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Jammer Excision Based on ComputationalIntelligence Techniques
Author
Imran Zaka
05-UET/PhD-CASE-CP-13
Supervisor
Syed Ismail ShahProfessor, Department of Electrical and Computer Engineering
DEPARTMENT OF ELECTRICAL AND COMPUTERENGINEERING
CENTRE FOR ADVANCED STUDIES IN ENGINEERINGUNIVERSITY OF ENGINEERING AND TECHNOLOGY
TAXILA
NOVEMBER 2011
To
My parents
iv
Acknowledgments
I am thankful to my supervisor Dr. Syed Ismail Shah for the guidance and support
without which it would not have been possible to complete this research work. I am
also thankful to members of my PhD advisory committee for their worthy advices. I am
grateful to my PhD fellows especially Habib ur Rehman, Imran Shafi, Sajid Bashir and
Adnan Ahmad Khan for the useful discussions and inspiration.
I acknowlege enabling role of the Higher Education Commission (HEC) Islamabad,
Pakistan and appreciate its financial support through “Development of S&T Manpower
through Indigenous PhD (300 Scholars).
Imran Zaka1
2011
1E-mail: [email protected]
v
Abstract
This thesis deals with the removal of jamming signal in Code Division Multiple Access
(CDMA) system. Nature inspired computational intelligence techniques have been stud-
ied and applied for the removal of jamming signal from the corrupted received CDMA
signal. CDMA systems are generally immune from interference however if power of in-
terferer is higher than the immunity provided by processing gain, degradation in Bit
Error Rate (BER) performance is observed. Particle Swarm Optimization, Genetic Al-
gorithm, Artificial Bee Colony and Ant Colony Optimization are the computational in-
telligence techniques being proposed for removal of jammer from received CDMA signal.
These techniques have been optimized for fast convergence and minimum complexity.
Performance comparison with existing techniques has also been provided. Performance
improvement is shown by BER mininmization.
vi
List of Publications
The work presented in this thesis is based on the following publications:
Journal Publications
1. H. Rehman, S. I. Shah, I. Zaka and Jamil Ahmad, “An MBER-BLAST Algorithm
for OFDM-SDMA Communication using Particle Swarm Optimization” in Inter-
national Journal of Communication Systems, Vol 24, Issue 2, pp. 185-201, doi:
10.1002/dac.1149, February 2011.
2. I. Zaka, H. Rehman, S. I. Shah, and J. Ahmad, “GA and PSO based Jammer
Excision in CDMA,” in JCSC 19, No. 1, World Scientific Singapore, pp. 123-138,
Feb. 2010.
3. I. Zaka, H. Rehman, M. Naeem, S. I. Shah, and J. Ahmad, “Jammer Excision
in CDMA Using Particle Swarm Optimization,” in LNCS 5226, Springer-Verlag
Berlin Heidelberg, pp. 601-609, Sep. 2008.
4. H. Rehman, I. Zaka, and S. I. Shah, “MC-IDMA Communication in Frequency
Selective Multipath Fading Channels,” Mehran University Research Journal of
Engineering and Technology, Mehran University of Engineering and Technology,
Jamshoro, Pakistan, Vol. 27, No. 2, pp. 229-242, April, 2008.
5. H. Rehman, I. Zaka, M. Naeem, S. I. Shah, and J. Ahmad, “Minimum Bit Error
Rate Multiuser Detection for OFDM-SDMA Using Particle Swarm Optimization,”
LNCS 4681 Springer-Verlag Berlin Heidelberg, pp. 1247-1256, Aug., 2007.
6. H. Rehman, M. Naeem, I. Zaka, and S. I. Shah, “IDMA Assisted Multicarrier,
Multiantenna Communication In Fading Channels,” WSEAS Trans. Commun.,
vol. 5, pp. 549-555, March, 2006.
vii
Conference Publications
1. H. Rehman, I. Zaka, S. I. Shah and J. Ahmad, “Combined Equalization and
Channel Estimation for MC-IDMA Uplink Transmissions,” in Proc. IEEE Int Con-
ference on Networks and Communication (INCC, 2008 ), LUMS, Lahore Pakistan,
pp. 34-38, May, 2008.
2. H. Rehman, I. Zaka, M. Naeem, and S. I. Shah, “Multicarrier Interleave Division
Multiple Access Communication with Adaptive Subchannel Allocation,” in Proc.
IEEE Int conference on Electrical Engineering (ICEE 2007 ), Lahore Pakistan,
April, 2007.
3. H. Rehman, I. Zaka, M. Naeem, S. I. Shah, and J. Ahmad, “Multicode Multi-
carrier Interleave Division Multiple Access Communication ” in Proc. IEEE Int.
Multitopic Conference (INMIC’06 ), Islamabad, Pakistan, pp. 37-41, Dec., 2006.
4. H. Rehman, M. Naeem, I. Zaka, and S. I. Shah, “Multicarrier Interleave-Division
Multiple Access Communication in Multipath Channels,” in Proc. 5 th WSEAS
Int. Conf. Electronics, Hardware, Wireless and Optical Commun., Madrid, Spain,
pp. 20-25, Feb., 2006.
5. I. Zaka, H. Rehman, M. Azam, and S. I. Shah, “Comparison of Jammer Exci-
sion Techniques ” in Proc. IEEE Int. Multitopic Conference (INMIC’05 ), Karachi
Pakistan, Dec., 2005.
6. H. Rehman, M. Azam, I. Zaka, and S. I. Shah, “Design and Performance of
OFDM-CDMA System in Fading Channels,” in Proc. IEEE Int. Conference on
Emerging Technologies (ICET’05 ), Islamabad Pakistan, pp. 172-177, Sep., 2005.
viii
Contents
Acknowledgments v
Abstract vi
List of Publications vii
List of Figures xiii
List of Tables xv
List of Acronyms xvi
1 Introduction 1
1.1 Types of Jammers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Full band jamming . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.2 Partial band jamming . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.3 Narrowband jamming . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.4 Tone jamming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.5 Swept jamming . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.6 Pulse jamming . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Techniques for Jammer Excision . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Frequency Domain Techniques . . . . . . . . . . . . . . . . . . . . 4
1.2.1.1 Time Frequency Distributions . . . . . . . . . . . . . . . 6
1.2.2 Predictive Techniques . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.3 Code Aided Techniques . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.4 Wiener Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Performance Improvement using Jammer Excision Techniques . . . . . . 12
1.3.1 Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.2 Acquisition Capability . . . . . . . . . . . . . . . . . . . . . . . . 13
ix
1.3.3 Detection of Spread Spectrum Signals . . . . . . . . . . . . . . . . 14
1.4 Estimation of Instantaneous Frequency of Jammer . . . . . . . . . . . . . 14
1.5 Purpose of Research/Motivation . . . . . . . . . . . . . . . . . . . . . . . 15
1.6 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.7 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.8 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2 Code Division Multiple Access 18
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Code Division Multiple Access . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 Multiple Access Capability . . . . . . . . . . . . . . . . . . . . . . 22
2.2.2 Immunity from Narrowband Interference . . . . . . . . . . . . . . 22
2.2.3 Resistance to Multipath Interference . . . . . . . . . . . . . . . . 23
2.2.3.1 RAKE Receiver . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.4 Antijamming Capability . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.5 Synchronous CDMA . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.6 Asynchronous CDMA . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.7 Advantages of Asynchronous over Synchronous CDMA . . . . . . 30
2.2.7.1 Efficient Utilization of Spectrum . . . . . . . . . . . . . 30
2.2.7.2 Flexible PN Code Allocation . . . . . . . . . . . . . . . 30
2.3 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.4 Advantages of CDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.1 Dynamic Power Control . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.2 Soft Handover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.3 Frequency Reuse . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.4.4 Multiuser Detection . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.5 Frequency Hopping CDMA . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
x
3 Nature Inspired Computational Intelligence Techniques 37
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2 Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3 Variants of PSO Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.1 Adaptive PSO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.2 Constricted Version of PSO . . . . . . . . . . . . . . . . . . . . . 43
3.3.3 The Binary PSO . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4 Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4.1 Initialization of the Population . . . . . . . . . . . . . . . . . . . 48
3.4.2 Natural Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4.3 Pairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4.3.1 Random Pairing . . . . . . . . . . . . . . . . . . . . . . 49
3.4.3.2 Rank Weighting Pairing . . . . . . . . . . . . . . . . . . 49
3.4.4 Mating or Cross-over . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4.5 Mutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4.6 Fitness Function . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.4.7 Choice of the Parameters of GA . . . . . . . . . . . . . . . . . . . 52
3.5 Artificial Bee Colony (ABC) Algorithm . . . . . . . . . . . . . . . . . . . 53
3.5.1 Initialization Phase . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.5.2 Employed Bees Phase . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.5.3 Onlooker Bees Phase . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.5.4 Scout Bees Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.6 Ant Colony Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.6.1 Update of Pheromone . . . . . . . . . . . . . . . . . . . . . . . . 62
3.6.2 Continuous Ant Colony Optimization . . . . . . . . . . . . . . . . 62
3.6.3 Convergence of ACO . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.6.4 Applications of ACO . . . . . . . . . . . . . . . . . . . . . . . . . 65
xi
4 Jammer Excision in CDMA based on Computational Intelligence Tech-
niques 66
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3 Wiener Filtering for Jammer Excision in CDMA . . . . . . . . . . . . . . 68
4.4 PSO for Jammer Excision in CDMA . . . . . . . . . . . . . . . . . . . . 70
4.4.1 Optimization of PSO for Jammer Excision . . . . . . . . . . . . . 73
4.5 CGA for Jammer Excision in CDMA . . . . . . . . . . . . . . . . . . . . 74
4.6 ABC for Jammer Excision in CDMA . . . . . . . . . . . . . . . . . . . . 77
4.7 ACO for Jammer Excision in CDMA . . . . . . . . . . . . . . . . . . . . 80
5 Numerical Results and Discussions 83
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.2 Computational Complexity and Implementation Issues . . . . . . . . . . 83
5.3 Simulation and Numerical Results . . . . . . . . . . . . . . . . . . . . . . 84
5.3.1 Comparison with Existing Techniques . . . . . . . . . . . . . . . . 89
5.3.2 Comparison between GA and PSO and ABC . . . . . . . . . . . . 90
5.3.3 Comments on ACO . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6 Conclusions and Directions for Future Research 96
6.1 Directions for Future Research . . . . . . . . . . . . . . . . . . . . . . . . 97
A Gaussian Elimination Matrix Inversion 98
A.1 Gaussian Elimination Algorithm . . . . . . . . . . . . . . . . . . . . . . . 98
A.2 Computational Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Bibliography 100
xii
List of Figures
1.1 Jammer types based on channelized spectrum . . . . . . . . . . . . . . . 2
1.2 Basic structure of a transform domain exciser . . . . . . . . . . . . . . . 4
1.3 Adaptive transform domain interference suppression . . . . . . . . . . . . 5
1.4 Interference suppression using notch filter . . . . . . . . . . . . . . . . . . 6
1.5 Interference suppression using open loop adaptive filter . . . . . . . . . . 7
1.6 TFD of spread spectrum signal with Linear FM chirp Jammer . . . . . . 8
1.7 TFD of spread spectrum signal after excision . . . . . . . . . . . . . . . . 9
1.8 Basic structure of a predictive exciser . . . . . . . . . . . . . . . . . . . . 10
1.9 Structure of a tapped delay line predictor . . . . . . . . . . . . . . . . . . 10
1.10 Basic structure of a radiometer . . . . . . . . . . . . . . . . . . . . . . . 13
1.11 Radiometer with transform domain interference suppression . . . . . . . 14
2.1 Multiple access schemes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Block diagram of DS-CDMA transmitter. . . . . . . . . . . . . . . . . . . 20
2.3 Block diagram of DS-CDMA receiver. . . . . . . . . . . . . . . . . . . . . 21
2.4 Multiple access in CDMA. . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.5 Interference rejection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.6 Principle of RAKE receiver. . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.7 An example of four mutually orthogonal digital signals. . . . . . . . . . . 28
2.8 Principle of CDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.9 Soft handover. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1 Flowchart of PSO algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 Modification of searching point of PSO . . . . . . . . . . . . . . . . . . . 44
3.3 Flowchart of Genetic Algorithm. . . . . . . . . . . . . . . . . . . . . . . . 46
3.4 Flowchart of Artificial Bee Colony algorithm. . . . . . . . . . . . . . . . . 54
3.5 Choice of shortest path by ants . . . . . . . . . . . . . . . . . . . . . . . 60
xiii
3.6 Flowchart of ACO algorithm. . . . . . . . . . . . . . . . . . . . . . . . . 61
3.7 Bit selection of ants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.1 Block diagram of a CDMA System with an Excision Filter. . . . . . . . . 67
4.2 Surface plot of the cost function. . . . . . . . . . . . . . . . . . . . . . . 69
4.3 Flow chart of the PSO algorithm for jammer excision. . . . . . . . . . . . 72
4.4 Flow chart of the GA for jammer excision. . . . . . . . . . . . . . . . . . 76
4.5 Flow chart of the ABC for jammer excision. . . . . . . . . . . . . . . . . 78
4.6 Flow chart of the ACO for jammer excision. . . . . . . . . . . . . . . . . 81
5.1 Bit Error Rate Performance of CDMA system . . . . . . . . . . . . . . . 84
5.2 BER performance vs Interfer power . . . . . . . . . . . . . . . . . . . . . 85
5.3 Convergence of fitness or objective function for different variants of PSO. 86
5.4 Convergence of fitness or objective function for various heuristic algorithms. 87
5.5 Frequency domain view of CDMA signal with jammer. . . . . . . . . . . 88
5.6 Time Frequency domain view of CDMA signal with jammer. . . . . . . . 89
5.7 Filter visualization after 50 iterations. . . . . . . . . . . . . . . . . . . . . 90
5.8 Filter visualization after 250 iterations. . . . . . . . . . . . . . . . . . . . 91
5.9 Filter visualization after 500 iterations. . . . . . . . . . . . . . . . . . . . 92
5.10 TF plot of CDMA signal with chirp jammer . . . . . . . . . . . . . . . . 95
xiv
List of Tables
3.1 Key terms used in PSO. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.1 Inertial Weights for types of PSO . . . . . . . . . . . . . . . . . . . . . . 74
4.2 General Parameters for Simulation of GA . . . . . . . . . . . . . . . . . . 75
4.3 General Parameters for Simulation of ABC . . . . . . . . . . . . . . . . . 77
4.4 General Parameters for Simulation of ACO . . . . . . . . . . . . . . . . . 80
xv
List of Acronyms
ABC Artificial Bee Colony
ACO Ant Colony Optimization
AJ Anti Jamming
APP A Posteriori Probability
BER Bit Error Rate
BPSK Binary Phase Shift Keying
CATV Cable Television
CFIW Constriction Factors Inertial Weight
CDMA Code Division Multiple Access
CG Conjugate Gradient
CGA Continuous Genetic Algorithm
DS Direct Sequence
DSSS Direct Sequence Spread Spectrum
DTTB Digital Television Terrestrial Broadcasting
EA Evolutionary Algorithm
FIR Finite Impulse Response
FDMA Frequency Division Multiple Access
FEC Forward Error Correcting Codes
FFT Fast Fourier Transform
GA Genetic Algorithm
IEEE Institute of Electrical and Electronics Engineering
IF Instantaneous Frequency
IFFT Inverse Fast Fourier Transform
INLP Integer Nonlinear Optimization Problem
ISI Inter Symbol Interference
LAN Local Area Network
xvi
LDIW Linearly Decreasing Inertial Weight
LLR Log Likelihood Ratio
LMS Least Mean Squares
LPI Low Probability of Intercept
MAI Multiple Access Interference
MINLP Mixed-Integer Nonlinear Optimization Problem
ML Maximum Likelihood
MMSE Minimum Mean Square Error
MRC Maximum Ratio Combining
MT-CDMA Multitone-Code Division Multiple Access
MUD Multiuser Detector
NBI Narrowband Interference
NEIW Natural Exponential Inertial Weight
PIC Parallel Interference Cancellation
PN Pseudo Noise
PSO Particle Swarm Optimization
QAM Quadrature Amplitude Modulation
QoS Quality of Service
QPSK Quadrature Phase Shift Keying
RIW Random Inertial Weight
RF Radio Frequency
SD Sphere Detection
SDMA Space Division Multiple Access
SIC Serial Interference Cancellation
SNR Signal to Noise Ratio
SS Spread Spectrum
SSMA Spread Spectrum Multiple Access
STFT Short Time Fourier Transform
xvii
TDD Time Division Duplex
TDMA Time Division Multiple Access
TF Time Frequency
TFD Time Freqency Distribution
ZF Zero Forcing
xviii
Chapter 1
Introduction
Noise in a communication channel can be intentional or un-intentional. Intentional noise
is generally referred to as jamming and un-intentional as interference. Jamming is a
procedure that attempts to block the reception of a desired signal by the intended receiver
[1]. It is usually a signal with large power that cohabits the desired signal in frequency
spectrum, time slot or space with an objective to block or try to block the receiver from
getting desired signal. Jammer excision techniques intend to counter this threat. These
techniques attempt dimensional separation of the jammer. A jammer is analyzed for its
dimensions in terms of time, frequency or space and thus segregated from the desired
signal on this basis. Jammer excision techniques results in some degradation of the
desired signal, for example suppressing jammer frequencies will also lose desired signal
that occupies the same frequency band.
