layer Activation function Logistic
7. Iterations 500
8. Performance Metric MSE
9. Learning algorithm SCG
54
3.4.4 Simulation Results
The feature vectors and target vectors are concatenated to form the
data set. The data set is divided in to three portions; 50% used for training
while rest 50% are used for validation and testing the proposed algorithm. The
performance of proposed is evaluated under the effects of different channel
models at SNR of 10dB. The simulation results in the form of confusion matrix
show that performance of classification is approximately 100 at SNR of 10dB.
The Figure III-16, shows that the FFBPNN output result for the case of
PSK 2 to 64 modulation format. From the Figure III-16, it is clear that probability
of failure is approximately zero and the proposed classifier perfectly classifies
the modulation formats. Table III-13, shows the percentage of correct
classification at fixed SNR of 10dB. The overall performance of classifier is
99.62% in case of FSK, 99.55% in case of PSK, 99.56% in case of PAM and
99.34% in case of QAM.
Table III-14, shows that the percentage of correct classification in case
of FSK 2 to 64, PSK 2 to 64, PAM 2 to 64 and QAM 2 to 64 at fixed SNR of
10dB. The performance of classifier in the form of confusion matrix shows that
approximately 98% classification. The overall performance of classifier is
98.07% in case of FSK, 98.15% in case of PSK, 97.98% in case of PAM and
98.34% in case of QAM.
Table III-15, shows that the percentage of correct classification in the
form of confusion matrix. The overall performance of classifier is 96.99% in
case of FSK, 97.13% in case of PSK, 96.84% in case of PAM and 97.35% in
case of QAM.
55
Figure III-16: The FFBPN result for the proposed classifier {PSK 2 to64} on AWGN channel at SNR of 10dB.
Table III-13: Percentage of correct classification on AWGN channel at 10 dBof SNR
FSK M=2 M=4 M=8 M=16 M=32 M=64M=2 99.61M=4 99.92M=8 99.99M=16 99.94M=32 99.54M=64 98.76
PSK M=2 M=4 M=8 M=16 M=32 M=64M=2 99.99M=4 99.92M=8 99.54M=16 98.93M=32 99.32M=64 99.64
PAM M=2 M=4 M=8 M=16 M=32 M=64M=2 99.98M=4 99.32M=8 99.59M=16 99.65M=32 99.29M=64 99.55
QAM M=2 M=4 M=8 M=16 M=32 M=64M=2 99.99
56
M=4 99.64M=8 99.87M=16 99.29M=32 99.13M=64 98.12
Table III-14: Percentage of correct classification on Rician flat fading channelplus AWGN at 10 dB of SNR
FSK M=2 M=4 M=8 M=16 M=32 M=64M=2 98.79M=4 98.32M=8 97.47M=16 98.61M=32 97.15M=64 98.10
PSK M=2 M=4 M=8 M=16 M=32 M=64M=2 99.18M=4 98.12M=8 97.83M=16 97.95M=32 98.53M=64 97.31
PAM M=2 M=4 M=8 M=16 M=32 M=64M=2 97.72M=4 98.93M=8 97.45M=16 98.23M=32 97.51M=64 98.05
QAM M=2 M=4 M=8 M=16 M=32 M=64M=2 99.37M=4 99.23M=8 98.57M=16 98.37M=32 97.34M=64 97.19
Table III-15: Percentage of correct classification on Rayleigh flat fadingchannel plus AWGN at 10 dB of SNR
FSK M=2 M=4 M=8 M=16 M=32 M=64M=2 96.32M=4 97.81M=8 97.62M=16 96.43M=32 96.15
57
M=64 97.62PSK M=2 M=4 M=8 M=16 M=32 M=64
M=2 97.40M=4 97.93M=8 96.23M=16 97.11M=32 97.02M=64 97.13
PAM M=2 M=4 M=8 M=16 M=32 M=64M=2 97.23M=4 96.54M=8 96.78M=16 97.01M=32 96.29M=64 97.19
QAM M=2 M=4 M=8 M=16 M=32 M=64M=2 98.45M=4 98.54M=8 96.59M=16 96.82M=32 96.99M=64 96.72
3.4.5 Proposed Algorithm using SVM
The concept behind SVM is to provide a learning technique for
classification by constructing hyper planes, it provides regression based
estimation, it combines learning and optimization theory and gives an
optimized solution as opposed to artificial neural networks or decision test and
most important is that it uses Kernel trick to extract features. The working
principle of SVM is based upon construction of hyper planes for linearly
separable data pattern and nonlinear separable data pattern by Haykin (2008).
Suppose that training data samples 1
,N
i i ix d
, , { 1,1}d
ix R d can be
separated by hyper plane 0Tiw x b , where x is the input pattern (total
58
number of patterns are N ), b is the bias, w is the weight vector and d is the
desired response. The decision function is 0TiD x w x b , if this hyper
plane maximizes the margin then ( ) 1 ( ) -1 0T Ti i i iy w x b or d w x b . The
margin of hyper plane is 2 /M w , as 0, w M where
2 2 21 2 . . . .. . . Mw w w w . The problem is to maximize the margin by
minimizing w subject to constraint ( ) -1 0Ti id w x b . The minimization of w
is same as minimizing 21 1
2 2Tw w w . The cost function is
1
1[ 1]
2
NT T
i i ii
J d b
w w w x (Eq.III.37)
Differentiating the cost function with respect to bias b , yields
1 1
1( )
2
N NT T
i i i ii i
J d
w w w x (Eq.III.38)
1 1 1
1
2
N N NT
i i j i j i ji i j
d d
x x (Eq.III.39)
( )J should be minimized under the constraints1
0N
i ii
d
and 0,i
for 1, 2, .,i N . The training points for which the ( b) 1Ti id w x becomes
equality are called support vectors (SV). The optimal bias for any support
vector ix is given by
* *Ti ib d w x (Eq.III.40)
Then optimal decision function (ODF) is given by
59
* *
1
NT
i i i ii
D sgn d b
x x x (Eq.III.41)
where *i are optimal Lagrange multipliers. It is not possible to
construct hyper plane without encountering error of class recognition, thus we
will find out an optimal hyper plane that minimizes the probability of correctness
error. SVM uses soft margins for high noise level in the input data. To set
correct recognition method, the new set of non-scalar variables are
transformed into separable hyper planes called slack variables i( ). These
slack variables will measure the deviation of data points from ideal condition.
Thus the separable hyper planes are as follows,
Ti i iy w X b) ( 1 (Eq.III.42)
For 0 1 , the data point falls inside the region of separation but
on the right side of the decision surface. For 1 , it falls on the wrong side of
the separation hyper plane. The support vectors are those particular data
points that satisfy the new separating hyper plane equation precisely even if
0. The weight vector w and the slack variable minimize the cost function:
N
Ti
i=1
1φ C2 w w w (Eq.III.43)
Here C is the user specified positive parameter known as penalty
parameter. For the nonlinear separable scenario, SVM maps use kernel
function )( ,i jK x x . The radial basis function (RBF) is used as kernel function
in the simulation and given by:
60
2 2, exp / 2K x y x y (Eq.III.44)
where is width of radial basis kernel function. The problem will be
1 1 1
1,
2
N N N
i i j i j i ji i j
D d d K
x x x (Eq.III.45)
* arg(max ), 0 , 0 , 1, 2,. ,N
i i i ii
D C y i N
The optimal decision function becomes
* *
1
,N
i i i ji
D sgn d K b
x x x (Eq.III.46)
Proposed Algorithm based on SVM:-
Step 1. Extraction of Key features:
Following two sets of feature are extracted
(i) Spectral features
(ii) Higher order cummulants
Step 2. Select Kernel Function
Radial basis function is used as kernel function
Step 3. Calculate parameters of kernel function
Select the best parameters with cross validation
Step 4 Train the samples
Step 5. Test of Network
61
3.4.6 Simulation Results
The features used for the SVM are spectral features and higher order
cummulants. The realization taken for each modulation format is 1200. Based
on the experiments, value of 1 and 10C is selected for SVM. The
performance of classifier on different channels is shown in Table III-16. The
average classification performance on fading channels and AWGN is 97.66%
at 10dB of SNR.
Table III-16. Performance of Recognizer at SNR of 0 to 10 dB
SNRTesting
AWGN Channel
Testing
Rayleigh Flat fading
0 70.14% 60.35%
1 74.52% 66.89%
2 78.26% 71.73%
3 82.56% 75.54%
4 86.50% 79.69%
5 89.75% 82.88%
6 92.85% 86.91%
7 94.74% 89.39%
8 97.42% 92.42%
9 99.92% 95.59%
10 100% 97.66%
62
3.4.7 Comparison with Existing Techniques
Table III-17, shows the performance comparison of using normalized
higher order cummulants with the existing schemes on AWGN and fading
channels. Table III-18, shows the performance comparison of using spectral
features with the well-known techniques in the literature on fading channels. It
is shown from the Table III-17 and III-18, that the classification accuracy at
10dB of SNR of the proposed classifiers is much better than the existing
classifiers.
Table III-17. Performance comparison of Spectral Features with existingtechniques
Author & Year Features +Algorithm
% ClassificationAccuracy
Azzozu et al., (1995) Spectral Features 90% (AWGN)
Wong et al., (2004) Spectral Featuresand MLP+ GA 98% (AWGN)
Ye et al., (2007) Time FrequencyFeatures + MLP 97.6% (AWGN)
Bouttee et al., (2009)
IndependentComponent
Analysis (ICA)+SVM
93% (AWGN)
Abaviasani et al., (2009)
EuclideanDistance and
ConstantModulation (CM)
Equalization
60.1% (Fading)
Ebrahimzadeh, (2009)
SpectralFeatures+ RadialBasis Function
(RBF)
90% (Fading)
Avci et al., (2009)Discrete wavelet
(DW) neuralnetwork
90.24%
63
Avci et al., (2009) DW ANFIS 96.51%
Hassan et al., (2010) Wavelet featuresand MLP 98% (AWGN)
Valipour et al., (2012) Spectral Features,HOM and SVM 98.5% (AWGN)
Valipour et al., (2012) Spectral Features,HOM and MLP 97% (AWGN)
Proposed Method
2014
Spectral Features
SVM and MLP
99% (AWGN)
95 % (FadingChannels)
Table III-18. Performance comparison of HOC features with existingtechniques
Author & Year Features +Algorithm
% ClassificationAccuracy
Swami et al., (2000) Cummulants 90% (AWGN)
Dobre et al., (2003)Higher order
cycliccummulants
70% (AWGN)
Mirarab et al., (2007) HOC 85% (Fading)
Wong et al., (2008) Navie BayesClassifier 94.4% (AWGN)
Chen et al., (2008)Normalized 4th
orderCummulants
85% (Fading)
Orlic et al., (2009)Normalized 6th
orderCummulants
88% (Fading)
Orlic et al., (2010) Sixth ordercummulants 70% (Fading)
Chaithanya et al., (2010) HOC and HOM 90% (AWGN)
Aslam et al., (2011) Cummulants andGP-KNN 96.4% (AWGN)
Proposed Method NormalizedHigher Order
99 % (AWGN)
64
2014 Cummulants +LDA
90% (FadingChannels)
Proposed Method
2014
NormalizedHigher Order
Cummulants +ML
99% (AWGN)
91% (FadingChannels)
3.4.8 Summary
In this chapter, higher order normalized cummulants and spectral
features are used as features set to classify the modulation formats effectively.
The classifiers proposed are based on ML, LDA, FFBNN and SVM. The
classifiers performance is evaluated on different channels. Also when
comparison with the existing techniques, our proposed classifier shows better
classification performance.
65
CHAPTER IV
AUTOMATIC MODULATION CLASSIFICATION USINGGABOR FILTER NETWORK
4.1 Introduction
In this chapter, Gabor filter (GF) network is proposed for the joint
feature extraction and classification of digital modulation formats. The digital
modulations considered are PSK2, PSK4, PSK8, PSK16, PSK32, PSK64,
FSK2, FSK4, FSK8, FSK16, FSK32, FSK64, QAM2, QAM4, QAM8, QAM 16,
QAM 32, and QAM 64. The proposed classifier structure has been divided into
two phases. In the training phase of the classifier, the GF parameters are
adjusted using delta rule and weights of adaptive filter using LMS algorithm to
minimized the cost function. For each considered modulation format, the
Gabor filter network is trained and GF parameters are saved. In testing phase,
minimum error of the classifier corresponds to desired modulation formats. The
proposed algorithm gives high classification accuracy even at lower SNRs.
A modified GF network is also proposed for classification of M-PAM
signals. We have made some changes in the previous proposed method to
make it efficient for M-PAM signals. The performance of classifier is evaluated
on Rician and Rayleigh flat fading channels. The classifier performance is also
compared with the well-known existing techniques.
66
4.2 System Model
The system model for classification of modulation formats is shown in
Fig. IV-1. Firstly the PSK, QAM and FSK modulation formats are classified
using the GF network and then modification in the proposed algorithm is done
to enable it, for classifying the PAM signals. The received signal is corrupted
by AWGN plus with the channel effects. The features are extracted from the
received signal using GF network and input to classifier, which makes decision
about the modulation format of the received signal.
4.3 Gabor filter for Classification and FeatureExtraction
Gabor atom is efficient tool for feature extraction from the received
signal. The Gabor atom in simple form can be written as:
, ,
1cos 2c f i
t cg t g f t
(Eq.IV.1)
where , c and f are shift parameter, scale parameter and
modulation parameter, respectively.
Figure IV-1: System Model for Modulation Classification
67
Figure IV-2: Gabor filter bank with input layer and output layer
In Fig IV-2. GFN is shown which have two layers. Inputs to the filter
are first serial to parallel converted , 1, 2,3, ..{ },i i Nx and the outputs are
, 1,2,3{ },k k Ny . Let , 1, 2,3, ..{ },i i Ng be the ith class gabor atom
and is defined as
1cos 2i
i iii
t cg t g f t
(Eq. IV. 2)
The Gabor atom parameters ( , , )c f are required to be adjusted until
cost function is minimized. The input layer have N nodes 1 2, , ., N also
called gabor nodes. The output of the ith gabor atom node is i corresponding
to the input signal ix . Thus output of gabor atom is defined as:
,i i ig x (Eq. IV.2)
-* -1( )ijf ti
i iii
t cg e x t dt
(Eq. IV.3)
INPUT SIGNALX
SERIAL TO PARALLEL CO
NVERSIO
N (S T P)
==
68
where
2
1cos 2
i
i
t c
i i
i
g t e f t
(Eq. IV.4)
The output layer consists of N nodes , 1,2,3, ..,ky k N and for
convenience N is usually set to 1. The output of the Gabor atom node i in
the input layer is weighted by iw i.e.
1
1, 2,3 .., N
kn in ini
y w n K
(Eq. IV.5)
GFN constitutes of two layers: In input layer, features are extracted
and second layer have GF weights, which constitute the linear classification
part. Gabor atom parameters and GF weights are adjusted to minimize the
sum of squared error. The difference between the desired outputs kd and
actual output of GF ky is defined as:
-k k ke d y (Eq. IV.6)
In training phase of modulation classification, the two adaptive
algorithms are performed by GFN. 1) The updating of Gabor atom parameters
( , , )c f . 2) For given set of Gabor atom parameters, algorithm updates the
weight of Gabor filter. In testing phase, shown in Fig IV-3, the modulated signal
may be PSK 2 to 64, FSK 2 to 64 and QAM2 to 64. The modulated signal is
passed through GFN that updates four parameters ( , , , )c f w and based upon
these parameters error is calculated. The minimum error corresponds to
decision about the received signal modulation format.
69
Figure IV-3: Testing Scheme for Modulation Classification
4.4 Training and Testing of Gabor filter network
The training of GFN is partitioned into two phases: the first phase is
training of Gabor atom parameters ( , , , )c f w , while in second phase, updating
the weights of adaptive filter. Let γi denote one of ith Gabor node parameter
including shift parameter ic , scale parameter i and modulation parameter
if . (Ghauri et al. (2014)). According to Delta rule
γ ( )γi
i
J k
(Eq. IV.7)
70
where is learning rate. The cost function is square of difference
between desired response and output of Gabor function i.e.
2( ) ( ) ( )J k E d k y k (Eq. IV.8)
The partial derivatives of cost function with respect to shift parameter
ic , scale parameter i and modulation parameter if are as follows:-
( 1) ( )i i ic c n c n (Eq. IV.9)
2 2
c c ii
i i i
J k J kc
c c
(Eq. IV.10)
( 1) ( )i i in n (Eq. IV.11)
2 2
ii
i i i
J k J k
(Eq. IV.12)
( 1) ( )i i if f n f n (Eq. IV.13)
2 2
f f ii
i i i
J k J kf
f f
(Eq. IV.14)
From (Eq. IV.9)
2( )( ) ( )
2 ( ) ( ) ( ) ( )
2 ( ) ( ) ( )
i i
i
i
J kd k y k
d k y k d k y k
d k y k y k
(Eq. IV.15)
71
From (Eq. IV.6)
1
1
( )
M
j jji i
M
iij jj
y
w
k w
w
(Eq. IV.16)
Putting (Eq. IV.17) into (Eq. IV.16), we get
( )2 ( ) ( ) i
i
J kd k y k w
(Eq. IV.17)
From (Eq. IV.11), (Eq. IV.13) and (Eq. IV.15)
( ) ( ) ii c i
i
c d k y k wc
(Eq. IV.18)
( ) ( ) ii i
i
d k y k w
(Eq. IV.19)
( ) ( ) ii f i
i
f d k y k wf
(Eq. IV.20)
From (Eq. IV.5),
2
i
1cos
i
i
t c
i i
i
x e f t
(Eq. IV.21)
For real valued signals, Gabor atoms are also real, in such case the
partial derivatives of i with respect to shift parameter ic , scale parameter i
and modulation parameter if are as follows:-
72
2
2
5
1
2
i
i
i
i
ii i
i i
t c
i ii i
t c
ii i
i
x gc c
x e cos f tc
xcos f t t c e
(Eq. IV.22)
2
22
3
1
2 1
2
i
i
i
i
t c
ii i
i i i
t c
i i i
i ii
x e cos f t
x cos f t t ce
(Eq. IV.23)
2
2
1 i
i
i
i
t c
ii i
i i i
t c
i i
i
x e cos f tf f
tx e sin f t
(Eq. IV.24)
The updating of Gabor atom parameters (shift parameter ic , scale
parameter i and modulation parameter if ) according to Delta rule are:
2
5
( ) ( ) 2i
i
t c
ii c i i i
i
xc d k y k w cos f t t c e
(Eq. IV.25)
2
5
1) ( ) ( ) ( ) ( )2(i
i
t c
ii i c i i i
i
xc n c n d k y k w cos f t t c e
(Eq. IV.26)
73
2
2
3
2 1( ) ( )
2
i
i
t c
i i ii i
i ii
x cos f t t cd k y k w e
(Eq. IV.27)
2
2
3
1 ( ) ( )
2 1
2
i
i
i i i
t c
i i i
i ii
n n d k y k w
x cos f t t ce
(Eq. IV.28)
2
( ) ( )i
i
t c
i f i i i
i
tf d k y k w x e sin f t
(Eq. IV.29)
2
1 ( ) ( )
i
i
i i f i
t c
i i
i
f n f n d k y k w
tx e sin f t
(Eq. IV.30)
Eq. IV.27, Eq. IV.29 and Eq. IV.31 shows the updated shift parameter,
scale parameter and modulation parameter of GFN. The weights of adaptive
filter are updated as follows:-
) )( 1 ( i i iw w n w n (Eq. IV.31)
2
2
2
wi
i
w
i
J kw
w
d k y kw
wi
d k y k y kw
(Eq. IV.32)
1
( )
N
j j iji i
y kw
w w
(Eq. IV.33)
74
Substituting (Eq. IV.34) in (Eq. IV.32), we get
( ) ( )i w iw d k y k
From (Eq. IV.32)
( 1) ( ) ( ) ( )i i w iw n w n d k y k (Eq. IV.34)
Eq. IV. 35 shows the weight updating of the adaptive filter.