Jammer excision techniques often need to be time varying because of the dynamic
or changing nature of the jamming signal and the channel. A-priori information on the
statistics of the data being processed is needed for designing an optimum filter.
There exist many diverse techniques for jammer excision, which includes notched
filters [2], direct jammer synthesis [3], amplitude domain processing and adaptive anten-
nas. These techniques are classified broadly as adaptive notch filtering, decision feedback,
adaptive analog to digital conversion and non-linear techniques [4, 5].
The methods for suppressing interference/jamming of various types in Direct Sequence
(DS) and Frequency Hopped (FH) spread spectrum systems are discussed in [6] and it has
been concluded that linear and nonlinear filtering methods are particularly effective in
suppressing continuous-time narrowband interference. In [7–9] performance improvement
has been shown by the use of transversal filters in DS spread spectrum (DSSS) system
1
Figure 1.1: Jammer types based on channelized spectrum. (a) and (b) full band jam-ming, (c) contiguous partial band jamming, (d) noncontiguous partial band jamming,(e) narrowband noise jamming, (f) single tone jamming and (g) multi tone jamming.
in the presence of Narrowband Interference (NBI). Various methods have been proposed
for NBI suppression in [10–13].
1.1 Types of Jammers
There are several types of jammers that can be employed against a communication sys-
tem. Jammers are classified according to their distribution of jammer power in fre-
quency [14]. Some of these are illustrated in Figure 1.1 and briefly discussed as follows.
2
1.1.1 Full band jamming
A full band jammer occupies all the bandwidth being used by the affected communication
signal. It is also known as barrage jamming or broadband noise jamming. This type of
jamming directly corrupts the capacity of the channel. In this case jammer power is low
because limited jammer power is spread over a very wide bandwidth. This type of jam-
ming essentially raises the background (thermal) noise level for the receiver thus making
the communication system difficult to operate. It also decreases the range over which
the communication system is effective. It also disrupts the process of synchronization.
1.1.2 Partial band jamming
Partial band jamming puts energy of jamming signal into several channels of spectrum
under utilization but also leaving some of them unaffected. Channels being jammed
sometimes can be and other times can not be adjoining. This type of jamming when
optimally employed is able to perform even better than a full band jammer.
1.1.3 Narrowband jamming
All the energy is put in a single channel by a narrowband jammer.
1.1.4 Tone jamming
Single or multiple jammer tones are put in the spectrum by a tone jammer. A single
tone is put by a single tone jammer also known as a spot jammer. A number of tones
are placed by a multi-tone jammer. A multi-tone jammer is called comb jammer if the
tones placed by it are in adjoining channels.
1.1.5 Swept jamming
A tone sweeps the spectrum of interest in time by a swept jammer. The jamming tone
consists of a single frequency at any given instant of time. Its ever changing frequency
3
SS Receiver
Received Signal
H( )Estimated
Bit
Figure 1.2: Basic structure of a transform domain exciser
is able to jam a wide spectrum within a limited interval of time.
1.1.6 Pulse jamming
A pulse jammer continuously cycle through ‘ON’ and ‘OFF’ states. Pulses with short
width in time have a wider spectrum. It is comparable to partial band jamming.
1.2 Techniques for Jammer Excision
This section introduces jammer excision techniques in brief. The numerous techniques
for suppressing NBI can be classified into three fundamental categories.
1) Frequency Domain Techniques
2) Predictive Techniques
3) Code Aided Techniques
1.2.1 Frequency Domain Techniques
These techniques apply a notch filter however the implementation is unlike processing
in time domain. The signal received is converted from time domain to a new domain,
thus enabling an easy separation of desired and jamming signal. The jamming signal is
removed by a notch filter and then afterwards converted back to time domain. This signal
is then used for additional processing in the next stages of receiver. The general structure
of transform domain technique is shown in Figure 1.2. An adaptive version of transform
4
FourierTransform
MatchedFilter
InverseTransform
Switch orattenuator
EnvelopeDetector
ThresholdDevice
Corruptedinput
OutputData
Figure 1.3: Adaptive transform domain interference suppression
domain method is shown in Figure 1.3. The adaptive method is advantageous in the
situations when jammer do not severely distort the desired signal. In these situations the
excision can cause more degradation than the jammer. Various transforms for excising
jammer have been recommended including Real Time Fourier Transform, Time Frequency
Distributions, Wavelet Transforms, etc.
The insights into the spectral features of a signal are given by their analysis. Fourier
analysis is one of the most widely used tool for it [30]. It converts the time domain signal
into frequency domain in the form of a weighted sum of distinct frequency sinusoids. This
transformation gives the major frequencies constituting the time domain signal. The
received signal is transformed into frequency domain in real time and then its product
with a waveform suppresses the jammer power without significant loss of desired signal
power. Figure 1.4(a) shows the output of Fourier transform of received signal corrupted
by interference. The spectrum of excision filter is shown in Figure 1.4(b). The result
of multiplication of the two spectra is shown in Figure 1.4(c). This type of technique is
very practical for situations in which the jammer varies slowly or it is stationary. Fast
varying and nonstationary jammers require other transformations like Time Frequency
Distributions (TFD) [31].
5
Magnitude
Magnitude
ω
ω
InterferenceSpectrum
SignalSpectrum
H (ω)
ProductSpectrum
ω
Magnitude
(a)
(b)
(c)
Figure 1.4: Interference suppression using notch filter
1.2.1.1 Time Frequency Distributions
Time Frequency Distributions show the characteristics of signals in both frequency and
time domains at the same time [25]. TFD based techniques have great potential for their
usage in applications involving multiple disciplines. Jammers with non stationary char-
acteristics, e.g linear FM chirps and sinusoidal FM signals can be suppressed using TFDs.
Signals with random variations of instantaneous frequency (IF) can also be removed by
it efficiently. Figure 1.5 shows the application of TFD for jamming excision using open
loop adaptive filters. The IF of jammer is identified in the received signal and adaptive
6
Received Signal Bit EstimateAdaptive Notch Filter
Time Frequency Distribution
SS Receiver
Figure 1.5: Interference suppression using open loop adaptive filter
notch filter suppresses the jammer components in it.
Another more powerful technique based on time frequency distributions is Time Fre-
quency Masking. In this method the jammer signals can be localized in the T-F plane
and then removed without severely distorting the original signal [18–22]. First the Time-
Frequency analysis of the signal e.g. Short Time Fourier Transform (STFT) have to be
performed to compute an estimate Ax (n, ω) of the two-dimensional energy distribution
function of the signal. The time frequency masking is achieved by modifying the Ax (n, ω)
with a binary masking matrix M as
Ay (n, ω) = Ax (n, ω)M (n, ω) (1.1)
Where Ay (n, ω) is the two-dimensional energy distribution function of the masked signal.
The entry M (n, ω) is set to zero for an (n, ω) T-F point which corresponds to the
Instantaneous Frequency (IF) of interference and otherwise it is one. The output can be
synthesized by taking inverse transform e.g inverse STFT. TF masking techniques can
be applied using any one of the two possible approaches [23]. One approach first masks
out jammer then synthesize the desired signal which is further used for processing. In
the second approach the desired signal is masked out and jammer signal is synthesized
and afterwards subtracted from the received signal. Both methods are practical and the
7
Figure 1.6: TFD of spread spectrum signal with Linear FM chirp Jammer
choice is made on the ease of synthesis. TF analysis methods include Short Time Fourier
Transform, Wavelet Transform and Lapped Transform.
To illustrate the excision of jammer an example of a spread spectrum signal was taken
with AWGN and chirp jammer. T-F mask was applied for excising chirp jammer. Figure
1.6 shows spectrum of spreaded signal along with AWGN and chirp jammer. Figure
1.7 shows the spectrum after applying the TF Masking. It is evident that TF masking
suppresses the non stationary chirp jammer effectively.
1.2.2 Predictive Techniques
The predictive techniques work in time domain. These techniques take advantage of the
difference in ability to predict a broadband signal and a narrowband signal. In a sum
of broadband and narrowband signals, the narrowband can be predicted accurately and
8
Figure 1.7: TFD of spread spectrum signal after excision
its subtraction from the composite signal removes the narrowband signal. Hence this
method is of great importance for removing narrowband jammers from wideband signals.
The signal after subtraction of predicted signal from the received signal is used for further
processing in the receiver. Figure 1.8 shows the basic structure and process of this type
of techniques.
The predictive techniques can be either linear or non-linear. The most commonly used
linear predictor is finite impulse response (FIR) linear predictor which has a structure
of tapped delay line as shown in the Figure 1.9. In this structure a FIR filter with L
number of taps acts as a one step predictor. The discretized received signal r convolves
with FIR filter having coefficients α. The predicted sample rn is subtracted from the
current sample rn thus giving a residual sample En free from jammer. For a stationary
jammer optimal filter coefficients can be found by Levinson algorithm [33]. This structure
can easily be converted to an adaptable form by finding the coefficients using Least Mean
9
Estimating Filter
Received Signal
SS Receiver Bit Estimate
Figure 1.8: Basic structure of a predictive exciser
Squares (LMS) algorithm. There are also nonlinear predictors both fixed and adaptive
for suppressing the jammer.
D DD D
X X X
+
-+
rn rn-1 rn-2 rn-L
1(n) 2(n) L(n)
rn
En
Figure 1.9: Structure of a tapped delay line predictor
1.2.3 Code Aided Techniques
These techniques show even additional enhancement of performance with the help of
the knowledge of the structure desired signal. Many of these techniques are based on
10
the linear multiuser techniques [32]. Two of the most widely used techniques are Zero
Forcing (ZF) and Minimum Mean Square Error (MMSE). The ZF detector is also known
as decorrelating detector. In this type of detector the soft output of a convetional CDMA
detector is multiplied to the inverse of correlation matrix containing entries of correlations
amongst all code pairs. This operation decouples the various user’s data and eliminates
the Multiple Access Interference (MAI) and narrowband interference. A disadvantage of
ZF detector is noise enhancement. In order to avoid noise enhancement MMSE detector
decouples users data without enhancement of background noise. It uses an inverse of
modified correlation matrix which has been modified to cater the background noise. It
performs better than ZF in the presence of noise but its drawback is that it requires
estimate of received amplitudes. ZF detector has been proposed for NBI suppression
in [34] while MMSE was proposed in [35].
1.2.4 Wiener Filtering
Wiener filter reduces the effect of jamming by comparison with the desired noiseless
signal. Pilot sequence is transmitted for designing of filter and is known at the receiver.
Performance criterion of Wiener filter is minimum Mean Square Error(MSE). The MSE
is defined as:
MSE (w) = E[e2 (n)
]=
1
N
[N∑
k=1
(Pilotdata (n)− Filtereddata (n))2
](1.2)
The Wiener filter is designed to achieve an output close to the desired signal Pilotdata by
finding the optimum filter coefficients that minimize the MSE between the pilot signal
and filtered signal, which can be stated as:
wopt = arg min {MSE (w)} (1.3)
11
The Wiener filter coefficients wopt are given by:
wopt = R−1P (1.4)
Where R is the autocorrelation matrix of the received pilot signal and P, the cross
correlation matrix between the received signal and the pilot signal. Received signal is
filtered using this wopt as FIR filter weights to achive jammer free signal. The output of
the filter is further processed for detection.
1.3 Performance Improvement using Jammer Exci-
sion Techniques
Jammer excision techniques improve the performance of a communication system oper-
ating in a jamming environment. The performance improvement by these techniques is
reflected by the enhanced capacity, lesser error rate and greater acquisition capability
of the communication system. Another important application of these techniques is in
radiometer and intercept receivers. These are discussed in detail as follows.
1.3.1 Capacity
It is possible for narrowband users and DSSS users to coexist in the spectrum thus
enhancing overall capacity of the spectrum if only one of them has been utilizing it. This
coexistence requires either of them not to cause unbearable interference for the other.
Suppression of interference by narrowband users can be achieved using signal processing
techniques ensuring that DSSS users face only its bearable level. This performance
enhancement by suppression in DSSS system allows its users to reduce power thus in
turn providing relief to narrowband users [27]
12
Received Signal Bandpass
Filter IntegratorSquarer
Figure 1.10: Basic structure of a radiometer
1.3.2 Acquisition Capability
The synchronization of CDMA receiver with the transmitter with a preset uncertainty
is known as Code Acquisition. Once synchronization is achieved, it is maintained by the
tracking system that performs fine synchronization for the receiver. The vitally impor-
tant components of receiver include both code acquisition and tracking systems. The
desired signal can not be detected correctly if these systems stop functioning. Jamming
interference impairs the ability of the receiver to synchronize properly or keep itself in
synchronization. Narrowband jamming interference suppression enhances the code ac-
quisition system and helps tracking system keep the receiver in synchronization lock [28].
The two modes of acquisition system are Lock mode and Search mode. Search can be
either performed serially or in parallel. Narrowband suppression performs well for both
types of search. Multiple correlations are carried out concurrently in parallel search mode
while in serial search mode the received signal is correlated with reference waveforms one
after the other. The correlation that gives largest value indicates the synchronization
location. The lock mode follows sometimes directly after the preliminary result while at
other times the preliminary result is validated in search mode repeatedly before entering
it. In lock mode the position is continuously compared with a threshold that determines
whether to remain in lock mode or restart search mode synchronization.
Interference suppression makes the receiver invulnerable to interference during the
acquisition or synchronization. The system performance is enhanced in lock mode by
decreasing false alarm probability. The worst case of interference is a single tone jammer
positioned at transmitter’s carrier frequency [29].
13
Received Signal
Bandpass Filter IntegratorSquarerFourier
Transform X Inverse FourierTransform
H (ω)
Figure 1.11: Radiometer with transform domain interference suppression
1.3.3 Detection of Spread Spectrum Signals
The existence of SS communication is detected by using intercept receivers. A total power
radiometer is generally employed as an intercept receiver. The construction of radiometer
is given in Figure 1.10 and it includes bandpass filter, squarer and an integrator. This
instrument checks the presence of signal in a frequency range by monitoring integrator
output and comparing it with a threshold. A false alarm is generated if a narrowband
user is present in the same band even if no SS is present in the band. This is due to
its working principle of finding total received energy in the band. An excision filter as
shown in Figure 1.11 suppresses the narrowband interference and decrease the possibility
of false alarm. If interference is not suppressed, the system becomes useless [30].
1.4 Estimation of Instantaneous Frequency of Jam-
mer
Some of the methods mentioned in section 1.2 require perfect estimation of the IF of the
jammer to produce optimum results. Any error in its estimation will cause degradation
in signal to noise ratio (SNR). Instantaneous frequency can be estimated using time
frequency distributions [25]. Another method is time varying autoregressive model based
IF estimator [26].
14
1.5 Purpose of Research/Motivation
Computational intelligence techniques based on nature inspired heuristics have been ap-
plied to solve many diverse optimization problems. These problems include network
routing, scheduling and function optimization problems. Nature inspired optimization
algorithms are based on several natural models e.g. Evolutionary computation is based
on the natural process of evolution that includes Evolution Strategies [59], Genetic Pro-
gramming [58], Genetic Algorithms [56] and Evolutionary Programming [55]. The search
for food by ants led to Ant Colony Optimization [54], or social behavior of bird flock
inspired the Particle Swarm Optimization [57]. The universal application of these tech-
niques for solving diverse nature of problems is due to their generality. In order to get
superior outcome from these techniques, problem related alterations and hybrid versions
were evolved as well. This has led to existence of wide range of problems and vast number
of techniques. A researcher in this field therefore handles this multiplicity of problems
and techniques. It is essential to assess the recently developed techniques with variety
of problems. The suitability of variety of techniques is also tested for an optimization
problem. As a result, a model free situation that splits apart the algorithm and problem
realization compliments easy replacement of each of them. In this research, the problem
of optimal jamming excision is solved using generic, flexible and extensible computational
intelligence techniques.
1.6 Outline of the Thesis
Jammer excision can be achieved by designing an excision filter in time domain and then
can be applied on received signal, thus removing jamming signal from the desired signal.
Computational Intelligence techniques are a promising tool for efficient design of excision
filter. Computational Intelligence based techniques have been employed in this thesis
for jammer excision for CDMA system without any prior knowledge of instantaneous
frequency of the jammer. These are nature inspired and population based techniques.
15
These include
• Particle Swarm Optimization
• Continuous Genetic Algorithm
• Artificial Bee Colony
• Ant Colony Optimization
These techniques are introduced and discussed in more details in the subsequent chapters.
These techniques have been adapted and modified for optimal excision in this thesis. A
new variant of PSO is also proposed that outperforms existing ones. Optimal values of
control parameters for this application have been found out by experimentation. The
performance of designed filter is checked for Bit Error Rate of CDMA system and the
techniques are evaluated for their fast convergence.
1.7 Summary of Contributions
The author’s contribution in the field of jammer excision using computational intelligence
techniques is summarized as follows.
• Optimized Jammer Excision based on non-conventional Computational Intelligence
techniques has been presented for the first time according to the best of author’s
knowledge.
• Several Computional Intelligence techniques i.e. Particle Swarm optimization (PSO),
Genetic Algorithm (GA), Artificial Bee Colony (ABC) and Ant Colony Optimiza-
tion (ACO) have been applied for the first time to optimize a real-life jammer
excision problem.
• These techniques were optimized for the jammer excision by the tuning and choice
of parameter values.
16
• The proposed excision techniques have reasonably low complexity overhead, while
keeping a near optimal performance.
• The above research work has been presented in International Conference on In-
telligent Computing (ICIC 2008) and IEEE International Multitopic Conference
(INMIC 2005)
• Most of the work has been published in journals of international repute such as
Lecture Notes in Computer Science (LNCS), 5226, Springer-Verlag Berlin Heidel-
berg, pp. 601-609, 2008 and Journal of Circuits, Systems and Computers(JCSC)
vol. 19, No.1 (2010) pp. 123-138.
1.8 Organization of Thesis
The thesis is organized as follows. Initial part of the thesis deals with the basic concepts
of wireless communications and jammer excision. Chapter 2 discusses Code Division
Multiple Access Communication System. Nature inspired computational intelligence
techniques are discussed in chapter 3. Jammer excision using computational intelligence
techniques is given in chapter 4. Chapter 5 presents numerical results and discussions.
Finally chapter 6 concludes the thesis with recommended future work.
17
Chapter 2
Code Division Multiple Access
2.1 Introduction
Wireless communication is passing through its fastest growth of developments and chal-
lenges in the history. The desire for enormous increase in throughput and bandwidth
efficiency is also increasing. The greatest current challenge for future wireless commu-
nication systems is therefore to provide broadband mobile data access with a quality of
service (QoS) as high as possible. The key role in mobile radio techniques is played by
the effective bandwidth availability and only a limited bandwidth for data transmission
is available to each wireless service. It means that spectrum is a very scarce commodity
and it should be exploited as efficiently as possible. The desired increase in communica-
tion speed requires smarter and more complicated communication algorithms that can
exploit the available resources through various multiple access methods, as efficiently as
possible. At present following are the available means.
• Time
• Frequency
• Code
• Space
The first three resources above find applications in Time Division Multiple Access
(TDMA), Frequency Division Multiple Access (FDMA) and Code Division Multiple Ac-
cess (CDMA) respectively, even in combination, in existing systems. The resource of
space is now becoming popular for multiple access communication as Space Division
18
frequency
FDMA
timetimetime
frequencyfrequency
TDMA CDMA
Figure 2.1: Multiple access schemes.
Multiple Access (SDMA). It is accessed through the use of multiple antennas both on
the transmitter and the receiving side.
A part of the spectrum called channel is allocated to a pair of communicators for all
of the time in FDMA. All or at least a large of chunk of spectrum is allocated to a pair
of communicator for a part of the time known as slot in TDMA. CDMA is unique in
allotting whole spectrum for the entire time to every user. CDMA uses orthogonal codes
to distinguish users. Figure 2.1 shows pictorial view of all the schemes.
2.2 Code Division Multiple Access
Code Division Multiple Access is an emerging commercial communication technique. Its
origins are in the military and navigation systems. It provides a secure digital com-
munications that is now being used extensively for industrial and commercial purposes.
Spread spectrum communication will touch everybody’s life in the coming years. Appli-
cations for commercial spread spectrum range from wireless local area networks (LANs),
palmtop computers, radio modem devices for warehousing, integrated bar code scanner,
digital cellular telephone communications, city, area, state or country wide networks for
19
Figure 2.2: Block diagram of DS-CDMA transmitter.
passing faxes, computer data, e-mail, or multimedia data.
A type of CDMA known as time hopping spread spectrum multiple access [36] carries
asynchronous signals over a shared medium. CDMA was introduced in 1949 [36] that
exhibited interference averaging effect. De Rosa-Rogoff proposed in 1950 another sys-
tem called Direct Sequence Spectrum-Spectrum (DS-SS) with the concept of processing
gain. The cellular application of spectrum-spectrum WAN was suggested by Cooper
and Nettleton in 1978 [38]. Qualcomm investigated DS-CDMA technique which finally
commercialized the cellular Spectrum-Spectrum communication in the form of narrow
band CDMA IS-95 standard in July 1993 which started commercial operation in 1996.
Wideband CDMA technique have been studied during 1990s throughout the world
and several trial systems have been developed [39] having bandwidths of 5 MHz or more.
More multipaths can be resolved using the bandwidth of 5 MHz than a narrow bandwidth
thus enhancing performance and increasing diversity. Higher data rates can be supported
more efficiently by even wider bandwidths.
In CDMA, each user is allocated a distinct code for spreading its data. The receiver
decodes the received signal after reception and recovers the original data. This is possible
because the cross correlations between the code of desired user and the codes of other
20
Datademodulator
Codesynchronization/
tracking
CarrierGeneration
CodeGeneration
DespreadingData
Figure 2.3: Block diagram of DS-CDMA receiver.
users are small. Because the transmission bandwidth of the code is substantially greater
than the information bandwidth to achieve this particular operational advantage. The
encoded signal enlarges the spectrum of the signal and is therefore known as spread
spectrum modulation. The resulting signal is also called a spread-spectrum signal and
CDMA is often denoted as spread-spectrum multiple access (SSMA). These signals are
intentionally made to be much wider band than the information signal to make them
more noise-like. Being noise like, it is hard for an opponent to intercept or demodulate
the spread spectrum signals. The multiple access capability of CDMA is due to this
spectral spreading of the transmitted signal. The basic structure of a CDMA transmitter
is shown in Figure 2.2. If the spreading code have a duration Tc (also known as chip
duration), then
L =Tb
Tc
(2.1)
where Tb is the duration of the the transmitted bit (also known as bit duration of the
digital signal) and the bandwidth expansion factor L is also known as processing gain.
The bandwidth Wt of digitally transmitted signal is assumed to be limited within (1/Tb).
Note that Wt is equivalent to (1/Tc), and the data rate R is equivalent to (1/Tb), (2.1)
can also be written as
L =Wt
Wi
21
Block diagram of CDMA receiver is shown in Figure 2.3. The desired user code is
generated at the receiver, which is synchronized with the transmitter. The received
signal is correlated with this locally generated code for obtaining the information from
the received signal. The receivers necessarily require the desired users spreading code for
despreading received data.
While other communication techniques try to minimize the transmission bandwidth,
CDMA enlarges the transmission bandwidth. A number of properties of CDMA signals
differ from those of narrow band signals. Some of these are the following
2.2.1 Multiple Access Capability
Every user in CDMA utilizes same bandwidth all of the time, yet it has the ability to
discriminate each user’s signal by its distinct code. The only constraint on user codes for
distinguishing is to have low correlation with each other. The despreading operation of
the received signal with the desired user’s code only despreads the desired user’s signal
while other users signals remain spreaded. Thus the power of the desired user will be
larger than the power of the other interfering users and the desired user’s signal can be
extracted provided there are not too many users. Figure 2.4 shows an example which
shows signals of two CDMA users before and after spreading. Composite signal of both
users is shown in Figure 2.4(e) and Figure 2.4(f) shows the despreaded signal using code
of user 1.
2.2.2 Immunity from Narrowband Interference
Narrowband interference having energy below a threshold power level do not seriously
affect CDMA communication. As only a small fraction of spread spectrum signal is af-
fected by the narrowband signal, therefore it can be removed using a notch filter with
negligible loss to desired signal. The spreading operation of the narrow band signal with
the code signal spreads the narrow band signal thereby reducing the power of the interfer-
ence signal in the interference bandwidth as shown in Figure 2.5. The receiver despreads
22
1
2
1
2
1 & 2
2
1
(a)
(b)
(c)
(d)
(e)
(f)
Figure 2.4: Multiple access in CDMA.
the SS signal while spreading the interfering signal. This results in a strong despread
signal with interference reduced to a background noise. Forward Error Correcting Coding
(FEC) and interleaving can be used to assist in recovering this lost data.
2.2.3 Resistance to Multipath Interference
There is generally no direct line-of-sight path between transmitter and the receiver and
several time delayed and attenuated versions of the transmitted signal reach the receiver
23
s
i
(a)
i
s
(b)
Figure 2.5: Interference rejection.
as a consequence of reflections, scattering and diffractions off the buildings, hills and the
other obstacles in the environment. These signals, called multipath waves are added at
the receiver with different phases as a result of propagation delays and provide an effective
combined signal which can vary widely in amplitude and phase. Due to multipath effects,
the receiver goes on receiving copies of the transmitted signal and there is a sufficient time
difference between first and the last copy. This produces ISI in the received signal relative
to the transmitted signal. CDMA signals are designed withstand effects of multipath
fading. Multipath causes fading only in a fraction of the very wide bandwidth being
utilized by the SS signal. The loss caused by it is very minimal and recoverable similar
to the loss by narrowband interferer. The immunity of CDMA to multipath interference
is due to property of having very low correlation of the original pseudorandom code with
its delayed version. Even a delay of one chip duration induced by multipath channel
appears uncorrelated hence it is not taken into account.
Some CDMA receiving sets have the ability to exploit multipath components of the
signal by using a RAKE receiver. A simple receiver has only one correlator which is
tuned to the delay of strongest component of signal. On the other hand RAKE receiver
has a number of correlators that are tuned to different delays. These correlators combine
24
their outputs for improved performance.
2.2.3.1 RAKE Receiver
The CDMA receiver can resolve multipath signals that are delayed by more than a single
chip duration. TDMA and FDMA are not immune from multipath fading because these
are narrowband systems unable to resolve different multipath signals received. Equaliza-
tion is employed to mitigate effects of multipath by TDMA and FDMA. CDMA being
wideband takes advantage of multipath signals by combining their energy. Multiple cor-
relators (fingers) exist in a RAKE receiver which keep searching for various multipath
signals. Each correlator after despreading and demodulating a different multipath com-
bine together using for example, maximal ratio combining (MRC) to make the signal
stronger. Because the received multipath signals are faded independently from each
other, the performance is improved. Figure 2.6 illustrates the principle of RAKE re-
ceiver. Binary data is spread by the spreading code and is transmitted through a three
path channel after modulation. The multipath channel is modeled by a delay line, each
path having delays D1, D2, D3 and a1, a2, a3 corresponding attenuations. The composite
signal is demodulated at the receiver and is correlated by three fingers of the RAKE. In
each finger the code is time-aligned with the delay of the multipath signal. Each signal
is weighted by the complex conjugate path gain and after despreading the signals are
combined using MRC.
2.2.4 Antijamming Capability
CDMA has antijamming capability i.e. it is harder to jam than the narrowband signals.
Due to these features, the military has used SS for so many years. These applications
including guidance and communication systems. Although in recent times SS has mi-
grated to commercial communications from the military applications. The SS signals are
collected onto their original frequency at the receiver by despreading operation.
SS uses a much broader bandwidth than actually required for a signal in order to have
25
Binary Data Wideband
modulator
Code Generation
x
Carrier Generation
D1
D2
D3
+
a1
a2
a3
+
a1
a2
a3
x
x
x
C(t-D1)
C(t-D2)
C(t-D3)
RAKEReceiver
Demod
Figure 2.6: Principle of RAKE receiver.
improved signal to noise ratio. It uses spreading codes that give the signals after spreading
the properties of a broadband noise. These properties provide the communication a
feature known as Low Probability of Intercept (LPI). It is not possible by conventional
methods of narrowband communications to detect an ongoing SS communication.
Spread spectrum signal has energy spread in a wide frequency band with having low
noise like spectral density. Spread spectrum system is not affected by the presence of a
narrowband signal as the correlation receiver performs integration over a much broader
bandwidth. A narrowband interference signal is spread out by the correlator over the
entire bandwidth during detection. SNR at the receiver input is a factor to determine the
occurrence of interference. An interference threshold level exists for every spread spec-
trum system beyond which it is not possible to communicate. This level is associated
with the systems processing gain. Ratio of bandwidth after spreading to the bandwidth
of users signal before spreading is the processing gain. The interference rejection capa-
bility of a spread spectrum system is defined by its jamming margin. Following are the
parameters for calculating it.
S = received power for the desired signal in W.
J= received power for undesired signals in W (jamming, other multiple access users,
multipath, etc.).
Eb=received energy per bit for the desired signal.
26
N0=equivalent noise spectral power density in W/Hz.
Then the ratio of the equivalent noise power J to S is
J
S=N0W
Eb/Tb
=W/R
Eb/N0
(2.2)
When the value of Eb/N0 is set to that required for acceptable performance of the com-
munications system, then the ratio J/S bears the interpretation of a jamming margin.
Spread spectrum signals are resistant to jamming and interception by un-intended
user. Its signal can not be exploited especially in military applications where a non
network member can not listen or use information. Another feature is that it is hard to
spoof in which false traffic is introduced in a network. Security of the communication
is another feature that ensures secrecy and privacy. More than one levels of secrecy is
available using encryption without any significant increase in complexity. These features
are not required in routine applications or needs of a LAN however these are important
concepts.
2.2.5 Synchronous CDMA
Data strings are represented by mutually orthogonal vectors in synchronous CDMA.
The sum of the product of corresponding components of two vectors is called a dot
product. Two vectors are orthogonal if they satisfy the condition that their dot product
is zero. Two real-valued waveforms x (t) and y (t) are said to be orthogonal if their
cross-correlation Rxy (0) over Tb is zero, where
Rxy (0) =
∫ T
0
x (t) y (t) dt (2.3)
=
∫ Tb
0
am (t)Cm (t) an (t)Cn (t) dt (2.4)
= 0 (2.5)
27
Figure 2.7: An example of four mutually orthogonal digital signals.
where Cm (t) and Cn (t) are spreading codes assigned to users m and n respectively.
In discrete time, the two sequences x (t) and y (t) are orthogonal if their cross-product
Rxy (0) is zero. The cross product is defined as
Rxy = xTy =N∑
i=0
xiyi (2.6)
= amCm (i) anCn (i) (2.7)
= 0 (2.8)
Figure 2.7 shows few orthogonal signals.
28
2.2.6 Asynchronous CDMA
Two users were multiplexed using orthogonal Walsh codes in the preceding example for a
synchronous system. This multiplexing technique is known as Code Division Multiplexing
(CDM). All the users are synchronized so that their transmitted signals arrive at the same
time at the receiver. This method is employed for the link from base station to the mobile
stations because the coordinated transmissions are only possible from here.
However synchronization of mobile to base link is not perfectly possible due to the
motion of handset. It requires a special method to handle it. As the code sequences start
randomly it is not achievable mathematically to have mutually orthogonal code sequences
with different starting points. Asynchronous CDMA therefore employs distinct code
sequence for each user. Encoding and decoding is similar to the synchronous CDMA. The
codes used in Asynchronous CDMA are statistically uncorrelated but still summation of
many code sequences produce Multiple Access Interference (MAI). Central limit theorem
is applicable to approximate MAI as Gaussian noise when large number of simultaneous
users exists. MAI increases proportionally with the number of users if all of them are
received with equal signal strength. In this manner the desired signal will be slightly
impaired by the noise due to signals of other users when compared with synchronous
CDMA.
All the variants of CDMA employ processing gain to distinguish and recover signal
of desired user in the presence of signals of other users and interferers. At the receiver
the de-spreading only recovers the signal that is encoded with same PN code whereas
the signals encoded with different code become a wideband noise. The codes are either
unique or part of the same PN sequence with different offsets in time.
The control of transmitted signal’s power is very critical in CDMA to minimize MAI
produced by all users. Use of orthogonal signaling schemes in TDMA, FDMA and Syn-
chronous CDMA systems rejects any powerful signal. Asynchronous CDMA systems can
only partially reject the undesired signals. In the presence of strong interfering signals
of other users, the detection of desired users signal becomes impossible. It is therefore
29
necessary in Asynchronous CDMA to receive all signals with matching power. This issue
is known as Near Far Problem. It is addressed using a closed loop power control strategy
at base station to monitor and control transmit power of each of the mobile stations.
The privacy of sent data is ensured in asynchronous CDMA by spreading it with the
help of PN code. The spreading gives the modulated signal properties of noise. It is not
possible to decode spread spectrum signal by any receiver without having the actual code
that was used for encoding it. Unlike narrowband communications CDMA is immune
to jamming. The jamming signal can either corrupt the entire bandwidth or a part of
signal only with its limited power.