4.5 The proposed Algorithm for ModulationClassification
The parameters of GFN (shift, scale and modulation) are updated
before they are input to the adaptive filter where weights of adaptive filter are
adjusted to minimize the error function. The error is calculated, if error is less
than the threshold training process stops otherwise update the GF parameters
and weights of the adaptive filter until the cost function is minimized. In test
phase of the classifier algorithm, input modulated signal is fed to the trained
GFN. The parameters of GFN and weights of the adaptive filter are updated
and error is calculated. The minimum error corresponds to the desired
modulation format.
The proposed algorithm for the training and testing of GFN for the
problem of modulation classification is presented by Ghauri et al. (2014). The
algorithm 1 shows the training of gabor filter network and algorithm 2 shows
the testing of gabor filter network for the classification of M-QAM, M-FSK and
M-PSK signals.
75
Algorithm 1: Training of Gabor filter Network
Step1. Initialization of Gabor atom parameters (shift parameter ,ic
scale parameter i and modulation parameter if ) and
weights of Gabor filter ( ).iw
Step2. Calculate the Gabor atom using (Eq. IV.4) and using (Eq.
IV.22), compute all Gabor atom nodes.
Step3. The Gabor atoms node ( )i are now input to the Adaptive
filter, and adjust the weights of the adaptive filter using LMS
(Eq. IV.32)-( Eq. IV.35).
Step4. Evaluate error which is defined in (Eq. IV.7). If error is less
than chosen threshold, then training of algorithm is stopped
and save Gabor atom parameters and Gabor filter weights
( , , , )c f w .
Step5. If error is not less than threshold, repeat step (3) by using
the error calculated in step (4).
Step6. Tune the Gabor atom parameters ( , , )c f using (Eq. IV.8),
(Eq. IV.27), (Eq. IV.29) and (Eq. IV.31).
Step 7. Stoppage Criterion
Step8. Save Gabor atom parameters and Gabor filter weights
( , , , ).i i i ic f w
Algorithm 2: Testing of Modified Gabor filter Network
76
Step1. Input digital modulated signal which may be PAM 2 to
64 modulated.
Step2. Compute the output of each GFN.
Step3. Compute the error function of each GFN.
Step4. Minimum error corresponds to the desired modulation
format of the input signal.
4.6 Simulation Results
The modulation classification using Gabor filter is evaluated in this
section. Firstly the training of algorithm is presented and then the testing of
algorithm in the presence of AWGN channel. The PCC curves are simulated
against number of iterations and SNR, for three different modulation scenarios.
Table IV-1 to IV-3 and Fig IV-4 to Fig IV-9 shows the training of GFN
for the considered modulation formats (PSK, FSK & QAM) up to order 2 to 64.
The GFN parameters (shift, scale & modulation) and weights are updated
according to each considered modulation formats. For minimized error
function, the Gabor atom parameters and weights of Gabor filter ( , , , )i i i ic f w
are stored.
The updated Gabor atom parameters and weights of Gabor filter
( , , , )i i i ic f w are shown in Table IV-1 to IV-3. Fig IV-4 to Fig IV-6 shows the
training of GFN for different number of iterations in case of PSK modulation,
FSK modulation and QAM, respectively. The training process for different
77
SNRs is also shown in Fig IV-7 to Fig IV-9. The training shows that the mean
square error dies down as number of iterations is increased and also by
increasing the SNR. Fig IV-10 to Fig IV-15, shows that the testing of GFN for
the considered modulations formats (PSK 2 to 64, FSK 2 to 64 & QAM 2 to 64)
in the presence of AWGN channel. The probability of correctness is plotted
against signal to noise ratio (SNR) and different number of iterations to
evaluate the classification accuracy of the proposed GFN. The simulations
results shows the classification accuracy for the examples of PSK4, FSK16
and QAM32 which are 100% for fixed SNR and different number of iterations.
Table IV-1 and Table IV-2 shows the updated Gabor atom parameters
for the modulation formats of PSK of order 2 to 64. The Table IV-1 have four
parts; first part shows the updated scale parameter for PSK 2 to 64, second
part shows the updated shift parameter, third part shows the updated
modulation parameter and forth shows the updated weights of the adaptive
filter. The all values of updated GF parameters and weights of adaptive filter
are for minimum mean square error.
Table IV-3 and Table IV-4 shows the updated Gabor atom parameters
for the modulation formats of FSK of order 2 to 64. The table IV-2 have four
parts; first part shows the updated scale parameter for FSK 2 to 64, second
part shows the updated shift parameter, third part shows the updated
modulation parameter and forth shows the updated weights of the adaptive
filter. Table IV-5 and Table IV-6 shows the updated Gabor atom parameters
for the modulation formats of QAM of order 2 to 64. The all values of updated
GF parameters and weights of adaptive filter are for minimum mean square
error. The table IV-3 have four parts; first part shows the updated scale
78
parameter for QAM 2 to 64, second part shows the updated shift parameter,
third part shows the updated modulation parameter and forth shows the
updated weights of the adaptive filter.
Table IV-1: Updated Shift and Modulation Parameter for PSK modulation 2-64
Shift Parameter (c)PSK2 PSK4 PSK8 PSK16 PSK32 PSK645.54 5.07 5.77 5.65 4.81 5.275.77 5.90 4.25 4.45 4.18 4.294.69 4.24 4.33 5.20 4.56 5.564.63 4.72 4.83 4.17 4.67 4.565.02 4.29 5.00 4.08 5.13 4.595.03 5.18 5.68 5.89 5.23 4.795.16 5.09 5.89 4.91 5.79 4.634.61 4.67 5.52 5.91 4.35 4.474.48 4.59 5.13 5.62 5.61 4.475.43 5.14 5.13 4.94 4.15 4.75
Modulation Parameter (f)PSK2 PSK4 PSK8 PSK16 PSK32 PSK642.35 -0.05 0.80 3.14 -0.53 1.82-2.72 -0.56 -0.37 -0.53 2.90 -3.021.91 2.52 -1.90 0.95 -1.33 -2.24-1.02 0.10 -1.55 1.46 2.47 0.381.73 1.08 1.83 1.51 -0.75 -1.89-2.75 -1.83 -2.57 -1.42 2.66 1.100.47 0.20 -2.79 -2.21 0.54 -1.570.32 0.11 -0.93 -1.56 -0.94 -0.551.88 0.33 -2.59 0.31 -1.28 0.68-0.76 -2.27 0.07 2.83 -1.01 -1.70
Table IV-2: Updated Scale and weight Parameter for PSK modulation 2-64
Scale Parameter ( )PSK2 PSK4 PSK8 PSK16 PSK32 PSK6415.63 16.25 10.25 16.76 1.67 2.4516.03 8.57 8.17 5.18 13.53 16.2114.87 14.08 2.55 18.87 6.78 5.331.92 18.27 12.31 6.63 13.33 4.666.44 3.16 11.89 18.48 9.38 5.94
13.32 3.17 4.80 6.85 11.90 2.5011.49 12.94 12.83 15.33 7.44 15.29
79
14.39 3.33 7.33 7.58 6.03 5.2119.04 14.23 7.39 5.13 18.00 12.818.67 2.94 8.48 1.05 12.56 2.59
Weights (w)PSK2 PSK4 PSK8 PSK16 PSK32 PSK645.059 -2.65 -0.74 -0.119 0.837 -4.310-1.83 -1.97 0.671 0.297 1.309 -3.0736.844 -2.42 -0.53 -0.371 -3.033 8.3331.847 2.528 0.499 -0.356 -0.894 -3.8025.384 -0.09 0.677 -0.346 -1.484 1.4138.671 1.923 0.256 -0.917 -0.843 3.8870.058 -2.85 -0.70 -0.455 0.449 -1.762-1.36 1.852 -0.56 -0.487 -1.844 2.6821.899 1.055 0.481 -1.498 0.844 -3.901-3.6 -2.7 0.402 -0.664 1.832 2.549
Table IV-3: Updated Shift and Modulation Parameter for FSK modulation 2-64
Shift Parameter (c)FSK2 FSK4 FSK8 FSK16 FSK32 FSK644.25 4.36 5.35 4.67 5.74 4.224.09 4.88 5.80 4.20 4.55 5.934.58 4.59 5.54 5.94 4.01 5.895.50 5.81 5.71 5.35 5.57 5.254.46 5.55 4.60 5.83 4.59 5.965.36 4.93 4.28 4.01 5.50 5.894.27 4.49 4.16 4.31 5.15 5.954.38 5.28 4.75 5.70 5.76 5.404.35 5.03 4.41 5.04 5.39 4.774.38 4.29 5.58 5.97 5.31 5.84
Modulation Parameter (f)FSK2 FSK4 FSK8 FSK16 FSK32 FSK64-0.15 -2.97 2.87 1.64 2.42 -1.701.15 2.77 0.84 0.76 -1.48 -2.071.22 1.82 2.69 -2.54 -1.23 -0.84-1.50 2.91 -0.67 2.37 0.77 3.102.87 1.94 -0.99 -2.95 0.16 0.450.66 2.08 2.29 0.04 -3.00 -2.56-2.45 -0.72 2.18 -1.43 -1.85 0.410.19 2.87 -1.23 2.59 2.05 -1.09-0.44 1.69 -1.04 -2.30 0.69 0.342.55 -0.76 1.41 -1.80 0.79 -0.54
80
Table IV-4: Updated Scale and weight Parameter for FSK modulation 2-64
Table IV-5: Updated Shift and Modulation Parameter for QAM modulation 2-64