2.2.7 Advantages of Asynchronous over Synchronous CDMA
2.2.7.1 Efficient Utilization of Spectrum
The key benefit of Asynchronous CDMA in contrast to FDMA, Synchronous CDMA and
TDMA is its efficient use of spectrum in applications of mobile telephony. In TDMA
based systems it is ensured that transmission times of all users are synchronized to avoid
interference and received in respective time slot. Controlling synchronization perfectly
in a mobile scenario is not possible without allowing a guard time in each slot. This
additional time slot decreases the chance of interference by other users with a cost of
reduced spectral efficiency. FDMA systems in the same way uses guard bands inserted
between neighboring channels. The fast moving users in FDMA experience Doppler
effect due to which the frequency of the user may change and cause interference for the
neighboring channel’s user. Adjacent channels will be farther apart by using guard band
to avoid interference while consuming more spectral resource.
2.2.7.2 Flexible PN Code Allocation
There is a benefit of flexible allocation of PN codes to simultaneous users in asynchronous
CDMA system. There are limitations of frequency slots, time slots and orthogonal codes
30
in case of FDMA, TDMA and Synchronous CDMA respectively. These limitations make
the utilization of these systems under bursty traffic conditions. Asynchronous CDMA can
support any number of users only limited by the bit error rate. Bit error rate is increased
as the users increase due to rise in interference level. Mobile telephone systems have an
uneven load of calls and at times it has to face sharp increase in load. Under these spikes
of load asynchronous CDMA has to pay in terms of performance that varies randomly.
The mean performance is determined by the number of users and the utilization factor.
The users with higher usage get a constant probability of bit error while occasional users
experience a random rate.
The asynchronous CDMA suits well for a large number of users that have very less
data to send after unequal gaps of time. Under such bursty conditions of data traffic
FDMA, synchronous CDMA and TDMA can not give improved performance due to their
limitations of frequency channels, orthogonal codes and time slots respectively. These
limited resources need to be allocated and deallocated quite frequently. In contrast
asynchronous CDMA transmitter come on the air only when required otherwise they
remain off the air retaining the same code.
2.3 System Model
Consider CDMA system for uplink transmission shown in Figure 2.8. There are M active
users, each transmitting Binary Phase Shift Keying (BPSK) symbols. At the transmitting
side, say mth user bits are spread by a spreading code Cm so that the symbol is now
represented by a sequence of chips am.
At the receiver, the received signal is the result of the summation of the M spread
messages. Originally transmitted messages are recovered by multiplying the received
signal r by corresponding orthogonal codes. After multiplication, signal power is added
over a time interval of Tb, then integrators output is used to determine whether the bit
is -1 or +1. A positive output of integrator results in a decision of +1 and -1 is decided if
31
r
s1 h1
+sM
aM
na1 Enc
hMEnc
a1^
aM^
x
x
C1
CM
x
C1
x
CM
Figure 2.8: Principle of CDMA. M users are sending M separate bits, a1,a2,...,aM , si-multaneously in the same frequency band and at the same time. Through the use oforthogonal codes C1,C2,..., CM respectively, the receiver recovers the bits perfectly.
integrators output is negative. In an ideal case, the recovered messages a1 (t) and a2 (t)
match perfectly the original baseband messages a1 and a2.
When a code sequence is modulated over a carrier, it generates a signal which is
centered at the carrier frequency and having a frequency spectrum of [sin (x) /x]2. The
width of main lobe and side lobes is dependent on the modulating code’s clock speed.
The spectrum of DS-SS signal varies to some extent due to the modulated data and the
carrier.
The digital data to be encoded employs a local PN code for transmission in a Direct
Sequence (DS) spread spectrum system. The rate of this code is a lot more than the
rate of the data. Encoding operation involves exclusive OR operation between binary
data and the PN. This encoded output can further be secured using a scrambler. The
modulation used is double sideband suppressed carrier which is analogous to binary phase
shift keying (BPSK) which is most common modulation used for SS modulation.
At the receiver PN code is generated which is synchronized with that of transmitter.
This locally generated PN is used for decoding or correlating the required users signal
out of mixture of all users signal. This correlator is a special type of matched filter that
gives output for a signal encoded with the same PN code. If local PN code is changed
the correlator will be able to recover signal encoded by that PN. As the noises and
32
interferences have no correlation so these are ignored or suppressed by this correlator.
Component of received signal which is encoded with same PN is only decoded by it.
2.4 Advantages of CDMA
The advantages of CDMA are discussed as follows.
2.4.1 Dynamic Power Control
The limitation in CDMA system is due to interference. Every user is using the same
frequency that creates interference which degrades the call quality and system capacity.
Each user must transmit with minimum power so as to reduce interference while at the
same time maintaining the requisite Eb/N0. This ensures that the quality of service is
satisfactory. Eb/N0 is kept to lowest value for all users in order to achieve maximum
capacity. A mobile station receives constantly varying signal due to many factors that
includes interference, fading (both slow and fast), shadowing. etc. Dynamic power
control is used in the system to transmit with a limited power by both base station and
mobile station to keep the quality of the link under these changing conditions. Power
control also extends the life of battery and power amplifiers of base station.
2.4.2 Soft Handover
When a user travels from one cell to another during a call, the call is also transferred to
the new cell and it is known as a Handover. Conventionally in a handover the connection
with current cell is broken and reconnected to the new one, termed as hard handover.
Hard handover is also called break-before-make. Same frequency is used in all the cells of
CDMA system thus providing an opportunity to connect to new cell prior to disconnection
from current cell, this method is called soft handover or make-before-break. Shaded region
in Figure 2.9 shows a 3-way soft handover scenario. Power requirements of soft handover
are also less that helps in increasing capacity due to reduced interference.
33
Figure 2.9: Soft handover.
2.4.3 Frequency Reuse
The multiple access schemes like FDMA and TDMA use frequency planning to reuse
frequency being used at one cell in the system at other cell sites. The planning guaran-
tees that the various cells using the same frequency do not create interference for each
other. However CDMA uses same frequency in all the cells because the codes provide the
necessary channelization. This removes the overhead of frequency planning in CDMA
system. Instead of frequency planning the codes have to be planned so that neighboring
cells have no correlation between their codes or they are completely orthogonal.
Soft handovers are possible in CDMA systems as adjoining cells are also making use
of same frequencies. When a mobile station is simultaneously communicating with more
than one cells base station it is known as soft handover. Hard handovers are used in
other cellular systems which is different from soft handover. A mobile user experiences
sudden variation of signal strength. On the other hand, soft handover used in CDMA is
unnoticeable by user and offers better quality of signal.
34
2.4.4 Multiuser Detection
Multiuser or joint detection and decoding techniques (known as multiuser detection or
MUD) deal with demodulation of mutually interfering digital signals, which can improve
the capacity of the systems. Optimum multiuser detector refers to maximum likelihood
(ML) detector as suggested by Verdu [41]. The complexity of optimum multiuser detector
grows exponentially with the number of users. Several sub-optimal detectors both linear
and non-linear have been developed by researchers in order to overcome ML detector’s
complexity. Linear techniques are the decorrelating detector [42], the Minimum Mean
Square (MMSE) detector [43] while nonlinear techniques are the successive interference
cancellation (SIC) [44], parallel interference cancellation (PIC) [45] and the decision
feedback detector [46]. Another branch of multiuser detection scheme, referred to as
sphere detection (SD), has been proposed which is capable of achieving ML performance
at lower complexity [47, 48]. Furthermore the performance can be improved by using
forward error correcting codes such as turbo codes [49]. The success of turbo codes
inspired the researchers to study iterative multiuser detection [50–53].
2.5 Frequency Hopping CDMA
The simplest spread spectrum modulation according to usage is the frequency hopping.
All that is needed to convert a radio to frequency hopping radio is to have frequency
synthesizer controlled digitally. The transmission or reception frequencies are selected
by a PN code generator. Typically a band of frequencies is used for uniform hopping
of frequency. If the frequencies to be skipped are known before hand to the receiver
and the transmitter then uniform hopping over a band is not necessarily required. The
design of frequency hopped system can utilize narrowband radio methods using either
of the analog or digital modulation. PN code generator at the receiver is synchronized
for de-hopping. This synchronized PN code generator drives the frequency synthesizer
of local oscillator.
35
2.6 Conclusions
The technical challenges of progressing wireless communication are significant. The new
opportunities created by this new CDMA technology are also significant. We’ve discussed
here some of the very basic principles in spread spectrum.
36
Chapter 3
Nature Inspired Computational
Intelligence Techniques
3.1 Introduction
The growing advancements in computational power gave boost to the scientist’s and
engineer’s desire to explore optimum solutions for complicated filtering problems. The
normally employed brute force design methods are ever increasingly being substituted
by the modern optimization techniques. Numerical methods are able to be used for
perfect and efficient characterization of comparitive superiority of a particular design has
thrilled the engineers to apply stochastic global evolutionary optimizers. Some of these
techniques have been able to arouse much interest including Genetic Algorithm (GA) ,
Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO) and Artificial Bee
Colony (ABC).
This chapter describes in brief the basic properties of PSO, GA, ACO and ABC
algorithms. GA has been founded on the natural evolution process which is an iterative
process and Darwinian evolution tries to evolve an organism with desirable features with
slow steps of a gradual process. GAs are well suited for combinatorial problems. Birds
and fishes move around in search of food, these living creatures achieve this objective
with a compound fusion of knowledge and random elements. PSO method with real
values is well suited for continuous domain problems nevertheless, employing a particular
representation allows PSO to solve binary problems also. Binary version of PSO is based
on continuous probability processes with certain thresholds. ACO algorithm is based on
social activities of ants in their colony. These have an ordered social organization which
37
enables the colony to carry out complex tasks which a single ant can never achieve.
ACO has been found very suitable for optimal resource allocation and combinatorial
optimization. ABC is derived from the ability of bees in a colony to find food source
positions containing high amounts of nectar. ABC can be employed to solve numerical
optimization problems of both constrained and unconstrained types.
3.2 Particle Swarm Optimization
Particle swarm optimization is a great optimization technique described by Eberhart and
Kennedy [60,61] predicated on the motion and learning ability of swarms. It employs the
rules of social communication inside a swarm to solve complex problems by constituting
a swarm of agents or particles that explore the whole search space in quest of the best
solution. In an N-dimensional space each particle is considered as a point that sets its
“flying” corresponding to its own flying experience in addition to the flying experience of
other particles. Every particle continues to record its position in the search space along
with the position which is best solution (fitness) found out until that time by it. This
is called personal best or pbest. There is also another position whose record is kept, is
the best value obtained until that time by any particle in the swarm. It is called gbest.
Main theme of PSO is to accelerate each particle in the direction of its pbest and the
gbest positions and randomly changing acceleration weights in every iteration. In each
iteration these two best positions are found out and every particle calculates its velocity
and position using following equations
vi+1s = φvi
s + α1γ1s
(ps − xi
s
)+ α2γ2s
(g − xi
s
)(3.1)
xi+1s = xi
s + vi+1s (3.2)
where s is particle index, i is the iteration index, v is the velocity of the particle, x is
the position of the particle, p is the pbest found by the particle, g is the gbest, and γ1
38
and γ2 are random numbers in the interval [0,1]. Two independent random numbers are
used to stochastically vary the relative pull of pbest and gbest. In (3.1), α1 and α2 are
the acceleration constants used to scale the contribution of cognitive and social elements
respectively and these can also be termed as learning factors and φ is the inertia function.
Table 3.1 summarizes the key terms used in the PSO algorithm.
PSO is dynamic, easily understandable, easy to implement and has low computational
overhead. The algorithm is very simple. Few lines of code are used iteratively. It is
faster by an order of magnitude than other Evolutionary Algorithms (EAs). It resists
getting stuck in a local optima. PSO has been applied as an engineering methodology in
many diverse fields i.e. determination of state of charge of batteries in a hybrid vehicle,
human performance assessment and diagnosis of human tremor. PSO also gives proof
of hypothetical aspects of mind, perception and intelligence. Ever since its discovery in
1995 PSO has sustained phases of advancement and alterations. It has been analyzed
and modified by many researchers for solving problems in various fields of science and
technology [63–67]. The earliest versions of PSO were continuous. Later on, a binary
version of PSO was formulated by Kennedy and Eberhart [66]. The particle position in
binary PSO is not real valued rather it is either a binary 0 or 1.
Researchers and scientists have simulated a variety of versions of the movement of
individual in a swarm i.e. a fish school or a flock of birds. Particularly, Heppner [70]
and Reynolds [71] have shown simulations of flock of birds. Heppner being a zoologist
was fascinated by the birds that flock in complete harmony while they suddenly alter
direction, scatter and regroup. Reynolds was attracted by the beauty of dance routine
type movement of bird flocks. These two scientists knew that the local processes modeled
by cellular automata have the key to predict or understand bird flock movement. In both
these models the key parameter was the distance between individuals and synchronous
flocking manners were thought to depend on keeping these distances between neighbors
within an optimum range. It seems reasonable to suppose all the animals forming a swarm
follow the same kind of laws for their social behavior. A sociobiologist E. O. Wilson has
39
Table 3.1: Key terms used in PSO.Term Explanationfitness A number representing goodness of a given solutionSwarm The entire collection of agents or particlesPosition Agent’s coordinates which represent solution to the problempbest Best fitness returned for a specific particlegbest Best fitness returned for the entire systemv Velocity of the particlex Position of the particleφ Inertia coefficientγ1 Random number ε[0, 1]γ2 Random number ε[0, 1]
written, in reference to fish schooling, “In theory at least, individual members of the
school can profit from the discoveries and previous experience of all other members of
the school during the search for food. This advantage can become decisive, outweighing
the disadvantages of competition for food items, whenever the resource is unpredictably
distributed in patches” [72]. It is concluded that an evolutionary advantage is achieved
by the information sharing between individuals. PSO has been developed using this
conclusion.
The modeling of human social behavior was the purpose behind this simulation, al-
though the bird flocking and fish schooling differ a lot. The biggest disparity is its
non-representational model. The motion of birds and fish is optimized for seeking food,
evading rapacious creatures and finding mates. Humans can change their bodily mo-
tion along with mental and observational parameters. Humans unlike some other social
creatures do not move in harmony with a group but they change their viewpoint and
thoughts to match that of their society. Another difference is the collision in computer
based simulation. Two creatures can not have same position unless they collide but
two humans may have similar thoughts and behavior. Humans are capable of avoiding
physical collisions and move around N-dimensional psychological space. Steering in the
psychological multidimensional space needs years of experience.
40
Initialize population with random position
(x) and velocity (v) vectors
For Each Agent
Evaluate Fitness
If fitness (x) > fitness (gbest)gbest = x
If fitness (x) > fitness (pbest)pbest = x Update Velocity
Update Position
Next Agent
gbest = parameters of best solution
Figure 3.1: Flowchart of PSO algorithm.
3.3 Variants of PSO Algorithm
There are different versions of PSO algorithms, but they all can be seen from an infor-
mational point of view: what kind of information each particle has access to, and how it
uses it. To illustrate this, here two versions, a constricted one and an adaptive one, are
analyzed in terms of probability to find a solution.
3.3.1 Adaptive PSO
Equations (3.1) and (3.2) describe velocity and position update equations including in-
ertia weight φ. Each particle calculates new velocity based on its previous velocity, its
personal best (pbest), global best (gbest) positions and update its position using the new
velocity in the solution space. The velocity is applied for a given time-step, and the par-
41
ticle moves to the next position. Figure 3.2 shows a graphical view of the modification
of searching point of a particle. The parameter φ is very important in determining the
type of trajectory the particle travels. Global search takes place when inertia weight
has a large value whereas local search is performed for a small value of inertia weight.
Suitable pick of inertia weight gives the equilibrium among the local and global search
ability of the swarm. If the value of φ is kept at zero the particle has velocity only due
to the positions pbest and gbest. Thus having no inertia the velocity of the particle can be
changed immediately if its motion is directed away from the known best positions. When
the value of inertia weight is kept low it allows the particle to search locally. Conversely
if the φ has a high value the chance of change in velocity of the particle is very low (parti-
cle keeps its actual path due to its high inertia) although when superior values of fitness
are available. Consequently inertia weight’s high value enhances global searching ability.
Selection of parameters affects the algorithm for its speed of convergence and ability of
finding the optimum. However the values are unique for each type of problem. Methods
based upon adaptive parameters have also been used [81, 82]. A class of these methods
is called deterministic which employ deterministic laws of changing values of parameters
i.e. when iterations increase the inertia weight decreases linearly [63, 81]. Experimental
results suggest it better to initially set the inertia to a large value and then gradually
decrease its value to obtain the refined solution [63]. Also, in [78, 79] it is proposed and
observed that decreasing the value of inertia as the iterations progress will allow global
exploration in the beginning and local exploration near the termination of algorithm.
Another class is that of adaptive methods in which the values of parameters are changed
on the basis of feedback information. An example of such a method is fuzzy adaptive
inertia weight [82]. In [84], an algorithm is developed that adapts swarm instead of pa-
rameters on individual level. The worst performing particles are substituted with fresh
particles so that all the particles contribute their due share in achieving their swarm’s
objective.
In this method choice of values of social and cognitive factors is not very significant
42
for the algorithm; however appropriate choice of their value might cause improved per-
formance. Performance is enhanced equally in terms of avoidance of local minima and
convergence rate. The values of these factors need to be catered for while selecting in-
ertia weight. Many diverse values are suggested for these parameters by various studies.
Presently the association between various parameters and their effects in various cases of
a single problem are not fully grasped. An example of this is that of dynamic optimization
problem [83] in which there is no simple relationship between the parameters.
Instead of adapting cognitive and social factors, PSO can also adapt a dynamic sys-
tem. In a dynamic system, the state changes in a repeated or non-repeated manner. The
changes may occur frequently or even continuously. Adaptive PSO for dynamic systems
has been considered in [86–88].
3.3.2 Constricted Version of PSO
In order to choose a right mixture of parameter values which can perform satisfactorily for
a broad variety of problems, a great deal of effort has been made by researchers. In [77]
it has been shown that the use of a constriction factor is necessary to ensure convergence
of particle swarm algorithm. A simplified expression incorporating constriction factor
can be written as
vi+1s = K
(vi
s + α1γ1s
(ps − xi
s
)+ α2γ2s
(g − xi
s
))(3.3)
ψ = (α1 + α2) > 4 (3.4)
χ =2∣∣∣2− ψ√ψ2 − 4ψ
∣∣∣ (3.5)
In [75], “Swarm Explosion ”phenomenon is avoided using the effect of velocity clamp-
ing. If the maximum velocity of particles is unbounded then velocity can increase limit-
lessly and resulting in an ever increasing swinging motion of particle around an optimum.
In [85], the parameter vmax is called velocity clamping which is kept at highest value for
43
xi
φvipipi-x
i
g
g-xivi+1
xi+1
xi
-xi
-xi
α2γ2(g-xi)
α1γ1(pi-xi)
Destination
O
Cognitive part
Social part
Figure 3.2: Modification of searching point of PSO, xi is the current position, and xi+1
is the modified position, similarly vi is the current velocity and vi+1 is the modifiedvelocity, xiand vi are the position and velocity of the particle, p and g are pbest and gbest
respectively.
the xmax positions in the solution space and significantly improved performance results
are obtained when using constriction factor approach. Additional studies show that this
method is not sufficient to keep particle’s velocities restricted and manageable. Com-
parison of evolutionary computational techniques [76], shows PSO can speedily locate
the area in which optimum is present but face difficulty in regulating velocity to make a
delicate search of the solution space.
In [77, 80], theoretical studies of convergence were performed. In [80], a method for
choice and adjustment of parameters is proposed. The proposed method is established
on the speed of convergence of the diverse combinations of parameter values. In [85],
the combination of both the velocity clamping and the constraint were used and yielded
excellent outcome. They employed values wmax= xmax.
44
3.3.3 The Binary PSO
Binary version of PSO is proposed in [66]. In earlier works this variant was not of much
interest. The particle position in binary version is not real valued, rather it is either binary
1 or 0. The probability distribution for position has been founded on mathematical
function of particle’s velocity. This distribution is used for randomly generating the
particle position. The particle position is updated using the following equation
xi+1s =
1
0
if γ3 <1
1+e−vi+1s
otherwise(3.6)
where γ3 is a number in [0,1] interval. If (γ1 and γ2) have value equal to zero that
results in the nulling of both cognitive and social parts of velocity then still binary PSO
randomly searches the solution space. In [106] PSO has been employed for sorting tasks.
A quantum based approach is suggested in [105] for amending equations of binary PSO
algorithm. Another version of binary PSO is proposed and analysed by Clerc [107] which
outperforms others.
3.4 Genetic Algorithm
Genetic Algorithms (GAs) derive their name from the genetic processes of natural evo-
lution. They were developed by Holland in the mid-1960s and have been implemented
successfully in a broad range of engineering applications, e.g., control engineering, the
design of neural and fuzzy systems etc. During the 1980s, the rapid progress in computer
technology permitted the use of the EAs in difficult large-scale optimization problems
and the methods rapidly diffused into the scientific community. Today, new applications
of EAs are being reported in large numbers and the field has finally achieved general
acceptance. Both exact and approximate solutions are found using GA. It is classified as
a global search heuristic. It belongs to special category of EA that use methods based
on biological evolutionary processes of crossover, inheritance, selection and mutation.
45
Initialize Population
SELECTIONselect parent #1 and #2
MUTATIONwith p=pmutation
Replace Population
2.3 0.210.5
Parameter Gene Chromosome
CROSSOVERwith p=pcross
Until Temporary Population is Full
Evaluate Fitness
Until Termination Criteria is met
Figure 3.3: Flowchart of Genetic Algorithm.
Every organism has a set of rules that determine the built up of an organism with
the help of life’s very minute building blocks. Genes are an organism’s encoded rules
that form thread like structures known as chromosomes. Particular quality/feature of an
individual corresponds to a gene. For example the color of skin, height, sex etc., all are
dictated by the particular gene combination. An individual’s genotype is its genes and
their combination while phenotype is the bodily manifestation of the genotype.
Genes are divided when two individuals/parents breed. The brood/child gets half of
its genes from its either parent. This process of making up of genes of child in such a
fashion is known as recombination. A gene can possibly get mutated but its occurrence
is very rare. The mutated gene does not usually show up in growth of phenotype but
sporadically it can introduce an entirely new feature.
The GAs for function optimization in computation, is applied in [56]. Many versions
46
of such evolutionary programming have been tried in various fields with varying degree of
success. The tunable optimization parameters of GA algorithms are key to the immensity
of its target applications. These parameters along with the borrowed fundamental ideas
of genetics construct search algorithms that are robust and require minimal problem
information. The algorithm starts with definition of three entities cost, cost function and
optimization variables. While solving the problem all prospective solutions are coded
as binary strings called chromosomes that act as an input to the cost function. An
experiment, a mathematical function or a game can be the cost function. The input
variables and output are related by the cost function. The choice of input variables
can change the output in the required manner also changing the cost which is difference
between the desired and actual output. The cost function is carefully selected by keeping
in view the variables that will be used. Algorithm starts with generation of an initial
population which is comprised of a group of chromosomes. The size of population and
length of chromosome are parameters depending upon the problem and are normally
kept fixed for a particular problem. All individuals in every generations are checked
for their fitness value based on the cost functions output. This evaluation gives each
individual a probability of being selected as a parent for next generation. In order to
create offspring from the pairs of parents already selected for mating the operation of
crossover is performed. Mutation operator is applied to these offspring thus producing
new individuals of the next generation. The members of previous population having
worst fitness are replaced by newly generated offspring. Algorithm repeats till objective
function is satisfactorily optimized. Following are the issues that need to be tackled with
care for the considered problem [89].
Original GA was in binary form. Binary GA solves many optimization problems that
stump traditional techniques, binary GA limits its performance to some extent when
used to solve problems in continuous domains due to quantization errors, and limited
number of bits to represent continuous variables. On the other hand, each variable re-
quires may many bits to represent it. If the number of variables is large, the size of the
47
chromosome is also large. When the variables are naturally quantized, the binary GA
fits nicely. However, when the variables are continuous, it is more logical to represent
them by floating-point numbers. This continuous GA also has the advantage of requir-
ing less storage than the binary GA because a single floating-point number represents
the variable. The continuous GA is inherently faster than the binary GA, because the
chromosomes do not have to be decoded prior to the evaluation of the cost function. In
this research we used continuous GA (CGA). The format of CGA is as follows.
3.4.1 Initialization of the Population
Initially GA randomly generates a big population of chromosomes. Each chromosome
is an array of real numbers and represents a possible solution of problem under con-
sideration. The population size is kept constant throughout the optimization. If the
chromosome has N variables (an N -dimensional optimization problem), then the i th
chromosome is written as an array with 1×N elements
xi = (xi1,xi2.............xiN) (3.7)
The initial population is a matrix of S rows like (3.7)
3.4.2 Natural Selection
Natural selection decides which chromosomes in the initial population are fit enough
to survive and possibly reproduce offspring in the next generation. Good parents are
found out for the next generation by the operation of selection on the basis of their
fitness value. It emulates the natural phenomenon of survival of the fittest as described
by Darwin’s theory. This theory implies that best individuals have greater chance to
survive and reproduce. The selection operator picks the strings that are above average
from current population and probabilistically replicate them in mating pool assuming
that better individuals have increased chances to reproduce even better offspring. It
48
is based on the fact that high correlation exists among the fitness of parents and their
offspring. In Genetics this correlation is termed heredity. Of the S chromosomes in a
given generation, only the top Nkeep are kept for mating and the rest are discarded to
make room for the new offspring.
Nkeep = bselection× Sc
The parameter selection is set to 0.5 in this research.
3.4.3 Pairing
Mothers and fathers pairs are formed in a random fashion. Each pair produces two
offspring that contain traits from each parent. In addition the parents survive to be
part of the next generation. The more similar the two parents, the more likely are the
offspring to carry the traits of the parents. There are various strategies of pairing, few
of them are presented here.
3.4.3.1 Random Pairing
This strategy uses a uniform random number to select chromosomes and parents to be
crossed over.
3.4.3.2 Rank Weighting Pairing
This approach is problem independent and finds the probability from the rank n, of the
chromosome. Let M = d(S −Nkeep) /2e be the number of matings. The cumulative
probabilities are used in selecting a chromosome.
Pn =n∑
q=1
Nkeep − q + 1∑Nkeep
q′=1q′
, n = 1, 2, 3, ..., Nkeep (3.8)
49
Two lists of parents are formed containing the indices of parents taking part in cross
over, one from each list. The lists are formed as
ji (k) = n, provided that Pn < φik ≤ Pn+1, n = 1, 2, 3, ..., Nkeep (3.9)
where k = 1, 2, 3, ...,M, i = 1, 2 and φik is a random number in [0 1] for all i and
k. Through crossover (recombination) numerical information is exchanged between two
random individuals.
3.4.4 Mating or Cross-over
Cross-over is the way through which information is shared among the population. The
simplest method of cross over is to choose one or more points in the chromosome to mark
as the cross over points. Then the variables between these points are swapped between
the two parents. The two offspring cm & cm+1 are generated as
cm (i) =
wJ1m (i)
wJ2m (i)
1 ≤ i ≤ nm
nm < i ≤ N(3.10)
cm+1 (i) =
wJ2m (i)
wJ1m (i)
1 ≤ i ≤ nm
nm < i ≤ N(3.11)
where m = 1, 3, 5, ...,M − 1, nm is the cross over point and nm ∈ ncp where
ncp = [n1, n2, n3, ..., nM ] (3.12)
Each nm is a random positive integer such that 1 ≤ nm ≤ N. Also jkm ∈ jk, k=1,2
j1 = [j11, j12, j13, ..., j1M ]
j2 = [j21, j22, j23, ..., j2M ] (3.13)
50
Each jk is found using (3.9) for all k. The problem with point cross over methods is that
no new information is introduced. The remedy is to introduce new genetic material. New
methods of mating are designed to combine variables from two parents.
cm (i) =
wj1m (i)
wj1m (i)− γm {wj1m (i)−wj2m (i)}
1 ≤ i < nm & nm < i ≤ N
i == nm
(3.14)
cm+1 (i) =
wj2m (i)
wj2m (i) + γm {wj1m (i)−wj2m (i)}
1 ≤ i < nm & nm < i ≤ N
i == nm
(3.15)
where γm is a random number such that 0 < γm < 1 for all m = 1, 2, ..M. An alternative
form of cross over which combines the features of two individual parents is [117]
cm (nm) = βwj1m (nm) + (1− β)wj2m (nm) (3.16)
cm+1 (nm) = (1− β)wj1m (nm) + βwj2m (nm) (3.17)
where β is a random number such that 0 < β < 1.
Crossover operator during the mating process generates two offspring by merging
the parts of the two selected parent’s strings. Offspring for replacement of bad parents
in older generation are produced in this step. Most common among them is the 1-
point crossover as shown above. Along the chromosome at randomly selected point,
substrings are swapped among parents for producing offspring. Crossover probability
pcross is user defined and normally it is high valued. When crossover is not permitted the
next generation includes the parents and their replicas, without any change.
3.4.5 Mutation
The function of mutation is to introduce occasional perturbations to the variables to
maintain the diversity in the population. The mutation in CGA is governed by the
51
following relation.
w (pi, qi) = (xh − xl)φ+ xl (3.18)
Random numbers pi and qi are chosen to select the chromosome (row) and variables
(columns) to be mutated in the population (matrix). Also pi ∈ {p1, p2, ..., Nmute} , and
qi ∈ {q1, q2, ..., Nmute} are arrays of random integers such that 1 ≤ pi ≤ S, and 1 ≤ qi ≤ N
and 0 < φ < 1, xh is the upper and xl the lower bound of the variable Nmute. A mutated
variable is replaced by a new random variable. Nmute is the total number of mutations
given by
Nmute = (S − 1)Nµ (3.19)
Where µ is the mutation rate set to 0.2 in this research.
3.4.6 Fitness Function
As GA mimics the Darwinian theory that is founded on the survival of the fittest among
a population of organisms and it also utilizes the inherent searching ability of the na-
ture. Therefore GAs are suitable for maximization problems. Minimization problems are
usually transformed into maximization problems by some suitable transformation [90].
Generally fitness function is initially defined using the objective function and later ge-
netic operations are performed repeatedly using it. Fitness function aims to check the
grade of each and every chromosome.
3.4.7 Choice of the Parameters of GA
The main parameters that must be considered in the design of a GA are the popula-
tion size S and the values of the probabilities of recombination/crossover and mutation.
The optimal choice of GA parameters is strictly problem dependent. There are no stan-
dard guidelines for parameter selection however some general guidelines on values that
give acceptable results have been established from experience. Following choices are the
guidelines.
52
• Population size S ∈ [60, 100].
• Use the roulette wheel or rank weighting selection method.
• Employ the one-point crossover operator with probability of cross over pcross ∈
[0.6, 0.9].
• Apply the mutation operator with probability of mutation pm ∈ [0.001, 0.02]
Choosing population size is the most difficult decision among all the other parame-
ters. In fact there exists no fixed value which is optimal. The choice relies heavily on
problem while considering other factors as well. A large sized population in GA may
have fast convergence and maximum probability of finding global optimum at the cost
of tremendous computational complexity. But there may exist a GA with smaller pop-
ulation size and moderate computational complexity at the cost of reduced probability
of finding global optimum. Moreover frequent occurrence of early convergence is also
observed. The tradeoff has to be made between probability of finding global optimum
and computational complexity. These genetic operators are attractive because they are
simple. An elitist policy in GA proposes to keep the fittest member in next generation en-
suring inopportune loss of best optimum doesn’t happen due to operations like mutation
or crossover.
3.5 Artificial Bee Colony (ABC) Algorithm
The behavior of swarms has led to many optimization algorithms. Bees are one of the
social insects that successfully collect nectar and survive natural challenges by their
collective efforts in a hive. Karaboga proposed an optimization algorithm in 2005 [99]
inspired by the foraging habits of a swarm of honey bees. This algorithm named as
Artificial Bee Colony (ABC) is based on simple rules like other swarm based algorithms
e.g. PSO, ACO and their variants. Control parameters include population size or colony
size and number of maximum cycles (iterations).
53
Initialize food source positions
Evaluate fitness function of each employed bee
Determine new food positions for
employed bees
Evaluate fitness function
Memorize the position of best food
source
Select food source for onlooker
Determine a neighbour food
source for onlooker
All onlookers distributed
Is termination criterion met ?
Find abandoned food source
Produce new position for the exhausted food source
Final food position
Yes
No
No
Yes
Figure 3.4: Flowchart of Artificial Bee Colony algorithm.
54
In this algorithm a population of artificial bees explores food sources and keeps modi-
fying the food sources over time with an objective to find a source with maximum nectar.
The bees are categorized into three types which are employed bees, scout bees and on-
looker bees. Employed bees bring the nectar and information about the source to the
hive. Onlooker bees wait for employed bees in hive and infer this information from the
employed bees by the dance on their return. New food sources are searched by scout
bees in the hive’s neighborhood. Employed bees on their return to hive bring nectar and
perform dance in dance area which indicates the food source quality to onlooker bees.
The longer their dance is, greater is the quality of the source they have returned from.
Variety of dances is observed by the onlooker bees and these choose the food source of
good quality. High quality food source lures larger number of onlooker bees. Onlooker
and scout bees turn into employed bees on the discovery of a new food source. Each time
when depletion of a food source occurs, the employed bees become either onlookers or
scouts. Employed bees along with onlooker bees carryout the task of food gathering while
the scout bees in the meantime explore neighborhood for new and better food sources.