Shift Parameter (c)QAM2 QAM4 QAM8 QAM16 QAM32 QAM645.54 5.07 5.77 5.65 4.81 5.275.77 5.90 4.25 4.45 4.18 4.294.69 4.24 4.33 5.20 4.56 5.564.63 4.72 4.83 4.17 4.67 4.565.02 4.29 5.00 4.08 5.13 4.595.03 5.18 5.68 5.89 5.23 4.795.16 5.09 5.89 4.91 5.79 4.634.61 4.67 5.52 5.91 4.35 4.474.48 4.59 5.13 5.62 5.61 4.47
Scale Parameter ( )FSK2 FSK4 FSK8 FSK16 FSK32 FSK644.44 6.46 6.80 17.24 19.65 12.2714.22 2.53 3.57 3.73 6.25 19.222.11 8.02 15.44 10.10 17.67 6.865.89 10.94 4.75 11.42 4.03 6.9319.21 2.30 11.89 2.10 6.77 19.9619.44 2.78 14.26 5.46 4.12 14.0417.74 4.84 11.82 10.50 3.96 5.871.37 6.67 10.98 17.24 17.69 5.8719.53 15.99 13.96 8.73 19.91 3.7412.67 3.57 1.45 14.57 3.65 19.59
Weights (w)FSK2 FSK4 FSK8 FSK16 FSK32 FSK64-2.58 -7.1 0.931 0.124 -0.318 8.540-0.49 -0.57 -1.2 -0.239 -1.668 5.174-1.53 -3.56 -1.20 3.627 4.663 -1.5706.719 -5.81 -1.1 -0.984 -2.764 0.566-9.32 4.059 -0.08 -0.283 0.840 -2.799-8.05 -2.46 0.068 0.990 3.381 -1.6280.012 3.768 0.443 0.242 4.211 12.898-12.2 1.989 -1.49 1.298 -1.675 -6.2708.351 5.954 -1.45 -0.296 -4.969 4.876-4.07 -0.03 0.40 1.027 -5.423 -8.421
81
5.43 5.14 5.13 4.94 4.15 4.75
Modulation Parameter (f)QAM2 QAM4 QAM8 QAM16 QAM32 QAM642.35 -0.05 0.80 3.14 -0.53 1.82-2.72 -0.56 -0.37 -0.53 2.90 -3.021.91 2.52 -1.90 0.95 -1.33 -2.24-1.02 0.10 -1.55 1.46 2.47 0.381.73 1.08 1.83 1.51 -0.75 -1.89-2.75 -1.83 -2.57 -1.42 2.66 1.100.47 0.20 -2.79 -2.21 0.54 -1.570.32 0.11 -0.93 -1.56 -0.94 -0.551.88 0.33 -2.59 0.31 -1.28 0.68-0.76 -2.27 0.07 2.83 -1.01 -1.70
Table IV-6: Updated Scale and weight Parameter for QAM modulation 2-64
Scale Parameter ( )QAM2 QAM4 QAM8 QAM16 QAM32 QAM6415.63 16.25 10.25 16.76 1.67 2.4516.03 8.57 8.17 5.18 13.53 16.2114.87 14.08 2.55 18.87 6.78 5.331.92 18.27 12.31 6.63 13.33 4.666.44 3.16 11.89 18.48 9.38 5.9413.32 3.17 4.80 6.85 11.90 2.5011.49 12.94 12.83 15.33 7.44 15.2914.39 3.33 7.33 7.58 6.03 5.2119.04 14.23 7.39 5.13 18.00 12.818.67 2.94 8.48 1.05 12.56 2.59
Weights (w)QAM2 QAM4 QAM8 QAM16 QAM32 QAM64-0.031 -0.504 1.009 -1.428 -1.095 0.339-0.021 -0.446 -0.796 -1.339 -0.559 -0.835-0.043 -0.187 -0.285 -0.725 0.304 0.4420.194 0.794 0.299 -1.122 1.359 -0.5580.354 1.061 0.664 -0.476 -1.109 0.5060.250 -0.591 -0.306 0.044 -1.357 -0.2340.097 -0.622 -0.380 1.193 0.290 0.0220.007 0.247 -0.769 -0.316 0.624 -0.1770.245 0.467 -0.608 0.984 -0.334 0.6940.046 -0.117 0.536 0.552 -0.294 0.423
82
Figure IV-4, shows the training of GF network for the case of PSK
modulation format having order 2to64 for different number of iterations at fixed
SNR of 10dB. The parameters of GFN are trained for greater than 50 iterations
for the case of PSK 2, 4 and 8 while for the PSK 16, 32 and 64 the training of
GFN are for less than 50 iterations. The mean square error is minimized and
approaches to zero for all curves shown in Fig IV-4, as number of iterations
are increased.
Figure IV-5, shows the GFN training for the case of FSK modulation
format having order 2to64 for fixed number of iterations. As shown in Fig IV-5,
the mean square error is approaching to zero, when number of iterations are
increased. The training of GFN are done for maximum 50 iterations for the FSK
modulation case.
Figure IV-6, shows the training of GFN for QAM case with fixed SNR
of 10 dB and different iterations. The training of GFN shown minimized mean
square error for all curves shown in Fig IV-6 with less number of iterations. In
figure 6, QAM 16, 32 and 64 are trained for 20 iterations and for QAM 2, 4 and
8 are trained for above 50 number of iterations.
Figure IV-7, shows the training of GFN parameters and weights of
adaptive filter in case of PSK modulation up to order 2 to 64 with fixed number
of iterations and different SNR’s. As SNR increasing from 0 to 20, the mean
square error approaching towards zero. The training of proposed algorithm for
all cases of considered modulation is done successfully and Fig IV-7, shows
the proposed algorithm for the modulation classification is trained at SNR of
10dB.
83
Figure IV-4 Training of Gabor filter parameters and weights for modulationclassification in case of PSK modulation 2-64 for different no. of iterations at
SNR=10dB.
0 50 100 150 200 2500
5
10
15
Number of Iterations
Mean S
quare
Err
or
PSK2
0 50 100 150 200 2500
1
2
3
4
Number of Iterations
Mean S
quare
Err
or
PSK4
0 50 100 150 200 2500
5
10
15
Number of Iterations
Mean S
quare
Err
or
PSK8
0 50 100 150 200 2500
2
4
6
Number of Iterations
Mean S
quare
Err
or
PSK16
0 50 100 150 200 2500
5
10
15
Number of Iterations
Mean S
quare
Err
or
PSK32
0 50 100 150 200 2500
2
4
6
8
10
Number of Iterations
Mean S
quare
Err
or
PSK64
84
Figure IV-5 Training of Gabor filter parameters and weights for modulationclassification in case of FSK modulation 2-64 for different no. of iterations at
SNR=10dB.
Figure IV-6 Training of Gabor filter parameters and weights for modulationclassification in case of QAM modulation 2-64 for different number of
iterations at SNR=10dB.
0 50 100 150 200 2500
0.2
0.4
0.6
0.8
1
Number of Iterations
Mean S
quare
Err
or
FSK2
0 50 100 150 200 2500
0.5
1
1.5
2
2.5
Number of Iterations
Mean S
quare
Err
or
FSK4
0 50 100 150 200 2500
0.1
0.2
0.3
0.4
Number of Iterations
Mean S
quare
Err
or
FSK8
0 50 100 150 200 2500
0.5
1
1.5
Number of Iterations
Mean S
quare
Err
or
FSK16
0 50 100 150 200 2500
0.2
0.4
0.6
0.8
1
Number of Iterations
Mean S
quare
Err
or
FSK32
0 50 100 150 200 2500
0.5
1
1.5
Number of Iterations
Mean S
quare
Err
or
FSK64
0 50 100 150 200 2500
1
2
3
4
Number of Iterations
Mean S
quare
Err
or
QAM2
0 50 100 150 200 2500
2
4
6
8
10
Number of Iterations
Mean S
quare
Err
or
QAM4
0 50 100 150 200 2500
5
10
15
Number of Iterations
Mean S
quare
Err
or
QAM8
0 50 100 150 200 2500
5
10
15
Number of Iterations
Mean S
quare
Err
or
QAM16
0 50 100 150 200 2500
2
4
6
8
Number of Iterations
Mean S
quare
Err
or
QAM32
0 50 100 150 200 2500
5
10
15
20
25
Number of Iterations
Mean S
quare
Err
or
QAM64
85
Figure IV-7: Training of Gabor filter parameters and weights for ModulationClassification in case of PSK modulation 2-64 at different SNRs and fixed
number of iterations
Figure IV-8: Training of Gabor filter parameters and weights for ModulationClassification in case of FSK modulation 2-64 at different SNRs and fixed
number of iterations.
-10 -5 0 5 10 15 200
0.1
0.2
0.3
0.4
SNR
Mean S
quare
Err
or
PSK2
-10 -5 0 5 10 15 200
0.2
0.4
0.6
0.8
1
SNR
Mean S
quare
Err
or
PSK4
-10 -5 0 5 10 15 200
1
2
3
SNR
Mean S
quare
Err
or
PSK8
-10 -5 0 5 10 15 200
2
4
6
SNR
Mean S
quare
Err
or
PSK16
-10 -5 0 5 10 15 200
5
10
15
SNR
Mean S
quare
Err
or
PSK32
-10 -5 0 5 10 15 200
5
10
15
SNR
Mean S
quare
Err
or
PSK64
-10 -5 0 5 10 15 200
0.2
0.4
0.6
0.8
SNR
Mean S
quare
Err
or
FSK2
-10 -5 0 5 10 15 200
0.5
1
1.5
SNR
Mean S
quare
Err
or
FSK4
-10 -5 0 5 10 15 200
0.5
1
1.5
2
2.5
SNR
Mean S
quare
Err
or
FSK8
-10 -5 0 5 10 15 200
1
2
3
4
5
SNR
Mean S
quare
Err
or
FSK16
-10 -5 0 5 10 15 200
2
4
6
8
10
SNR
Mean S
quare
Err
or
FSK32
-10 -5 0 5 10 15 200
5
10
15
SNR
Mean S
quare
Err
or
FSK64
86
Figure IV-9: Training of Gabor filter parameters and weights for ModulationClassification in case of QAM 2-64 at different SNRs and fixed number of
iterations
Figure IV-8, shows the training of GFN parameters and weights of
adaptive filter in case of FSK modulation up to order 2 to 64 with fixed number
of iterations and different SNR’s. The training of FSK modulation formats are
done at SNR of 10-15dB. The training of GFN for QAM 2 to 64 at different
SNR’s and fixed number of iterations are shown in Figure IV-9. The parameters
of GFN and weights of the adaptive filter are updated and mean square error
is minimized as SNR is increased from 0 to 20dB.
The example considered in Figure IV-10 are PSK4, FSK16 and
QAM32. The probability of correctness versus different number of iterations at
SNR=10dB is shown in Figure IV-10. The PCC in Figure IV-10 is approximately
1 when number of iterations is increased up to 200.