The analogy of food source is used in ABC algorithm for getting optimum solution
for the problem under consideration from the possible solutions. Usually employed bees
and food sources are kept in same numbers. Initially food source positions are created
randomly. An ith food source is symbolized as
xi = (xi1,xi2.............xin)
where n is the number of parameters of the food source or dimensions of the solution de-
pending on the underlying problem. Following method is used for producing a contended
food source with the help of existing food source for each employed bee
x′
ij = xij + φij (xij + xmj) (3.20)
where φij is a uniform random variable in [-1,1], and xmj is a randomly selected jth
55
parameter of another randomly selected solution xm
xm = (xm1,xm2.............xmn)
It is noticeable that just a randomly chosen parameter is changed for getting a new
food source from previous source. ABC is a repetitive procedure. After the initialization
in each repetition of the algorithm, an employed bee determines a new food source
position by altering an existing food source position. The amount of nectar is determined
for the new position and compared with that of the previous source position. If new
position has greater nectar then it is remembered and the old position is disregarded or
else the previous position is remembered. If an existing food source position is discarded
then an employed bee turns into a scout bee until a new food source position is discovered.
Scout becomes an employed bee on finding new food source position. On its return after
newly found food source position the employed bee reports amount of nectar to onlooker
bees waiting in the hive. The amount of nectar is used by the onlookers to calculate
the probability. This probability selects a food source to be exploited. The food source
selection probability is calculated as
pi =fitness (xi)∑S
j=1 fitness (xj)(3.21)
Where S represents number of total food source positions. An employed bee discards a
food source to become a scout if it fails to improve a food source within a fixed number
of iterations. A scout searches the problem space randomly to find new food sources,
which is given by
xik = xmink +
(xmax
k − xmink
)× r (3.22)
where r is a random number. Allocation of the food source at random to a scout converts
it into an employed bee. The next iteration of ABC algorithm starts whenever a new
food source position is discovered. The algorithm is run repeatedly till the termination
56
criterion is satisfied. The ABC algorithm consists of following four phases.
3.5.1 Initialization Phase
In this phase scout bees randomly produce a set of food source positions. The amount
of nectar corresponding to these positions is calculated and control parameters are ad-
justed accordingly. Every food source position is a solution vector to the problem under
consideration for optimization. Each solution vector consists of variables that require
adjustment for minimizing the fitness or objective function.
3.5.2 Employed Bees Phase
The responsibility of employed bees is to find new positions of food sources close to the
memorized position with an aim to get more nectar. The amount of nectar or fitness is
also evaluated by them for the newly found positions. After evaluating the nectar amount
they compare it with the amount of previous position, the position of food source with
higher nectar is memorized and the other one is discarded. On their return to hive in
the dance area they provide the information to the onlooker bees about the amount of
nectar. The onlooker bees calculate the probability proportional to the nectar amount
and choose food source based on the probability. Each employed bee returns to search for
new position of food source around the position already memorized. Then again evaluate
the new position for nectar amount.
3.5.3 Onlooker Bees Phase
Employed bees return to hive and give details of food source to waiting onlooker bees.
Food sources are chosen by onlookers by calculating the probability which in turn depends
on the information of amount of nectar or the fitness value given in the dance area of
the hive by employed bees. An onlooker bee calculates the value of probability by using
the expression (3.21). Onlookers use equation (3.20) to determine fitness value of a
57
neighborhood food source of a selected food source.
3.5.4 Scout Bees Phase
Food source positions are randomly searched in a problems solution space by the scout
bees. Employed bees are converted to scout bees when their food sources are discarded or
when the solution do not get better after a preset number of iterations. After conversion
to scouts, they start looking for food positions/ solutions randomly. In this fashion
the food sources that are inferior at the start or become inferior after utilization, are
discarded and it can be treated as a negative feedback in the search. A review of ABC
algorithm is given below.
1. Initialize food source positions, set the value of limit and the maximum iteration
number.
2. Determine neighbour food source positions for the employed bees using (3.20) .
3. Calculate the nectar amounts or fitness value.
4. If all onlookers are assigned food sources, go to Step 7 . Otherwise, continue.
5. Select a food source for an onlooker using (3.21).
6. Determine a neighbour food source position for the onlooker using (3.20). and go
to Step 4.
7. Find the abandoned food source and allocate its employed bee as scout for searching
new food sources using (3.22).
8. Memorize the position of the best food source.
9. If the maximum iteration number is reached, output final food source positions and
stop otherwise go to Step 2.
58
Figure 3.4 shows the flow-chart of ABC algorithm. The development of the joint
cognition in a hive critically requires the sharing of information between the bees. In a
hive the site for information sharing is the dance area. Various types of dances that are
staged in this area include Tremble, Round and Waggle. The superiority of food source
is shared with other bees with the help of Waggle dance. Onlooker bees present on the
dance floor have the knowledge of the best currently available food sources because they
watch the several dances thus able to deduce the best among the sources. Employed
bees exchange their information according to the quality of their food sources. Onlooker
bees choose rich food source positions on the basis of probability based on the dance of
employed bees.
3.6 Ant Colony Optimization
Ant colony optimization algorithm (ACO) was proposed by Maco Dorigo in the year
1992 in his doctoral thesis [91, 92]. ACO is a method for finding solution to a problem
that requires extensive computation and in principle its working is based on probabilities.
This algorithm has got inspiration from the activities of ants in their colony in which they
act in perfect harmony. An ant colony has the ability of finding a minimum distance path
from their nest to a neighborhood food source in a limited time. Although individually
ants have restricted ability to learn but collectively these are able to accomplish great
tasks. Ants move haphazardly around their nest in search of food and if an ant finds
a food source it returns to the nest with the trail marked by pheromone. All the other
ants are attracted by the pheromone and follow the trail and also mark this trail by
their pheromone. As the amount of pheromone increases, it attracts more ants to follow
that same path. The pheromone also evaporates with time and paths that are longer
have greater evaporation and thus less attraction for ants than a shorter path with less
evaporation (more concentration of pheromone). In this manner shortest path amongst
the many paths between food source and nest is selected by ants. The longest path
59
Figure 3.5: Ants have two paths move from nest to the food source and eventually theshorter path is chosen by all the ants.
disappears with time due to evaporation and finally all the ants will follow the shortest
path as shown in Figure 3.5. The shortest path is retained because the rate of deposit
of pheromone is more than that of evaporation.
Surroundings are used by ants as means to share information. Pheromone deposit
is their indirect method for information swap about details of their work status. The
pheromone deposit can be regarded as positive feedback while evaporation can be consid-
ered as negative. Positive feedback reinforces the system while negative feedback saves
it from failure. Supposedly if equal amount of pheromone is over all the available paths
no path could be selected. The feedback allows overcoming that stagnation and allowing
selection of path. Thus the algorithm transits from an unstable to a stable state in which
searching and selection of the shortest path is continued.
The benefit of evaporation of pheromone is that it evades the possibility of convergence
at any solution representing local optima. The path selected by first ants will become
extremely striking for subsequent ones if evaporation does not take place. The search
of solution space will be very limited in such a scenario. The experimental observations
of biologists cite that if an ant colony has two alternate paths with different distances
between nest and a food source the ants have tendency to exploit the shorter path. [93,94].
ACO algorithm is based on imitating this social activity using simulation in which the
ants explore the graph depicting the problem under consideration for solution. Initially
60
Start
Launch new Iteration of Ants
Find new solutions
Solution Evaluation
Pheromone Deposition
Pheromone Evaporation
Solution Found
End
Is termination criterion met ?
Figure 3.6: Flowchart of ACO algorithm.
the algorithm tried to find the best possible path in a graph trying to imitate ants
movement in search of path between food source and the nest. Now a much broader
range of numerical problems can be solved based on different characteristics of ants
activities. Potentially good solutions are constructed by ACO using a pheromone matrix
τ={τij}. Initialization of τ are set τij = τinit > 0. It also takes advantage of heuristic
information using visibility
pkij (t) =
[τij(t)]
α·[ηij(t)]β
Pk∈j [τij(t)]
α·[ηij(t)]β
0
if the transition is allowed
otherwise(3.23)
61
where the visibility ηij (t) is defined as
ηij (t) =1
dij (t)
where dij (t) is the distance or arc length. The parameters α and β control the relative
significance of traversed path and its clarity. In the case of α= 0 the algorithm becomes
greedy and having several starting points. An early convergence is observed for high
values of α and weak convergence for low values. Typical values are in the range of 0.5 -
5.0. This is adjusted properly by repeated experiments.
3.6.1 Update of Pheromone
While building a solution, ants deposit pheromone on the paths they use. Consider the
kth ant that moves from node i across the path to node j changing amount of pheromone
τij as follows
τij (t+ 1) = γτij (t) + ∆τij (t)
where 0 < γ < 1 is the evaporation coefficient and it is set by usert, ∆τij (t) is sum of
contributions by all the ants that utilized move (ij) for constructing solution i.e.
∆τij (t) =∑
k
τ kij (t)
τ kij (t) =
Q
dij (t)
where Q is a constant
3.6.2 Continuous Ant Colony Optimization
The ACO algorithm discussed so far is for discrete combinatorial problems and the solu-
tion components are already known and it cannot be directly applied to the continuous
62
problems characterized by the decision variables having continuous domains. While ACO
algorithms originally developed to solve problems of discrete nature, they can be adapted
to solve continuous problems. There are various approaches for this adaption [101–104].
All these approaces are quite different conceptually from discrete ACO. In this research
we follow the approach proposed in [104]. As the solution here consists of M filter co-
efficients. Let each coefficient be represented by B bits. Then the ACO solution will
consists of B ×M bits. At each bit index b = 1 : B ×M , each ant have to select one of
the two option as shown in Figure 3.7. For example if an ant is at bit position 2, that is
0, it can either move to 0 (0→ 0) or to 1 (0→ 1). The probability for this selection can
be calculated as
P01 (t) =τ01
τ01 + τ00(3.24)
where, P01 is the probability associated with the sub-path (0→ 1), and τ00 and τ01 are
the artificial pheromones of the sub-paths (00, 01). In order to avoid the premature
convergence problems, a strategy established on the frequency-based memory has been
used. The frequency-based memory stores information about how often a sub-path is
followed by ants. By examining the pheromone amount, it is difficult to conclude whether
most ants follow a sub-path or not. But, it is very easy to do that by evaluating the
frequency information. The probability based on the frequency memory is calculated by
the following equation:
P01 (t) =
1
τ01(t)τ01(t)+τ00(t)
if (f × f01 < f00)
otherwise(3.25)
where f is a frequency factor chosen as 2. If the condition (f × f01 < f00) is satisfied, then
the path (0→ 1) is directly chosen; else the pheromone-based direction selection strat-
egy described in (3.24) is employed. Artificial pheromone is computed by the following
63
Figure 3.7: Bit selection of ants
formula
∆τ k01 (t, t+ 1) =
Q
objective value(k)
0
if kth ant passes the subpath (0→ 1)
otherwise(3.26)
After M ants in the colony complete the search process and produce their solutions,
the pheromone amount to be attached to the sub-path (0→ 1) between the time t and
(t+ 1) is computed as
∆τ01 (t+ 1) =M∑
k=1
∆τ k01 (t, t+ 1) (3.27)
The pheromone amount of the sub-path (0→ 1) at the time (t+1) is updated by the
following equation
τ01 (t+ 1) = ρτ01 (t) + ∆τ01 (t+ 1) (3.28)
ρ ∈ ]0, 1[ : Evaporation parameter. The selection is based on pheromone information of
each path.
3.6.3 Convergence of ACO
The global maxima or minima can be searched in limited time using some particular
variants of ACO. The convergence of ACO was first proved in the year 2000 for version
of ACO based on graph while for the other versions it was proved later. Estimation
of hypothetical convergence rate is extremely complex for such type of metaheuristic
techniques. Zlochin et. al. [97] have concluded that such type of techniques have possibly
a relationship with stochastic steepest descent based on cross entropy and distribution
estimation algorithm. These techniques were also classified by them as research based
64
model.
3.6.4 Applications of ACO
A wide ranging optimization problems of combinatorial nature have been solved using
ACO algorithm. These include optimal path finding for vehicles, resource allocation,
forecasting of many diverse phenomena, probabilistic problems, etc. ACO has also been
successful in finding near optimal solution for challenging problem of traveling salesman.
Initially ACO algorithm was known as ant system [98]. Its objective was to find solution
of the traveling salesman problem. In this multi-objective problem a shortest path is
sought for a number of cities to be visited in round trip with the constraint that each
city is visited only once. ACO shows better performance for the dynamic systems in
contrast to GA and simulated annealing. ACO algorithm is able to run endlessly and
adjust to any variations in allowable time constraints. In communication networks its
application is of special interest when its performance is required in a limited time.
ACO builds the shortest path from source to destination in a graph by grouping
together several paths. ACO has no exact description as it varies with respect to its ap-
plication and authors as well. Therefore a coarse definition of ACO is a population based
optimization technique in which an ant explores the search space. These ants keep record
of the best solutions and locate new best solution in the light of previous records. The
newly found best solutions are marked for optimizing further search. ACO is viewed as
population based algorithm employing probability distribution for changing in repeated
searches. The solutions are assembled in many repetitions for combinatorial problems.
It is likely to find an optimal solution for this type of problem. Considering traveling
salesman problem the optimal itinerary is devised by combining strongest sections of
best solutions alleviating the need of ant to travel the optimal route. The solution to
real valued problems can not be explained in this manner. ACO fits in the framework of
“Swarm Intelligence ”which generalizes the organizational behavior of social insects.
65
Chapter 4
Jammer Excision in CDMA based
on Computational Intelligence
Techniques
4.1 Introduction
In this chapter, the problem of jammer excision in Direct Sequence-Code Division Mul-
tiple Access (DS-CDMA) system is considered. The jammer excision is formulated as
an optimization problem and then solved by nature inspired computational intelligence
techniques.
Various optimization techniques have already been proposed for jammer excision in
DS-CDMA. Adaptive algorithms are proposed for estimation and suppression of NBI in
DS-SS system in [110]. Bijjani and Das have applied linear and non linear neural network
filters for suppression of NBI in DS spread spectrum system [111]. Higher order statistics
and GA has been used to reject NBI and has faster convergence than Least Mean Squares
(LMS) algorithm [112].
4.2 System Model
Considering a synchronous CDMA system. CDMA system with jammer excision is shown
in Figure 4.1 for a single user y. Consider the kth user transmitting Binary Phase Shift
Keying (BPSK) symbols. The users are separated by Pseudo Noise (PN) spreading
sequences of length L. The mth symbol of kth user is spread over L chips using a unit
66
Data Source
AWGN
Decision
PN Sequence
Excision Filter
PN Sequence
JammingSignal
X X+d d’
Figure 4.1: Block diagram of a CDMA System with an Excision Filter.
energy spreading sequence ck = {ck (1) , ck (2) , ..., ck (L)} ,where ck (l) ∈{±1/√L
}, l1 =
1, 2, .., L. The complex low pass equivalent transmitted signal for kth user can be written
as
sk (t) =∞∑
i=−∞
L−1∑l=0
ak (i) ck (l) p (t− lTc − iTs) (4.1)
where ak (i) and ck (l) are the i th information bit and l th chip of the spreading code of
k th user, L is the length of spreading code and is called the processing gain, L = Ts/Tc =
1/ (symbol rate). Ts is the symbol duration and Tc is the chip rate. In (4.1), p (t) is a
pulse satisfying the following relations:
p (t) =
1
0
−∆ ≤ t ≤ T′s −∆
otherwise(4.2)
The received signal in the presence of a jamming signal and Additive White Gaussian
Noise (AWGN) can be written as:
r (t) =K∑
k=1
∞∑i=−∞
L−1∑l=0
ak (i) ck (l) p (t− lTc − iTs) + J (t) + n (t) (4.3)
67
where K is the total number of users, n (t) is the AWGN and J (t) is the jamming signal.
J (t) can be written as sum of sinusoids:
J (t) =M∑
m=1
Am (i) sin (2πfmt+ φm) (4.4)
Where Am, fm and φm are amplitude, frequency and phase of m th sinusoid respectively.
The received signal r (t) is then sampled to get r (n) and convolved with a discrete excision
filter. The output of the filter with N filter coefficients/weights w is denoted by y (n)
and is given by:
y (n) =N∑
j=0
r (n− j)w (j) (4.5)
The received signal is then passed through a bank of K correlators or matched filter prior
to decision stage. This involves multiplication with users spreading code and averaging
it over symbol duration Ts. The output of the k th correlator at receiver is given by
uk (n) =1
L
Ts∑i=1
L−1∑l=0
y (i) ck (l) (4.6)
The bit is detected by a conventional single user detector by just determining the sign of
the correlator output. Let the detected bit be ak using a matched filter the detection is
made as
ak (n) = sign (< (uk (n))) (4.7)
where < (u) denotes real component of u.
4.3 Wiener Filtering for Jammer Excision in CDMA
Wiener filter reduces the effect of jamming by comparison with the desired noiseless
signal. Pilot sequence is transmitted for designing of filter and are known at receiver.