In Figure IV-11, the probability of correctness for different modulation
scenarios is shown for different SNR. The PCC curve shows the classification
-10 -5 0 5 10 15 200
0.1
0.2
0.3
0.4
0.5
SNR
Mean S
quare
Err
or
QAM2
-10 -5 0 5 10 15 200
0.2
0.4
0.6
0.8
SNR
Mean S
quare
Err
or
QAM4
-10 -5 0 5 10 15 200
0.1
0.2
0.3
0.4
0.5
SNR
Mean S
quare
Err
or
QAM8
-10 -5 0 5 10 15 200
0.2
0.4
0.6
0.8
SNR
Mean S
quare
Err
or
QAM16
-10 -5 0 5 10 15 200
0.1
0.2
0.3
0.4
0.5
SNR
Mean S
quare
Err
or
QAM32
-10 -5 0 5 10 15 200
0.1
0.2
0.3
0.4
0.5
SNR
Mean S
quare
Err
or
QAM64
87
performance is approximately 100% at SNR=10dB for fixed number of
iterations.
The simulation results shows the 100 % classification accuracy of the
proposed algorithm. The features extracted from the proposed architecture
and classifier based upon GFN provides correct classification among group of
considered modulation formats. Moreover the received signal is corrupted by
additive white guassian noise but the classification accuracy is approximately
100% at lower SNRs. The algorithm is also computationally less complex and
classification accuracy is attained at less number of iterations.
Figure IV-10: Probability of correctness (PCC) versus Number of Iterations atSNR=10dB
0 20 40 60 80 100 120 140 160 180 2000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
No. of Iterations
Pro
babi
lity
of C
orre
ctne
ss (P
CC
)
PSK
FSK
QAM
88
Figure IV-11: Probability of correctness (PCC) versus SNR for fixed Numberof Iterations
4.7 Modified Gabor Filter Network for Classificationof PAM-signals
This section presents Modified Gabor filter based efficient features
extraction from the received signal which to the best of our knowledge have
not been utilized for the problem of modulation classification of M-PAM signals.
The received signal has undergone additive white guassian noise (AWGN)
channel, Rayleigh flat fading channel or Rician flat fading channel. After the
successful extraction of features, weights of the adaptive filter are updated
using Recursive Least Square (RLS) algorithm. The previously proposed
algorithm in section 4.5 are capable to classify the M-QAM, M-PSK and M-FSK
but was not at all efficient for M-PAM signals. In modified Gabor filter network
-10 -5 0 5 10 15 200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR
Pro
babi
lity
of C
orre
ctne
ss (P
CC
)
PSKFSKQAM
89
(MGFN), we have made two important changes to make it efficient for M-PAM
signals.
4.7.1 Modified Gabor Filter Network
To classify the M-PAM signals, the training and testing of the proposed
algorithm have to be done. The training of GFN for the PAM2, PAM4, PAM8,
PAM16, PAM32 and PAM64 is carried out by adjusting the three parameters
of GFN which are shift, scale, modulation parameter ( , , )c f and weights of
the adaptive filter ( ).w The PAM formats are spread about x-axis, and as
increasing M which may vary from 2 to 64, the values of amplitudes are also
increased. The increased values of amplitudes destroy the convergence of the
algorithm. To cope up with the problem of divergence, following are the
proposed changes in the existing algorithm by Ghauri et al. (2014) for
classification of PAM formats (Ghauri et al. (2015)):
1. The absolute values of amplitude are taken instead of taking whole
input modulated signal, e.g. PAM4 have amplitudes 3, 1,1,3 but
after taking absolute values, amplitude becomes 1,3 .
2. The desired response for each of the considered modulation
formats are the average amplitudes i.e.1
Mj
j
Aa
M
where
7, 5, 3, 1,1, 3, 5,{ 7}jЄA for example, for PAM8 the desired
response is 4.
90
3. The weights of the adaptive filter are updated using RLS algorithm
instead of LMS algorithm for two motives. First the convergence
rate of RLS is sooner than the LMS. Second the mean square error
produced by RLS is lesser than the LMS.
4.7.2 Modified Proposed Algorithm for ModulationClassification
The weights of adaptive filter are updated using RLS algorithm which
are as follows:-
1
1T
n nn
n n n
Kk
K(Eq. IV.35)
1
M
i ii
e n d n y n d n w
(Eq. IV.36)
1n n n e n w w k (Eq. IV.37)
1 11 1Tn n n n n K K k K (Eq. IV.38)
To initialize the algorithm, weights are initialized (0) 1, 1, .. . . 1 ,w the
K is referred as inverse correlation matrix. The n is the input vector and
is the forgetting factor. The algorithm for training and testing the proposed
modified Gabor filter network for the classification of M-PAM signals are as
under:-
91
Algorithm 1: Training of Modified Gabor filter Network
Step1. Initialize the Gabor atom parameters
Step2. Compute all Gabor atom nodes using (Eq. IV-21).
Step3. Adjust adaptive filter using RLS (Eq. IV-36)-(Eq. IV-39).
Step4. After adjusting the weights, Calculate error using (Eq. IV-7).
Step5. If error is less than chosen threshold, then training of algorithm isstop and save Gabor atom parameters and Gabor filter weights( , , , ).i i i ic f w
Step6. If error is not less than threshold, repeat step (3) by using the errorcalculated in step (4).
Step7. Tune the Gabor atom parameters ( , , )i i ic f using (Eq. IV-27), (Eq.IV.29) and (Eq. IV.30).
Algorithm 2: Testing of Modified Gabor filter Network
Step1. Input digital modulated signal which may be PAM 2 to 64
Step2. Compute the output of each GFN by using the relation
1
M
i ii
y w
Step3. Compute the error function of each GFN.
Step4. Minimum error corresponds to the desired modulation format ofthe input signal
4.7.3 Simulation Results of Modified Gabor FilterNetwork
The training of MGFN is evaluated for the M-PAM signal classification
in tabular form and also simulation results for mean square error versus
number of iterations and signal to noise ratio. Tables and figures show that the
92
mean square error approach approximately zero when number of iterations
and SNR are increased. At the end of training the three parameters of MGFN
(shift, scale, modulation parameter) and adaptive filter weights are saved for
minimum mean square error. In second module the testing of GFN is carried
out by finding the error function of each Gabor filter network. The minimum
square error corresponds to the desired modulation format.
Table IV-7, shows the training performance of MGFN in the form of
diagonal matrix or accuracy matrix for the classification of considered
modulation formats. The training performance is approximately 100% under
no noise considerations. Table IV-8, shows the training performance of MGFN
in the form of diagonal matrix or accuracy matrix for the classification of M-
PAM signals under the influence of additive white guassian noise. The training
of MGFN is done at SNR of 10dB and accuracy is approximately 99.5% for
considered modulation formats.
Figure IV-12. Training of MGFN for the M-PAM formats under no Noise
0 10 20 30 40 500
0.2
0.4
0.6
0.8
1
No. of Iterations
MM
SE
PAM2
0 10 20 30 40 500
5
10
15
No. of Iterations
MM
SE
PAM4
0 10 20 30 40 500
20
40
60
No. of Iterations
MM
SE
PAM8
0 10 20 30 40 500
10
20
30
No. of Iterations
MM
SE
PAM16
0 10 20 30 40 500
2
4
6
8
No. of Iterations
MM
SE
PAM32
0 10 20 30 40 500
10
20
30
40
No. of Iterations
MM
SE
PAM64
93
Table IV-7. Training Performance of MGFN of M-PAM signal classificationwithout Noise
PAM 2 PAM 4 PAM 8 PAM 16 PAM 32 PAM 64
PAM 2 100%
PAM 4 100%
PAM 8 100%
PAM 16 99.2%
PAM 32 99.6%
PAM 64 100%
Figure IV-13. Training of MGFN for the M-PAM formats on AWGN channel
Table IV-8. Training Performance of MGFN of M-PAM signal classification onAWGN channel
-10 -5 0 5 10 15 200
0.5
1
1.5x 10
-3
SNR
MM
SE
PAM2
-10 -5 0 5 10 15 200
2
4
6
8
SNR
MM
SE
PAM4
-10 -5 0 5 10 15 200
20
40
60
80
SNR
MM
SE
PAM8
-10 -5 0 5 10 15 200
500
1000
1500
2000
SNR
MM
SE
PAM16
-10 -5 0 5 10 15 200
1000
2000
3000
SNR
MM
SE
PAM32
-10 -5 0 5 10 15 200
5000
10000
15000
SNR
MM
SE
PAM64
94
PAM 2 PAM 4 PAM 8 PAM 16 PAM 32 PAM 64
PAM 2 100%
PAM 4 99.9%
PAM 8 100%
PAM 16 98.4%
PAM 32 99.2%
PAM 64 99.3%
Table IV-9. Testing Performance of MGFN of M-PAM signal classification onAWGN channel
PAM 2 PAM 4 PAM 8 PAM 16 PAM 32 PAM 64
PAM 2 98.6%
PAM 4 97.8%
PAM 8 96.6%
PAM 16 96.1%
PAM 32 98.1%
PAM 64 97.6%
Table IV-10. Testing Performance of MGFN for M-PAM signal classificationat SNR=10dB on AWGN channel
PAM 2 PAM 4 PAM 8 PAM 16 PAM 32 PAM 64
PAM 2 99.5%
PAM 4 98.9%
PAM 8 99.9%
PAM 16 98.3%
PAM 32 98.5%
PAM 64 98.9%
Figure IV-12, shows the training of MGFN under no noise conditions.
From the Figure IV-12, it is clear that the minimum mean square error (MMSE)
95
is approaching to zero as number of iterations increases for all considered
modulation formats. The training of network is stop when MMSE reaches some
threshold or zero and the features are stored.
Figure IV-13, shows the training of MGFN under the influence of
AWGN channel with fixed number of iterations. The MMSE approach towards
zero as SNR increases from -10 to 20 dB for the considered modulation
formats as shown from the Figure IV-13.
Table IV-9, shows the testing performance of MGFN in the form of
diagonal matrix for the M-PAM signal classification. The performance is
evaluated at SNR of 5dB and it is shown from the table that percentage
accuracy for classifying the modulation formats is much better at low SNRs.
Table IV-10, shows the testing performance of MGFN in the form of
diagonal matrix for the M-PAM signal classification at SNR of 10dB and it is
shown that percentage accuracy for classifying the modulation formats is
98.7%. The testing performance is better due to two facts: first choice of
efficient features from the MGFN and second the classifier.
Figure IV-14, shows the probability of correctness (POC) plotted
against number of iterations and from Figure IV-14, it is clear that POC is
approximately 1 when number of iterations increased up to 500. The example
considered in the above figure is PAM 16 among class of M-PAM signals which
are classified correctly.
Figure IV-15, shows the probability of correctness (POC) plotted
against signal to noise (SNR) for fixed number of iterations and from Figure IV-
15 it is clear that POC is approximately 1, when SNR is increased up to 10.
96
The example considered in the above figure is PAM 16 and classification
accuracy is approximately 90% at greater than 3dB of SNR.
The classification performance of PAM 8 considered example among
the M-PAM signals is evaluated in Table IV-11. The Table IV-11, shows the
performance comparison of percentage classification on the AWGN channel,
Rician flat fading channel and Rayleigh flat fading channel. The classifier
performance is approximately 100 % on AWGN channel, 95% on Rician flat
fading channel and 92% for the Rayleigh flat fading channel at SNR of 10 dB.
The efficient features extraction from the MGFN easily classifies the
considered modulation formats with very low probability of error.
Figure IV-14. Probability of Correctness curve for the example of PAM16.
50 100 150 200 250 300 350 400 450 5000.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Number of Iterations
Prob
abilit
y of C
orrec
tness
(POC
)
Probability of Correctness Curve
97
Figure IV-15. Probability of Correctness curve under AWGN channel for theexample of PAM16
Table IV-11. Testing Performance Comparison of MGFN on AWGN andFading channels for the example of 8-PAM format
SNR indB AWGN Rician Flat
Fading Rayleigh Flat
-4 45.0% 35.1% 31.0%
-3 57.0% 45.6% 37.0%
-2 66.2% 55.44% 46.8%
-1 74.2% 64.64% 54.9%
0 81.0% 72.64% 63.4%
1 85.2% 78.84% 70.8%
2 88.4% 83.36% 76.8%
3 91.6% 87.16% 81.0%
4 94.4% 89.6% 85.1%
5 96.6% 91.4% 87.8%
6 98.4% 92.76% 89.8%
7 99.4% 93.76% 91.2%
8 99.8% 94.36% 91.8%
10 100% 94.87% 92.0%
-4 -2 0 2 4 6 8 100.4
0.5
0.6
0.7
0.8
0.9
1
SNR in dB
Prob
abilit
y of C
orrec
tness
(POC
)
Probability of Correctness Curve
98
4.8 Comparison with Existing Techiques
Table IV-12, shows the performance comparison with the existing
techniques. The table objects shows that the method proposed, the year,
number of modulation formats to be classified, classification accuracy in
percentage form at SNR of 10dB and number of features extracted from the
received signal. From the existing techniques, modulation formats considered
for classification are in less numbers and number of features used are more
and also classification accuracy is not above 90% for the maximum cases. The
efficient features which we extracted are only three and we successfully
classified maximum number of modulation formats at SNR of 8dB.
4.9 Summary
In this chapter, the proposed joint approach for feature extraction and
classification for multi-signal vector is used for modulation classification. In first
part, Gabor filter based approach is used to classify the digital modulated
signal {PSK2, PSK4, PSK8, PSK16, PSK32, PSK64, FSK2, FSK4, FSK8,
FSK16, FSK32, FSK64, QAM2, QAM4, QAM8, QAM 16, QAM 32, and QAM
64}. In second part, modified Gabor filter network based classification
algorithm is used to efficiently classify the M-PAM signals.
The proposed algorithm gives high classification accuracy at lower
SNRs. The performance of proposed modified classifier is also compared on
three different channels which shows the success rate of the classifier. In the
99
end, the proposed GFN and MGFN based modulation classification algorithms
is compared with the existing techniques.
Table IV-12. Performance Comparison with the Existing Techniques
Method Year &Reference
ModulationFormats to be
classified
ClassificationAccuracy in %
at 10dB ofSNR
No offeatures
Pdf of the receivedsignal, Zero Crossing
Hsue et al. (1990)
PSK, FSK
6
98
(15dB of SNR)
4
Spectral Features
Azzouz et al. (1995)
PSK,FSK
6
90 5
Spectral Featuresand Moments
Nandi et al. (1998)
PSK, FSK,other types
12
96
(15dB of SNR)
9
Constellation Shape
Mobasseri et al.(2000)
PSK, QAM
3
90
(5dB of SNR)
4
HOC
Swami et al. (2000)
PSK,QAM
4
96 2
Neural Networks
Zhao et al. (2003)
PSK,FSK, QAM
7
93
(8dB of SNR)
5
Back PropagationAlgorithm (BPA),
Resilient BPA Wonget al. (2004)
PSK, FSK,QAM
10
89.96
99.95
17
Time frequencyfeatures Ye et al.
(2007)
FSK,PSK
6
97.64 4
NormalizedCummulants Wu et
al. (2008)
PSK, QAM
5
97.5 1
100
CummulantsFeatures, Multiclass
SVM
Ebrahimzadeh et al.(2010)
PSK, QAM
9
97.56 12
Spectral features andMoments
Popoola et al. (2011)
FSK,QAM
12
99.95 8
HOC & SpectralFeatures, Multiclass
SVM
Ebrahimzadeh(2012)
PSK,QAM,FSK
11
97.45 11
Gabor Filter basedFeatures Ghauri et
al. (2014)
PSK,FSK,QAM
18
100 3
Modified Gabor Filterbased Features
PAM
6
100
(8dB of SNR)
3
101
CHAPTER V
AUTOMATIC MODULATION CLASSIFICATION USINGHIDDEN MARKOV MODELS
5.1 Introduction
In this chapter, we have proposed joint feature extraction and classifier
structure based upon GFs network and hidden markov model (HMM) for
classification of modulation formats that differ with the existing classifiers. The
proposed classifier structure uses Baum-Welch (BW) algorithm for training of
HMM, which computes the probability of observation sequence given the
model. The probability of observation sequence is maximized via updating four
parameters. Three parameters (shift, scale, modulation) of GFs network are
updated using GA, and one HMM parameter, the probability distribution in
each of the states, is updated using BW algorithm.
In training of the classifier, the probability of observation sequence has
to be maximized while updating four parameters. For each modulation format,
Gabor filter network and HMM is trained individually. We are simultaneously
optimizing the feature extractor (Gabor filter bank) and the classifier (hidden
markov model). In testing phase, proposed classifier classifies the considered
modulation formats. Efficient features extractor and HMM classifier are trained
simultaneously to formulate an optimal structure. The simulation results shows
the significant performance improvement when compared with other existing
102
techniques. The PAM & QAM signals are considered for classification and all
the experiments are done in MATLAB environment.
5.2 System Model and Gabor Filter Network
The system model for the Gabor filter is the same as discussed in
Chapter 3. The input to the GF is the received signal which is corrupted by
AWGN. First the proposed GF converts the input sequence from serial to
parallel. The GF layer has N nodes k1 k2, , , kNO O O also called gabor nodes.
The gabor atom is defined as:
1 1 i kjw tk i
i kii
t cg t g e k K
(Eq. V.1)
where 21/42 ktkg t e and ( , , ) c f are shift parameter, scale
parameter and modulation parameter, respectively. The output of the ith gabor
atom node is kiO corresponding to input signal .kix Thus output of gabor atom
which represents the inner product of gabor atom and the transmitted signal is
defined as:
,( )ki i k kiO g t x (Eq. V.2)
The outputs of the GF are input to the classifier structure, the HMM.
After maximizing the fitness function the parameters of GF become features
which we have used to classify the PAM and QAM signals.
103
5.3 Genetic Algorithm
Genetic Algorithms enjoys a lot of variety in terms of representation,
generation of initial population, selection criterion, mutation and crossover
methods. The parameters to be optimized, known as genes are concatenated
to make a string which is called a chromosome. In our problem GF parameters
(scale, shift and modulation) are a chromosomes. The major part of GA is the
fitness function, the fitness function in our problem is probability of observation
sequence given the model parameters i.e. [ | ]P O . There are a number of
ways to apply crossover, single point crossover, multipoint crossover and
uniform crossover but we use single point crossover. The purpose of mutation
is to avoid stagnation and premature convergence. In order to preserve best
individuals and promote them to next generation, the elitism operator is used.
The flow diagram of the genetic algorithm are shown in Figure V-1.
Start
Fitness Function Evaluation(Probability of Observation given Model)
Initialize population (Gabor filter parameters)[shift, scale, modulation]
Mutation
Crossover
Selection Best Individual
Stop
OptimizationCriteria Met
YESNO
Figure V-1. Flow Chart of Genetic Algorithm
104
5.4 Hidden Markov Model
The main characteristics of HMM are the states of HMM, state
transition probability, observation symbol probability and the initial state
distribution.
1. States of HMM
The state of HMM at time t instant is tq , thus tq takes value from
1 2{ , , . . . . . , },Nq q q where N is the number of states.
2.State transition Probability
The set of state transition probabilities { }ijA a , where
1 | ,1 ,ij t ta P q j q i i j N (Eq. V.3)
and1
0, 1N
ij ijj
a a
. We assume that for all constellations state transition
probabilities are equally probable i.e. 1 / ,M where M is the number of
distinct observation symbols.
3. Observation Symbol Probability
The probability of observing some specific symbol from a specific state
( ,)jB b l where
|j t l tb l P O v q j (Eq. V.4)
105
t1 & 1 ,j N l K O is the vector of outputs symbols and lv is the lth
observation symbol 1
0, 1.N
j jj
b k b l
Here we assumed jb l to be
flat and update that using BW algorithm.
4. Initial State Distribution
The probability of starting the process from specific state, the initial state
distribution is
1, 1/i i P q i N π (Eq. V.5)
A complete specification of an HMM requires three probability
measures ( , , )A B . Therefore , )( , A B is used to denote the complete set
of HMM with discrete probability distribution. There are some assumptions
which we made in HMM to reduce the computational complexity:-
1. Markov Assumption
1 |ij t ta P q j q i
The above statement is first order HMM due to one step memory
because next state is only dependent upon the current state.
2. Stationary Assumption
The state transition probability doesn’t change with the time.
1 11 1| |t t t tP q j q i P q j q i (Eq. V.6)
106
There are three basic problems of interest in HMM, evaluation
problem, learning problem and decoding problem.