Performance criterion of Wiener filter is minimum Mean Square Error(MSE). The MSE
68
−1
0
1
−1−0.500.511.50.5
1
1.5
2
2.5
3
3.5
Filter Coeff. 1Filter Coeff. 2
Mea
n S
quar
e E
rror
Figure 4.2: Surface plot of the cost function.
is defined as:
E[e2 (n)
]=
1
N
[N∑
k=1
(dpilot (n)− y (n))2
](4.8)
The Wiener filter is designed to achieve an output close to the desired signal dpilot by
finding the optimum filter coefficients that minimize the MSE between the pilot data and
filtered signal, which can be stated as:
wopt = arg min E[e2 (n)
](4.9)
The Wiener filter coefficients w are given by:
wopt = R−1P (4.10)
Where R is the autocorrelation matrix of the received pilot signal and P, the cross
correlation matrix between the received signal and the pilot signal. Jammer free signal
69
is achieved using this wopt in equation (4.5). The output of the filter is further processed
for detection.
The Wiener filter solution is based on the assumptions that the signal and the noise are
stationary linear stochastic processes with known autocorrelation and cross correlation.
In practice the exact statistics (i.e. R and P) are not known, needed to compute the
optimal Wiener filter hence degrading the performance. Larger size of R and P is required
for more accurate estimates of correlation values resulting in large and better wopt . The
large sizes of R, P and wopt are too expensive computationally in many applications e.g.
real time communication. Efficient methods are required for calculation of matrix inverse
(R−1).
Proposed jamming excision based on nature inspired computational intelligence tech-
niques do not require the known statistics of the signal and the noise. These also alleviate
cumbersome calculations for finding inverse of matrix.
4.4 PSO for Jammer Excision in CDMA
There are wide varieties of problems that have been solved using PSO [66–68]. PSO
has been applied for achieving global optimization in non-linear and recursive adaptive
filter structures [108,109]. We have applied PSO for jammer excision of CDMA signal to
minimize the Mean Square Error (MSE) or cost function (4.8) between the pilot data and
filtered signal. Particle position w represents the detector weights and particle velocity
∆w represents the updating increment in the weight matrix i.e.
∆wi+1s = φ∆wi
s + α1γi1
(ps −wi
s
)+ α1γ
i2
(g −wi
s
)(4.11)
wi+1s = wi
s + ∆wi+1s (4.12)
First the initial population is generated with random positions W and velocities ∆W in
the initialization block of dimensions S × N , where S represents the swarm size and N
70
is the filter length. The current searching point of each agent is set to pbest. The best
evaluated value of pbest is set to gbest and agent number with best value is stored. Each
particle evaluates the cost function (4.8). If this value is less than the current pbest of
the agent, the gbest is replaced by the current value. If the best value of pbest is less than
the current gbest, the gbest is replaced by the best value and the agent number with its
value is stored. The current searching point of each agent is changed using (4.11) and
(4.12). This process will continue until the termination criterion is finally met. The PSO
algorithm for jammer excision in CDMA is described as follows
PSO Algorithm for Jammer Excision
Initialize particles with initial weight matrix W and increment matrix ∆W with
dimensions S ×N. Let ws represent s th row of W
for i=1:iterations
for s=1:S
1. Evaluate cost function (4.8) for sth row of W
if (fitness (ws)) < fitness (wpbest)
fitness (wpbest) = fitness (ws)
wpbest=ws
end if
end
2. Update W and ∆W equations (4.11) and (4.12)
gbest=min (pbest)
wgbest=W
(arg min
1≤n≤N(Pbest)
)end
3. wgbestis the solution
71
s=s+1
YesNo
Evaluate MSE for sth row of Wrepresented by ws
s=1
YesNoMSE(ws)<MSE(wpbest)s
wpbest=wss
Initialize (S×N) dimensionalrandom matrices W and W
s=1
<Ss
No
Yes
YesNo
Convergence criterion met?
s
Stop: wgbest is the optimal solution
Update W and W
m=arg min[MSE(wpbest)]wgbest=wpbest
s
m
min[MSE(wpbest)]<MSE(wgbest)1 s S
Figure 4.3: Flow chart of the particle swarm optimization algorithm, where S is theswarm size, W, ∆W and Wpbest are (S ×N) dimensional matrices, ws is the sth row ofW.
72
4.4.1 Optimization of PSO for Jammer Excision
Three parameters of PSO which can be tuned for optimal performance are acceleration
constants α1,α2 and inertial weight φ. Different values of α1 and α2 lead to improved
performance [62] and therefore the values were tuned and optimal values were found to
be 2.0 and 1.75 respectively and resulted in faster convergence towards optima. The
parameter φ is very important in determining the type of trajectory the particle travels.
A large inertia weight facilitates the global exploration while with a smaller one, the
particle is more intended to do local exploration. A proper choice of inertia weight
provides the balance between the global and local exploration ability of the swarm. There
is a number of proposed shemes of assigng value to inertial weight that give enhanced
performance as compared to a basic PSO algorithm with fixed inertia. Experimental
results suggest that it is better to initially set the inertia to a large value and then
gradually decrease its value to obtain the refined solution [63]. If inertial weight decreeases
linearly then it is called linearly decreasing inertial weight (LDIW) strategy. A natural
exponential inertial weight (NEIW) scheme for optimized performance has been suggested
in [118] that decreases inertial weight based on natural exponential function making the
convergence faster. Another modification was suggested by Eberhert [63] called random
inertial weight (RIW) in which inertial weight takes a random value between 0.5 and
1.0 enabling global search for optimal solution. Clerc et al. [77] suggested constriction
factors for improved performance and ability to find optima. Values of inertial weight and
acceleration constants can be calculated using these constriction factors and PSO using
these values can be called constriction factors inertial weight (CFIW) PSO. Values and
expressions of inertial weights for these schemes are shown in Table 4.1. The parameters
of PSO need to be tuned like any other adaptive algorithm for its optimal performance.
The choice of parameter values is made depending on the landscape and characteristics
of the cost function. In this paper we propose optimum values of the parameters for
the designing of an optimal excision filter having minimum MSE. These values have been
obtained from intensive experimental observations and simulation results. It outperforms
73
above mentioned schemes in terms of convergence rate. The inertial weight takes the value
between 0 and 0.5 randomly. These values optimize the search capability of particles to
find the minima of cost function for N filter coefficients.
4.5 CGA for Jammer Excision in CDMA
CGA is applied to find coefficients or weights of excision filter so as to minimize the cost
function (4.8). The flowchart of GA based algorithm for jammer excision in CDMA is
shown in Figure 4.4. The number of filter coefficients is N and the population size is
S. The coefficients are assumed to be the chromosomes in this application. A S × N
dimensional random matrix is generated to get an initial population of S individuals
each having N chromosomes. Generation counter variable gen is initialized with value
1. As each row of this matrix represents a filter therefore the MSE is evaluated for all
S rows. Individuals are sorted according to their respective MSE. The individual with
least MSE stands first and the one with highest stand last. The fraction of population
with highest fitness is selected for mating. New offsprings are produced after crossover
and mutation operations. Fitness of new generation is evaluated and generation counter
is incremented. Process of selection, crossover, mutation and evaluation is repeated
until termination or performance criterion is met. When generation counter hits maxi-
mum value or minimum MSE of the population is achieved the iterations are stopped.
The best individual/ filter with least MSE amongst the last population is the optimal
excision filter. Like any other optimization technique the parameters have to be tuned
Table 4.1: Inertial Weights for types of PSOPSO Type φ
Proposed 0.5×randConstriction Factor Inertial Weight (CFIW) 0.729Random Inertial Weight (RIW) 0.5+(rand/2)Linearly Decreasing Inertial Weight (LDIW) 0.9−→ 0.4
Natural Exponential Inertial Weight (NEIW) 0.4+0.5e−10k/K
74
Table 4.2: General Parameters for Simulation of GAParameter Value or Type
Mutation Type RandomCrossover Type Single PointProbability of Crossover 0.02Genome Type ContinuousInitialization RandomTermination Criterion Max. no. of iterations
for optimal performance. Summary of parameters and their values are given in Table 4.2.
CGA Algorithm for Jammer Excision
1. Initialize chromosomes with initial weight matrix W with dimensions S × N. Let
ws represent sth row of W
2. Evaluate the fitness/cost measure for ws ∈W for all s
3. for i=1:iterations
4. Select chromosomes for replacement from W
5. Select two sets of recombination chromosomes j1andj2 using (3.8) and (3.9).
6. Choose individuals from j1and j2 to enter the mating pool (MP)
7. Find the vector of random integers ncp containing cross over points
75
opt
Stop: opt
Figure 4.4: Flowchart of GA algorithm for finding optimal weights of an Excision Filterfor CDMA, where P is population size, N is number of filter coefficients and gen is thegeneration number.
8. Recombine chromosomes in MP using (3.14) and (3.15) forming cm and cm+1.
cm replaces wm.
9. Mutate chromosomes in W using (3.18)
10. Evaluate the fitness/cost measure for ws ∈W for all s
end for
11. ws with the least cost is the optimum solution
76
Table 4.3: General Parameters for Simulation of ABCParameter Value or Type
Initialization RandomColony Size 32Max. Iterations 500No. of Parameters 32No. of Food Sources 0.5 × Colony SizeMax. Trials 100Termination Criterion Max. no. of iterations
4.6 ABC for Jammer Excision in CDMA
ABC algorithm was applied to solve jammer excision problem. The general parameters
selected for the algorithm are summarised in Table 4.3. ABC algorithm improves the
randomly initialized weights with several trials per iteration. Onlooker bees try to im-
prove the weights which are found by Employed bees. Filter weights that do not improve
after repeated trials are abandoned and replaced with the ones randomly found by scout
bees. At termination the solution with best fitness is the excision filter. The flow chart
of ABC algorithm for jammer excision is shown in Figure 4.5. The ABC algorithm for
jammer excision is described below.
1. INITIALIZATION
Initialize food sources with initial weight matrix W with dimensions S×N. Let ws
represent s th row of W. Trial counters for each row are intialized to zero. Number
of employed bees, onlookers and scouts is initialized.
2. Evaluate fitness value of each row for each employed bee
3. EMPLOYED BEE PHASE
While (termination criteria is not met)
77
Initialize W matrix and no. of employed onlookers and scouts
Evaluate fitness function of each row for employed bees
Determine new set of filter coeff. for
employed bees
Evaluate fitness of new. Replace coeff.
or inc. trial
Memorizethe row with best fitness
Select a row of W for onlooker
Determine a new set of filter coeff. for
onlooker
All onlookers distributed
Is termination criterion met ?
Findabandonedrow of W. Excesstrials
Produce new set of coeff. for
abandonedrow &
Evaluate
Best fitness row is wopt
YesNo
No
Yes
Figure 4.5: Flowchart of ABC algorithm for finding optimal weights of an Excision Filterfor CDMA
4. Find new solution for all employed bees w,s for ws using (3.20)
5. Evaluate fitness using (4.8) for w,s
6. if (fitness (w,s) > fitness (ws))
Replace ws by w,s and reset trial counter Ts to zero.
else
Increment trial counter Ts
78
7. Find Ps using (3.21)
8. ONLOOKER BEE PHASE
Initialize k = 1, j = 1;
9. While (all onlookers are assigned food sources)
Randomly generate ςk ∈ [0, 1] for each kth onlooker.
if (ςk < Pj)
Assign a randomly selected row of W to an onlooker.
Select another row randomly other than the previous one for finding new w,s for
ws using (3.20)
10. Evaluate fitness using (4.8) for w,s
if (fitness (w,s) > fitness (ws))
Replace ws by w,s and reset trial counter Ts to zero.
Increment k
else
Increment trial counter Ts
Increment j
End While (onlookers)
79
Table 4.4: General Parameters for Simulation of ACOParameter Value or Type
Initialization RandomAnt Colony Size 32Max. Iterations 500No. of Parameters 32Bits per Parameter 32Frequency Factor 2Evaporation Parameter 0.5Constant Q 1Termination Criterion Max. no. of iterations
11. SCOUT BEE PHASE
Determine the food sources whose trial counter exceeds the “limit ”value
if(Tindex > limit)
Find a random solution w,index to replace abandoned windexusing (3.22)
12. Evaluate fitness using (4.8) for w,index
13. Select the row with best fitness.
14. Go to Employed Bee Phase
15. End While (termination criteria)
4.7 ACO for Jammer Excision in CDMA
ACO searches for the optimal jammer excision filter weights. The parameters and their
values are given in Table 4.4. ACO is inherently discrete so the filter weights are encoded
into bits and then again decoded to real numbers for fitness evaluation. Ants decide their
choice of bits on the amount of pheromone. Flow chart of ACO algorithm for jammer
excision is shown in Figure 4.6. The steps of algorithm are given below.
80
Initialize W matrixrandomly
Launch new Iteration of AntsEncode to binary
Find Trans. Probab.
Find new solutions based on Trans.
Probability. Update Freq and Ph. Incr.
Decode binary to real. Evaluation of
each row of W. Identify best fitness
row of W
PheromoneDeposition
PheromoneEvaporation
Row of W having best fitness is wopt
End
Is termination criterion met ?
Figure 4.6: Flowchart of ACO algorithm for finding optimal weights of an Excision Filterfor CDMA
1. Initialize particles (ants) with initial weight matrix W with dimensions S×N with
random coefficients,
for i = 1 : iterations
for j = 1 : no of ants
2. Encode real solution jth solution wj into binary solution bj.Each real coefficient in
encoded into M binary bits. Therefore each binary solution consists of N×M bits.
3. Find transition probalities, new solution b′j, update frequencies f and and compute
pheromone ∆τ as follows:
81
for k = 1 : NM
4. Evaluate transition probability for the kth bit of jth solution using (3.25)
5. Based on the transition probability, decide transition from kth bit of bj solution to
kth bit b′j i.e. (0→ 0) or (0→ 1) if bj (k) = 0 or (1→ 0) or (1→ 1) if bj (k) = 1.
if bj (k) == 0 & b′j (k) == 0, f00 (k) = f00 (k) + 1, ∆τ00 (k) = Q
Fk,∆τ01 (k) = 0
end if
if bj (k) == 0 & b′j (k) == 1, f01 (k) = f01 (k) + 1,∆τ01 (k) = Q
Fk,∆τ00 (k) = 0
end if
if bj (k) == 1 & b′j (k) == 1, f11 (k) = f11 (k) + 1,∆τ11 (k) = Q
Fk,∆τ10 (k) = 0
end if
if bj (k) == 1 & b′j (k) == 0, f10 (k) = f10 (k) + 1,∆τ10 (k) = Q
Fk,∆τ11 (k) = 0
end if
end for
6. Update pheromone using (3.27) and (3.28)
7. Decode binary solution b′j into real solution w
′j
8. Evaluate fitness for w′j using (4.8)
end for
9. Find a final solution w′
f corresponding to minimum fitness.
end for
82
Chapter 5
Numerical Results and Discussions
5.1 Introduction
In this chapter, the numerical results for various heuristic algorithms for the problem
of jammer excision in DS-CDMA system are presented and computational complexity is
evaluated and compared.
5.2 Computational Complexity and Implementation
Issues
The computation of Wiener filter coefficients, involve calculation of inverse of the cor-
relation matrix R. As shown in the appendix A computational complexity of inverting
an N×N matrix by Gaussian Elimination leads to O(n3). Although Gaussian Elimina-
tion method is not optimal and there exists a method (Strassen’s method) that requires
only O(nlog2(7)
)= O (n2.807) operations for a general matrix. But the programming of
Strassen’s algorithm is so awkward, and often Gaussian Elimination is still the preferred
method. Complexity of LMS C(LMS) is function of iterations, i.e. C(LMS) = f (K). Each
iteration of LMS requires calculation of gradient and inverse of the correlation matrix R
for updating weights. Thus making it K times more complex than Wiener.
The computational complexity of the population based algorithms i.e PSO, GA, ABC
and ACO is C(PSO), C(GA) , C(ABC), C(ACO) respectively and approximately same because
no computational intensive mathematical operation is involved except evaluation of cost
function. Let us denote it by C(pop). Then C(pop) is a function of swarm/population
size S and number of iterations. i.e. C(pop) = f (S ×K). Although C(pop) is more in-
83
tensive than C(LMS), but population based techniques can be implemented on parallel
processing architectures making them most suitable when reduced convergence time is
the key design parameter. Population based algorithms do not necessarily require initial
guess for their convergence towards optimal performance. As already discussed, C(PSO),
C(GA) C(ABC), C(ACO) is comparable, among these, PSO is preffered over the other algo-
rithms.
0 5 10 15 2010
−4
10−3
10−2
10−1
100
Eb/N
0 (dB)
BE
R
OPTIMALPSONOFILTERAWGN
Figure 5.1: Bit Error Rate Performance of CDMA system
One of the key advantages of PSO is the ease of implementation due to simplicity.
Unlike computationally expensive matrix inversions and complex operators, PSO merely
consists of two straightforward equations (4.11) and (4.12) for weight updates and simple
decision loop to update the pbest and gbest.
5.3 Simulation and Numerical Results
In this section, simulation results are presented to show the performance of various al-
gorithms. In these simulations, number of users is 16, processing gain is 64, filter length
is 32, swarm size is 32, and number of iterations for PSO algorithm is 75. Figure 5.1
84
−10 −5 0 5 10 15
10−4
10−3
10−2
10−1
100
SIR (dB)
BE
R
OPTIMALPSOTIME FREQUENCYNOFILTER
Figure 5.2: BER performance with noise power being kept constant and varying inter-ference power.
shows the average BER performance of the system with varying bit energy and keeping
the interference power constant. PSO based excision filter achieves the performance as
that of a Wiener filter (optimal) with less computational complexity and ease of imple-
mentation. Performance is also shown for no excision filter and without jammer (NBI)
cases in order to provide reference. Jammer excision filters provide mitigation against
the jammer as evident when their performance is compared with the case of without
mitigation. Increasing the bit energy has almost no effect on performance in the without
mitigation case. Figure 5.2 shows the BER performance of the system with constant
noise power and varying interference power. It can be seen that PSO achieves the op-
timal Wiener filter performance. The performance of excision filter based on TFDs is
also shown. It is evident that PSO based filter outperforms the one based on TF mask-
ing. Mitigation against jamming is clearly evident when performance of excision filter
is compared with no mitigation scenario. Excision filters provide more than 12 dBs of
gain when their BER performance is observed at very low Signal to Interference Ratio
(SIR) values (i.e. in the presence of high power jammer), which is usually the case in a
85
0 100 200 300 400 500
10−1
100
101
102
No. of Iterations
Mea
n S
quar
e E
rror
(M S
E)
NEIW−PSORIW−PSOLDIW−PSOCFIW−PSOProposed−PSOOptimal
Figure 5.3: Convergence of fitness or objective function for different variants of PSO.
jamming scenario. Some performance degradation is observed only at relatively high SIR
values as excision of a low power jammer also removes part of the signal of interest. In
such a scenario a SIR threshold is decided beyond which excision filter is turned off and
received signal is directly used for detection. In this case SIR of 15dB is the threshold
point. The convergence rate of objective function (4.8) with the number of iterations for
different variants of PSO is shown in Figure 5.3. Initially MSE for RIW-PSO descends
sharply until 50 iterations but then stops converging at a value quite higher than the
optimal. NEIW-PSO and LDIW-PSO fall in first few iterations then slowly converge to
optimal after 200 and 320 iterations respectively. CFIW-PSO performs quite better and
converges in 150 iterations. GA performs similar to CFIW for the first 50 iterations but
then diverges to meet optimal after 300 iterations. Proposed PSO with tuned parameters
converge to optimal performance in just 75 iterations. At 50 iterations the performance
of proposed exciser is near optimal and all the other techniques have significantly higher
MSE for the underlying problem. These results have been obtained by averaging it over
many iterations. Figure 5.4 shows the comparison of all the heuristics based computa-
tional intelligence algorithms considered in the thesis for excising jammer. LMS achieves
86
0 100 200 300 400 50010
−1
100
101
102
Iterations/Generations
MS
E
LMSACOABCPSOGAOptimal Wiener
Figure 5.4: Convergence of fitness or objective function for various heuristic algorithms.
optimal performance by slowly converging after 300 iterations. ACO achieves near opti-
mal performance at 500 iterations. ABC shows better convergence rate than ACO and
achieves optimal value after 400 iterations. PSO converges fastest, in less than 100 it-
erations while GA achieves near optimal at 200 iterations and completely converge at
300 iterations. PSO is observed to perform the best amongst all the other considered
algorithms.
The frequency domain view of CDMA signal with jammer is shown in Figure 5.5.
The TF plot of narrowbannd jammer is shown in Figure 5.6. A notch filter is designed
for jammer excision using computational intelligence techniques. Figures 5.7, 5.8 and
5.9 displays the plot of magnitude response 10log10H(ω) versus normalized frequency for
multiple filters designed by optimal and nature inspired techniques. Figure 5.7 shows
the results after 50 iterations of algorithm. The optimal Wiener filter shows deep notch
at the frequency of NBI at 0.25π radians and for other frequencies its response is flat.
Nature inspired heuristics PSO, GA and ABC have not yet converged. These algorithms
have created notch at jammer frequency but it is not as deep as that of optimal and at
other frequencies their response is not flat causing considerable degradation of desired
87
0 0.2 0.4 0.6 0.8 10
50
100
150
200
250
300
Mag
nitu
de
Normalized Frequency
Figure 5.5: Frequency domain view of CDMA signal with jammer.
signal. In Figure 5.8 we observe that PSO has been able to achieve near optimal weights
with same position and depth of notch after 250 iterations while GA and ABC are still
converging towards the optimal. In Figure 5.9 we observe that after 500 iterations the
PSO has already achieved the same weights as that of optimal while GA and ABC have
achieved near optimal values as evident from its frequency domain view.
Among all these algorithms PSO is seen to outperform all the other algoritms and it
converges to the optimum in less than 100 iterations.
A broadband jammer like a chirp jammer as shown in Figure 5.10 is superimposed
on a CDMA signal. This type of jammer is treated in this thesis as an intantaneously
narrowband signal and same system model is used. This is achieved by taking short
intervals of signal over which the frequency of jammer does not change significantly.
Excision filter is designed for each interval.
88
Figure 5.6: Time Frequency domain view of CDMA signal with jammer.
5.3.1 Comparison with Existing Techniques
Computational Intelligence Techniques are iterative in nature therefore comparison on
the basis of number of iterations or convergence rate can be made with existing iterative
scheme like LMS. The convergence speed of LMS is shown in the Figure 5.4. PSO and
GA converge prior to LMS while ACO and ABC converge later for a single processor
implementation. These CI based techniqes can be implemented on parallel architectures
and their convergence rate can be speeded leaving LMS far behind as it is not eligible
for parallel computing. TFD based approaches are very robust against non-stationary
jamming scenario therefore the BER performance of TF Masking is compared with that
of proposed techniques, as shown in Figure 5.2. It is evident from the figure that pro-
posed techniques provide more than 2 dB of advantage in bit energy as compared to TF
Masking. Getting a concentrated TFD of received signal is a challenge and TFD has to
be calculated repeatedly for better results thus making it computationally intensive.
89
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9−30
−25
−20
−15
−10
−5
0
5
10
15
Normalized Frequency (×π rad/sample)
Mag
nitu
de (
dB)
Magnitude Response (dB)
PSO
GA
ABC
OPTIMAL
Figure 5.7: Filter visualization after 50 iterations.
5.3.2 Comparison between GA and PSO and ABC
The objective of this section is to statistically compare the performance of PSO,ABC
and GA, for the problem of jamming excision in CDMA. Although GA, ABC and PSO
have many common properties, there are some differences as well. Unlike GA, PSO does
not have operators such as crossover and mutation. ABC also uses mutation operator
for new solutions but have fewer control parameters than GA. In PSO, the individuals or
solutions called particles fly through the search space and they are led by current optimal
particle. These particles update themselves with the internal velocity and they also have
memory which is an important factor in implementing the algorithm. PSO algorithm
allows one-way sharing of information to others. GA uses selection, while PSO algorithm
does not, and thus has the advantage of saving a lot of time. In GA, chromosomes share
information with each other, and thus the whole population moves like a single group
towards an optimal area. ABC also makes a detailed search locally during the onlooker
bee phase, thus regions of search space with better fitness are thoroughly searched for
optimal solution in shorter time.
90
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9−25
−20
−15
−10
−5
0
5
Normalized Frequency (×π rad/sample)
Mag
nitu
de (
dB)
Magnitude Response (dB)
PSO
GA
ABC
OPTIMAL
Figure 5.8: Filter visualization after 250 iterations.
As far as the crossover operator is concerned, its effects often vary over a run. At the
beginning the population of solutions is randomly initialized. By applying the crossover
operator, the newly obtained chromosomes can vary in the search space. Some can be
situated near the solution; meanwhile others can go out from the search space. At the
end of a run, populations converged to the optimum solution, meaning that many, if
not all, of the chromosomes have similar structures. At this moment applying crossover
influences less the new chromosomes. This implies that the crossover probability should
be altered as the iterations progress. It has a higher value at the start of iterations
and gradually decreased to a small value till the end. The operation of crossover is not
present in PSO however path of a particle alters in a stochastic fashion towards its pbest
and the gbest. The particles that show behavior similar to crossover during search are
those which are in the middle of subswarms that have gathered around local minima and
the ones present between two consecutive global minima. Exploration of the middle area
between two prospective minima by PSO resembles crossover in GA. Generally, crossover
in GA operates on the randomly selected parents implying randomness in evolution of an
individual. In PSO, a particle does not exchange materials with other particle, but its
91
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9−20
−15
−10
−5
0
5
Normalized Frequency (×π rad/sample)
Mag
nitu
de (
dB)
Magnitude Response (dB)
PSO
GA
ABC
OPTIMAL
Figure 5.9: Filter visualization after 500 iterations.
move is influenced by the move of the other particle. In this way, the move of a particle
is influenced by its own previous best position and by the global best position. The effect
of mutation operator is opposite to that of crossover operator. Mutation has less impact
on the chromosome at the beginning of the run and a bigger effect at the end of the run.
This is because at the beginning the population is randomly generated and swapping a
weight now does not change the chromosome so evidently as swapping a weight at the
end of the run, when the population has converged to the optimum solution. That is
why, in general, it uses a relatively small value of the mutation rate at the beginning
and it is increased at the end. Because each particle has a velocity, PSO mutation-
like behavior is directional, with a kind of builtin momentum . The difference between
pbest and the present location has some of this same flavor, but the maximum velocity
is the same for all parameters. The selection operator of GA supports the survival of
the best chromosome. This selection operator can be implemented in many ways. In an
elitist strategy the chromosome with the best fitness value is always moved to the next
generation regardless of the selection used. All particles persist in PSO as members of
population during an entire run of iterations so selection is not employed in it. Among
92
the evolutionary algorithms PSO is the only one that does not include survival of the
best strategy that replaces worst performing members of population. The traversed path
of a particle shows its blood line in PSO. In ABC, random solution by a scout can replace
a the best one found over the iterations and is not saved for future iterations. In this
manner ABC is somewhat greedy in selection.
This comparison shows that PSO has more advantages than GA such as PSO is easy
to implement, take less time and there are few parameters to adjust. However, GA is
better in global search while PSO is better in local search. ABC like PSO has fewer
control parameters.
PSO has the same effectiveness (finding the true global optimal solution) as the
GA but with significantly better computational efficiency (less function evaluations) by
implementing statistical analysis and formal hypothesis testing. ABC has a very robust
local and global search mechanism.
5.3.3 Comments on ACO
The ACO is inspired by the foraging behaviors of ant colonies. At the core of this behavior
the indirect communication between the ants enables them to find short paths between
their nest and food sources. This characteristic of real ant colonies is exploited in ACO
algorithm to solve mainly discrete optimization problems. ACO is more applicable for
problems where source and destination are predefined and specific. While for jamming
excision, the optimal solution lies in a continuous multidimensional space. PSO, GA and
ABC are inherently suitable for jamming excision problem. An attempt is made to adapt
ACO for the underlying problem by converting the continuous space into a combinatorial
problem in which ants find shortest path among the bits, but due to a limited number
of bits for the representation of real numbers, ACO cannot achieve the performance of
other algorithms.
93
5.4 Conclusions
A jammer excision problem is presented as an optimization problem and several solu-
tions based on nature inspired algorithms are presented. Simulation results of all the
algorithms are compared with those of the optimum Wiener filter. Wiener filter involves
the calculation of inverse of a large matrix whose size depends upon the size of weight-
ing matrix. Consequently complexity increases exponentially with the increase in size
of weighting matrix. Among all the algorithms, PSO based algorithm shows excellent
performance and drastically reduces the computational complexity and simplifies imple-
mentation. We conclude that PSO outperforms all the algorithms. It is simple in concept,
easy to implement and computationally efficient. Unlike other heuristic techniques PSO
has a flexible and well-balanced mechanism to enhance and adapt to global and local
explorations abilities.
94
Figure 5.10: TF plot of CDMA signal with chirp jammer
95
Chapter 6
Conclusions and Directions for
Future Research
This chapter presents the main conclusions of this thesis and the future work possibilities.
The research works that have been presented in the previous chapters will be summarised
and concluded along with the overall achievement to fulfil the aims and objectives of the
research. After that, all the possible modification which could give moral or intellectual
benefit to the performance of the presented methodologies that are used for this work
will be discussed in details as the future work.
This research is focused on jammer excision in CDMA using computational intelli-
gence techniques that are capable to deal with such problems rather than on theoretical
developments. In this thesis, the literature review of computational intelligence tech-
niques such as PSO, GA, ABC and ACO are given. The majority of the research show
that a lot of improvement is achieved using computational intelligence techniques. Fur-
thermore, these techniques has played a main role in improving the performance of opti-
mization algorithms problem. In this research the overview of jamming excision problems
has been given in detail. The complexity of excision problem is illustrated. Several algo-
rithms have been developed such as PSO, GA, ABC and ACO to solve jammer excision
problem in CDMA that can be classified as complex problem. In fact, this complexity
is basically caused by objectives and the size of the search space. The results of these
algorithms demonstrated that they are working effectively where good results can be
determined.
Optimized Jammer Excision using non-conventional meta-heuristic based approach
has been presented for the first time according to the best of author’s knowledge. Several
96
variants of the PSO and basic models of other techniques like GA, ABC and ACO
have been applied for the first time to optimize a real-life jammer excision problem. The
proposed jammer excision techniques result in a significant reduction of complexity, while
keeping a near optimal performance.
6.1 Directions for Future Research
Following the investigations described in this thesis, a number of projects could be taken
up, involving improving and extending some parts of this work. In the following subsec-
tions, extending works are given based on the model function
• The heuristic algorithms can be analyzed for future enhancement such that new
research could be focused to produce better solution by improving the effectiveness
and reducing the limitations. More possibilities for dynamically determining the
best destination through ACO can be evolved and a plan to endow PSO with
fitness sharing aiming to investigate whether this helps in improving performance.
In future the velocity of each individual can be updated by taking the best element
found in all iterations rather than that of the current iteration only.
• Real time implementation of the system, testing, and validation can be part of the
future work. This work can be implemented in the industry. This work will verify
and validate the capacity of the system in real time. In this case, some parts of the
model may need setting or modification.
• Hybridization of feasible heuristics can be made to enhance their performance and
speed up convergence.
97
Appendix A
Gaussian Elimination Matrix
Inversion
A.1 Gaussian Elimination Algorithm
Gaussian Elimination algorithm is as follows [116]
1. for, i = 1 : n− 1 do steps 2-4
2. Find p, the smallest integer with ≤ p ≤ n and apk 6= 0 if no apk is found, no unique
solution
3. if p 6= k then {Ep ←→ Ei} % swap if needed
4. for, j = i+ 1 : n do steps 5 and 6
5. mji = aji/aii
6. Ej − mjiEi ←→ Ei % Elimination
7. if ann 6= 0, no unique solution, STOP
8. xn = an,n+1/aii % start of backward substitution
9. for, j = n− 1 : 1
xi =[ai,n+1 −
∑nj=i+1 ai,jxj/aii
]end
end
end
10. x is the solution
98
A.2 Computational Complexity
This section again refers to [116]. In step 5, n − i divisions are performed. In step 6:
The replacement Ej − mjiEi → Ei requires mji multiplied by each term Ei, resulting
(n− i) (n− i+ 1) multiplications. After this is completed, each term of the resulting
equation is subtracted from the corresponding term Ej. This requires (n− i) (n− i+ 1)
subtractions. Therefore for each i = 1 : n− 1, the operations required in Steps 5 and 6
are:
Mult/Div: (n− i) + (n− i) (n− i+ 1) = (n− i) (n− i+ 2)
Add/Sub: (n− i) (n− i+ 1)
As∑n
j=1 1 = n∑mj=1 j = m(m+1)
2∑mj=1 j
2 = m(m+1)(2m+1)6
therefor summing over i
Mult/Div:∑n−1
i=1 (n− i) (n− i+ 2) = (n2 + 2n)∑n−1
i=1 1− 2 (n+ 1)∑n−1
i=1 i+∑n−1
i=1 i2
=2n3+3n2−5n6
Add/Sub:∑n−1
i=1 (n− i) (n− i+ 1) = n3−n3
Now we go to the back substitution portion,
Steps 8 and 9:
Step 8: 1 division
Step 9: multiplies and adds for each summation term, then 1 subtract and 1 divide.
So the total operation count in Steps 8 and 9:
Mult/Div: 1+∑n−1
i=1 [(n− i) + 1] = n2+n2
Add/Sub:∑n−1
i=1 [(n− i− 1) + 1] = n2−n2
Total Operation count:
Mult/Div: 2n3+3n2−5n6
+ n2+n2
= n3+3n2−n3
Add/Sub: n3−n3
+ n2−n2
= 2n3+3n2−5n6
Therefore this algorithm is an O (n3) operation.
99
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