1. Evaluation Problem: Given a HMM model and a sequence of
observations O , what is probability that the observation are
generated by the model [ | ]P O ?
2. Learning Problem: Given a HMM model and a sequence of
observations O , how should we adjust the model parameters in
order to maximize the [ | ]P O ?
3. Decoding Problem: Given a HMM model and a sequence of
observations O , what is the most likely state sequence in the
model that produced the observation?
5.4.1 Baum Welch (BW) Algorithm
Since in this thesis, only first two problems are being exploited,
therefore solutions of the above mentioned problems based on forward
backward procedure which estimates iteratively the unknown model
parameters and maximizing the posterior probability [ | ]P O which is known
as Baum-Welch Algorithm. The following is the procedure to evaluate the
[ | ]P O :
The forward variable ( )t i is defined as the probability of partial
observation sequence 1 2, , . . . . . ,to o o when process terminates at state i ,
1 2( ) [ , , . . . . . , , | λ]t t ti P o o o q i
107
Initialization
1 1 1 1 1
1
(1) , λ
, 1] [
i
i i
P o q i P o q i P q i
b o i N
(Eq. V.7)
Induction
1 1 2 1 1
1 2 1
1 2 1
1 1
1 2 1
( ) [ , , . . . . . , , , | λ]
[ , , . . . . . , , 1|λ] | 1
[ , , . . . . . , , 2|λ] 2| 1
[ | ] .
.
[ , , . . . . . , , |λ] |
t t t t
t t t t
t t t t
t t
t t t t
j P o o o o q j
P o o o q P q j q
P o o o q P q q
P o q j
P o o o q N P q j q N
1 1 21
[ , , . . . . . , , | λ]N
j t t t iji
b o P o o o q i a
1 11
( )N
t j t t iji
j b o i a
(Eq. V.8)
Using the recursion formula we obtain
( ) [ , | λ]T Ti P O q i
Termination
The required probability of observation given model is given by
1 1
[ | λ] ( ) [ , | λ]N N
T Ti i
P O i P O q i
(Eq. V.9)
The backward variable ( )t i is defined as the probability of partial
observation sequence 1 2, , . . . . . ,t t To o o given that current state is i ,
1 2( ) [ , , . . . . . , , |λ]t t t T ti P o o o q i
108
Initialization
( ) 1, 1 T i i N
Induction
A recursive relationship which can be used to calculate
1 11
( ) () )(N
t t ij j tj
i j a b o
(Eq. V.10)
1 2 1 2( ) , , . . . . . , , λ , , . . . . . , , λ
[ , | λ]
( )t t t t t t T t
T
i P o o o q i P o o o q i
P O q
i
i
Termination
Therefore another way to calculate using [ | ]P O forward and
backward variables is as follows:-
1 1
[ | λ] [ , | ] ( ) ( )N N
T t ti i
P O P O q i i i
(Eq. V.11)
In addition to forward and backward variables, we need to define two
more auxiliary variables. The two variables are ( , )t i j probability of being in
state i at tth time and in state j at time 1t .
1
1
1
11 1
1
11 1
ξ ( , ) [ , | , λ][ , , | λ]
[ | λ][ , , | λ]
[ , ,
(
|λ]
( )
( )
) ( )
( ) ( )
t t t
t t
t tN N
t ti j
t ij j t t
N N
t ij j t ti j
i j P q i q j O
P q i q j O
P O
P q i q j O
P q i q j O
i a b o
i a
i
ib o
(Eq. V.12)
109
The posterior probability ( )t i , probability of being in state i at time t
given the observation sequenceO .
1
1
( ) [ | , λ][ , | λ]
[ |λ][ , | λ]
[ , | ]
( ) ( )
( ) ( )
t t
t
tN
tj
t tN
t ti
i P q i O
P q i O
P O
P q i O
P q i O
i i
i i
(Eq. V.13)
The relationship between ( )t i and ( , )t i j are as follows:-
1
ξ ( , )N
t tj
i i j
(Eq. V.14)
According to BW algorithm, given an initial model ,( , , )A B after
the calculation of forward ( )t i and backward ( )t i variables, ( , )t i j and ( )t i
are calculated. Finally HMM parameters are updated in such a way to
maximize the [ | ]P O according to following equations.
1 )ˆ (i r i (Eq. V.15)
1
11
1
ξ ( , )
( )ˆ
T
ttij T
tt
i ja
i
(Eq. V.16)
where,1
1
( )T
tt
i
is expected number of times are in state i or expected
number of transitions made from state i .
110
1
1 2 11
1 2 1
( ) ( ) ( ) ( )
| , λ | , λ [ | , λ]
T
t Tt
T
i i i i
P q i O P q i O P q i O
(Eq. V.17)
1
1
ξ ( , )T
tt
i j
is the expected number of transitions from state i to state j
.
1
1 21
2 3
1
ξ , , | , λ
, | , λ
.
.
+ , | , λ
T
tt
T T
i j P q i q j O
P q i q j O
P q i q j O
(Eq. V.18)
1
1
1 2
1
( ) ( )
ˆ
( )
t l
t l
Tt t
o vj T
tt
T o v
T
tt
j
b li
j j j
i
(Eq. V.19)
Using re-estimation formulas of (Eq. V-15, Eq. V-16, Eq. V-19), the
HMM parameters are updated in such a way to maximize the probability of
observation sequence i.e. [ | ].P O
5.5 Proposed Classifier and its Training
In the proposed classifier structure the objective is to maximize the
probability of observations given the model parameters [ | ].P O To maximize
[ | ],P O the we update the HMM parameters using Baum-Welch algorithm
111
and Gabor parameters using GA. The proposed classifier structure is shown
in Figure V-2. The symbols considered are K N and the observation vector
is given by
1 2 T
k k kNO O O O (Eq. V.20)
where,2
1
1
1 1 1cos( ), 1,2, .., .kt c
k k kO x e w t k K
The one of the HMM
parameter is probability of observing some specific symbol from a specific
state is updated using forward backward algorithm. The proposed classifier
structure have two phases; in first phase training of the classifier is carried out
while in second phase we test the classifier. In training phase, the probability
of observation sequence given the model [ | ].P O is to maximize. This
probability is the total likelihood of the observation and can be expressed as
[ | ].totL P O There is no way to analytically solve the model ,( , , )A B
which maximize the quantity totL . But the model parameters choice, made it
locally maximized using iterative procedure like Baum-Welch algorithm. The
structure of the proposed classifier is shown in Figure V-3.
Figure V-2. Proposed Classifier Structure
112
Digital Modulated Data Set
Training Set Testing Set
Extract Features from Gabor Filter
Build the Classifier Model
Fitness Function Evaluation
Meet Criterion?Optimized Classifier
parameters andFeature Subset
Yes
No
Cross Over
Selection
Mutation
Figure V-3. Structure of Proposed Classifier
5.5.1 Training of Classifier
In training phase of the classifier structure, the objective is to maximize
the probability of observation, for that we have solved the learning problem of
HMM in which we adjust the HMM parameters. We use GA to adjust the three
parameters of the GFs. The length of each chromosome is 3 number of GFs
parameters 1 1 1 1 1 1 1 1 11 1 1 2 2 2, , , , , , , , , .N N Nc f c f c f The fitness function for the
113
GA is probability of observation sequence i.e. [ | ].P O We also use BW
algorithm to maximize the [ | ]P O via updating one of the HMM parameter
which is probability distribution in each of the states. The proposed training
algorithm for the classifier is as follows:-
Algorithm for Training the classifier
Step 1. Initialize the HMM model parameters as stated in (Eq. V-3), (Eq. V-4) and (Eq. V-5).
Step 2. Input observation sequence using (Eq. V-6).
Step 3. Evaluate the [ | ]P O using (Eq. V-9) and (Eq. V-11).
Step 4. Calculate the ( , )t i j and ( )t i using (Eq. V-12) and (Eq.V-13) respectively.
Step 5. Update HMM parameters (re-estimation formulas) using(Eq. V-19).
Step 6. Evaluate the fitness function i.e. [ | ]P O using updatedHMM parameters.
Step 7. Update the gabor filter parameters using Figure V- 1.
Step 8. Evaluate the [ | ].P O
Step 9. Save the gabor filter and HMM parameters for maximum[ | ].P O
5.5.2 Testing of Classifier
In test phase of the classifier, we solve HMM evaluation problem which
is the observation sequence probability given the model parameters. Figure V-
4, shows the proposed classifier testing scheme in which received signal is fed
to the classifier which constitutes of bank of gabor filter (BGF) network and
HMM, where classifier evaluates the probability of observation sequence given
114
the model. The maximum among all the outputs of the classifier tells us the
modulation format of the received signal.
The steps involved in the testing phase are as follows:-
Algorithm for Testing the Classifier
Step 1. Input received signal corrupted by AWGN noise
Step 2. Evaluate the [ | ]iP O for each of considered modulation.format.
Step 3. Maximum [ | ]iP O gives the received signal modulationformat.
Figure V-4. Testing of Proposed Classifier
5.6 Simulation Results
The classification performance of the proposed classifier is evaluated
in this section. The considered modulation formats are PAM and QAM signals
which are corrupted by AWGN channel model. The training and testing of the
115
classifier is done using gabor features and HMM in conjunction with GAs. The
population size for the genetic algorithm throughout the experiment is 100. The
random values of the scale, shift and modulation parameter are selected in a
specified range to make the population.
Table V-1. Classification accuracy for the proposed classifier for different no.of samples and SNRs.
Method 512 1024 2048 4096
Feature Extractor
plus classifiers (FEPC)
0 dB 0.73 0.88 0.94 0.98
5 dB 0.84 0.97 1.00 1.00
10 dB 0.96 1.00 1.00 1.00
15 dB 0.99 1.00 1.00 1.00
The number of samples are 512, 1024, 2048 and 4096 at different
SNRs of 0dB, 5dB and 10dB. For each value of SNR and considered
modulation format samples, training is done with 10,000 realizations. The
training curves for the PAM and QAM signals are shown in Figure V-5. The
probability of correctness approaches 1, which is the objective of the training
at lower SNRs. The training of the classifier for considered modulation formats
are done at lower SNRs.
Table V-1, shows the performance accuracy for different values of
SNR and also for different number of samples. The performance is shown in
the form of average probability of correctness (PCC) versus different SNRs.
116
Figure V-5. Classifier training for the case of PAM and QAM signals
Figure V-6. Average classification performance for different number ofsamples.
-5 0 5 100.4
0.5
0.6
0.7
0.8
0.9
1
SNR in dB
Prob
abilit
y of
Cor
rect
ness
-5 0 5 100.4
0.5
0.6
0.7
0.8
0.9
1
SNR in dB
Prob
abilit
y of
Cor
rect
ness
PAM 4PAM 8PAM 16
QAM 4QAM 16QAM 64
-5 0 5 10 15
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
SNR in dB
Pro
babi
lity
of C
orre
ct C
lass
ifica
tion
512 samples1024 samples2096 samples4096 samples
117
Table V-2. Percentage Classification performance at different SNRs and2048 samples.
SNR PAM4 PAM8 PAM16 QAM4 QAM16 QAM64
0dB
PAM4 72.35
PAM8 70.94
PAM16 68.99
QAM4 72.35
QAM16 71.92
QAM64 69.96
PAM4 PAM8 PAM16 QAM4 QAM16 QAM64
5dB
PAM4 97.32
PAM8 98.01
PAM16 97.29
QAM4 97.57
QAM16 97.09
QAM64 97.78
PAM4 PAM8 PAM16 QAM4 QAM16 QAM64
10dB
PAM4 99.92
PAM8 99.89
PAM16 99.95
QAM4 99.99
QAM16 99.98
QAM64 99.84
Figure V-6, shows the performance of classifier for the considered
modulation formats at different number of samples. From the figure it is clear
that as number of samples increases the probability of correct classification
also increases. The PCC is 1 at 6dB of SNR when 4096 samples were taken.
118
The classification performance is much better at lower SNRs and with less
number of features.
Table V-2, shows the performance of classifier with 2048 samples at
different SNRs in the form of confusion matrix. It is also clear from the table
that classification of modulation formats are done at lower SNRs with 10,000
realizations. The joint PAM and QAM signals classification from the Table V-2
are approximately 100% at lower SNR below than 10dB. The confusion matrix
shows only for three different SNRs of 0dB, 5dB and 10dB.
5.7 Comparison with Existing Techniques
Table V-3, shows performance comparison with the well-known
existing techniques. The tabular arrangement shows the number of features,
considered modulation formats and classification accuracy. The classification
of proposed FEPC is much better at lower SNRs with less number of features
used.
Dobre et al., (2003) proposed 8th order cummulants to classify the
modulation formats with classification accuracy of 70% at 10dB of SNR. At the
same SNR, the classification accuracy we achieved is 100% for the six class
classification problem.
Shi et al., (2011) classifier, classification accuracy is 83% for higher
order QAMs at SNR of 10dB, while using characteristics function to
compensate the inefficiency of cummulants. Authors also introduced the timing
119
offset, but without timing offset we achieved 100% classification accuracy
while classifying the higher order QAM and PAM signals.
Puengnim et al., (2007), takes 2000 samples to classify the 4-QAM
and 16-QAM where the classifier accuracy is 90% at SNR of 12dB. While we
achieved 100% classification accuracy with 2048 samples at SNR of 10dB.
The classification accuracy achieved is 93.5% at SNR of 10dB with
1000 samples by Chaithanya et al., (2010), while we achieved 99% at same
SNR using novel gabor features and HMM+GA classifier.
The classification accuracy reported is 94% at SNR of 10dB using
2000 number of samples while they used cummulants as feature set by
Mirrarab et al., (2007), while we achieved 100% accuracy at SNR of 10dB
using 2048 samples using novel classifier and gabor features.
Xi et al., (2006) utilized 8th order cummulants to obtain a classification
accuracy of 94% with 2000 samples at SNR of 10dB, while our proposed
classifier classifies the higher order QAMs approximately 100% with same
SNR and number of samples considered.
He et al., (2008) classify the modulation formats with classification
accuracy of 97% at SNR of 15dB, while our classifier classifies the QAM16
approximately 100% at SNR of 10dB. The 4th order cummulants are used for
classifying the QAM signals and reported classification performance is 94% at
10 dB of SNR by Wu et al., (2008). The classification accuracy at same SNR
is 99.99% with our proposed model.
120
The classification accuracy using genetic programming with K nearest
neighbor for classifying the 2-class and 4-class problem is 98.55% at 15 dB of
SNR while using 1024 samples by Aslam et al., (2012). The classification
accuracy we achieved is 100% at SNR of 10dB for classifying the 6-class
problem at same number of samples. The overall classification accuracy for
the considered modulation formats is approximately 100% at 8 dB of SNR.
Ghauri et al., (2014) classifies the modulation formats at 10 dB of SNR
with classification performance of 99% for classifying the QAM signals, while
we classified the QAM signals with classification accuracy of 100% at 8dB of
SNR.
Table V- 3. Performance Comparison with the Existing Techniques
Features, Year & AuthorClassificationAccuracy at10dB of SNR
ProposedClassifier
ClassificationAccuracy at10dB of SNR
8th order cummulants
Dobre et al., (2008)70%
100%
(six class problem)
Characteristics Function +Cummulants
Shi et al., (2011)83%
100%
BW algorithm
Puengnim et al., (2007)
90% at 12db ofSNR
(4QAM & 16QAM)
100%
(six class problem)
HOM & HOC
Chaithanya et al., (2010)
93.5%
1000 samples
99%
1024 samples
Cummulants features
Mirrarab et al., (2007)
94%
2000 samples
100%
2048 samples
121
8th order cummulants
Xi et al., (2006)
94%
2000 samples
100%
2048 samples
Multifractal Features
He et al., (2008)97% at 15 dB of
SNR 100%
4th order cummulants
Wu et al., (2008)
94%99.9%
Genetic Programming + KNN
Aslam et al., (2012)98.55% at 15 dB
of SNR
100% at 8db ofSNR (overallclassification
accuracy)
5.8 Summary
In this chapter, the classification of PAM and QAM signals have been
done using novel classification approach. The proposed classifier structure is
basically a hidden markov model which evaluates the probability of
observation sequence. Genetic algorithm is used to adjust the GF parameters
such that to maximize the probability of observation sequence. The HMM
parameters are updated using BW algorithm. The proposed classifier,
classifies the considered modulation formats with higher classification
accuracy at lower SNRs. The classification performance of proposed classifier
is also evaluated for different number of samples. The classifier performance
is approximately 100% for the PAM and QAM signals classification at low SNR.
122
CHAPTER VICONCLUSIONS AND FUTURE DIRECTIONS
6.1 Summary of Results
Automatic modulation classification is one of the most prominent and
necessary feature of many current and future communication systems. In
AMC, the identification/classification of received signal modulation format with
high probability of correctness is one of the objectives of the research. In this
dissertation only feature extraction based pattern recognition approach is used
to solve the problem of classification. The extraction of new features and
modified classifiers had designed to classify modulation formats with low
probability of error.
In the literature many algorithms are investigated for the solution of this
problem, many of these algorithms are capable of classifying the limited
number of modulation formats at higher SNRs. The efficient feature extractor
and classifier structure formulates the optimum classifier. Hence the optimum
solution demands a novel features extraction and classification of modulation
formats with high classification accuracy. This has been the theme of this
dissertation described in chapters III, IV and V.
In chapter III, the proposed classifiers are based on ML, LDA, FFBPNN
and SVM. The features set used for classification are normalized higher order
cummulants and spectral features. The classification accuracy of the proposed
classifier using 8th order cummulants is much better than existing classifiers
123
which are based on 4th order and 6th order cummulants. The classifiers based
on spectral features are also capable to classify the considered modulation
formats efficiently. The classification accuracy is also compared with well-
known existing techniques and it is found that proposed classifier performs well
on AWGN channel and also on fading channels. The classifiers proposed in
chapter III, uses the existing features in such a way so as to classify the
maximum number of modulation formats with higher classification accuracy.
In chapter IV, the new efficient features are extracted from the Gabor
filter network named as Gabor features. The features extracted are capable of
classifying the M-QAM, M-FSK and M-PSK signals efficiently. For each
modulation format, one Gabor filter network is trained and parameter of GFN
is saved. The training and testing of the classifier shows that performance of
Gabor filter based classifier, efficiently classify the modulation formats on
AWGN channel. The classification process is difficult for M-PAM signals as the
signals are spread around axis. The modification in classifier algorithm makes
the classifier capable to classify the M-PAM signals at lower SNRs. The
performance is also compared with the existing schemes in the literature which
shows that the Gabor features are efficient enough to classify the M-PAM, M-
QAM, M-FSK and M-PSK under the effect of AWGN channel, Rayleigh flat
fading channel and Rician flat fading channel.
In chapter V, novel classifier structure and feature extractor is
proposed to formulate an optimum classifier. The classifier is based upon HMM
and bank of Gabor filter (BGF) network. The simulation results show that the
100% classification accuracy even at lower SNRs for classification of M-QAM
and M-PAM signals. The classifier performance is also compared with well-
124
known existing techniques which shows the supremacy of the proposed
classifier.
Moreover, it is shown by simulations that proposed schemes perform
significantly better than many existing schemes in the literature. Also the new
extracted Gabor features are compared with higher order cummulants and
spectral features and the performance of proposed features are much better
than that of existing features.
6.2 Future Directions
A lot of directions can be explored under the supervision of Gabor
features based classifier structure in application to adaptive communications.
Few of these directions are given as below,
The proposed classifier structure may be extended from single user
ACM to a multi-user AMC. In this regard multi-input multi-output (MIMO)
systems can also be investigated.
Performance of the classifier based on HMM+GA is demonstrated
over a AWGN channel; other channels like Rayleigh fading, Rician Fading and
Nakagami-m fading channels may also be investigated for different channel
parameters like Doppler shift and other fading characteristics.
The Gabor features may be optimized with any of the optimization
techniques. The techniques used for optimization may be nature inspired
algorithms and fuzzy rule based system. The performance of classifier may be
improved by optimizing the Gabor features and classifier structure.
125
The proposed classifier scheme may be extended for the application
of radar signal classifications and images classification. The use of genetic
programming may be used to improve the classification accuracy with Gabor
features set.
126
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