Equalizers are present in all forms of communication systems. Neuro-Fuzzy Equalizers for Mobile Cellular Channels details the modeling of a mobile broadband communication channel and designing of a neuro-fuzzy adaptive equalizer for it. This book focuses on the concept of the simulation of wireless channel equalizers using the adaptive-network-based fuzzy inference system (ANFIS). The book highlights a study of currently existing equalizers for wireless channels. It discusses several techniques for channel equalization, including the type-2 fuzzy adaptive filter (type-2 FAF), compensatory neuro-fuzzy filter (CNFF), and radial basis function (RBF) neural network.
Neuro-Fuzzy Equalizers for Mobile Cellular Channels starts with a brief introduction to channel equalizers, and the nature of mobile cellular channels with regard to the frequency reuse and the resulting CCI. It considers the many channel models available for mobile cellular channels, establishes the mobile indoor channel as a Rayleigh fading channel, presents the channel equalization problem, and focuses on various equalizers for mobile cellular channels. The book discusses conventional equalizers like LE and DFE using a simple LMS algorithm and transversal equalizers. It also covers channel equalization with neural networks and fuzzy logic, and classifies various equalizers.
This being a fairly new branch of study, the book considers in detail the concept of fuzzy logic controllers in noise cancellation problems and provides the fundamental concepts of neuro-fuzzy. The final chapter offers a recap and explores venues for further research. This book also establishes a common mathematical framework of the equalizers using the RBF model and develops a mathematical model for ultra-wide band (UWB) channels using the channel co-variance matrix (CCM).
•Introduces the novel concept of the application of adaptive-network-based fuzzy inference system (ANFIS) in the design of wireless channel equalizers
•Provides model ultra-wide band (UWB) channels using channel co-variance matrix
•Offers a formulation of a unified radial basis function (RBF) framework for ANFIS-based and fuzzy adaptive filter (FAF) Type II, as well as compensatory neuro-fuzzy equalizers
•Includes extensive use of MATLAB® as the simulation tool in all the above cases

The purpose of a communication system is to transfer information between two separate points over some medium in the presence of disturbances or dis-tortions such as noise and dispersion. This distortion is manifested in the time domain as pulse dispersion and is labeled as Inter-Symbol Interference (ISI). As data rates increase in modern digital communication systems, ISI becomes an inevitable consequence of the dispersive nature of band-limited propaga-tion channels. The receiver must include an equalizer to mitigate the effects of ISI. Thus, an equalizer undoes the distortion that the signal is subjected to while it propagates through the channel. Needless to say, equalizers are present in all forms of communication systems: from Plain Old Telephones Systems (POTS) to Co-axial communication systems, to RF and Microwave commu-nication systems, to Optical Fiber communication systems, and to wireless mobile communication systems. The function of the equalizer is to combat the ISI and to utilize the available spectrum most efficiently. Equalizers are cascaded to almost all kinds of channels, right from telephone lines to radio and optical fiber channels, to make the channel performance optimal. Ideally, an equalizer, when cascaded to the end of a channel, will make it behave like an ideal channel, one which will not distort the signals in any manner. In the case of mobile cellular channels, which are generally considered to be Linear Time Variant (LTV), the design of equalizers is not a trivial problem. Moreover, the above said channel has certain uncertainties in its behavior, which need to be tackled in the equalizer design. The Co-Channel Interference (CCI) due to frequency reuse and Adjacent Channel Interference (ACI) due to spectral leakage both contribute to the reduction in the overall Signal-to-Interference-Noise-Ratio (SINR) in mobile cellular channels.
In applications in which the Channel Impulse Response (CIR) is un-known and no training sequence is available, the equalizer must be com-puted/updated blindly from the received signal and knowledge of the statistics of the data source alone. A common approach in continuous transmission sys-tems is to blindly update a Linear Equalizer (LE) using the Constant Modulus Algorithm (CMA), and then switch to a Decision Directed (DD) mode when the Symbol Error Rate (SER) is low enough. Switching to a DD-based decision feedback equalizer (DFE) is also possible and desirable.
Modeling and simulation of mobile cellular channels have been success-fully carried out by several researchers. Various interference patterns including Ricean/Rayleigh fading, co-channel and adjacent-channel interferences can be found in the literature. This book is intended to discuss the modeling of the mobile cellular channel used in an indoor environment, where the channel can be taken to be of the slow fading type. The study is focused to consider the noise contributions from various sources, when they fall within the spectrum of the frequencies used in cellular telephony, and then to design an equalizer which will mitigate the noise present due to CCI and ACI. When the channel over which data is sent is unknown, which is common, one must employ adap-tive equalization. The DFE is one such adaptive equalizer. It is known that the DFE generally outperforms the LE for the same hardware complexity. Further, as indicated earlier, when the channel characteristics show Rayleigh/Rice an fading (due to the presence of a multipath), ACI and CCI, realization of equal-izers based on neuro-fuzzy techniques seems to be the most appropriate option for the mobile cellular channel.
Linear space-time equalization is shown to be effective in coping with the complicated propagation conditions for wireless broadband communication in an industrial indoor environment. This is demonstrated by realistic simula-tions that use a real channel sounder for modeling the influence of the radio channel. Industrial indoor environments like large factory halls typically show a complicated radio channel because of the presence of many reflecting ob-jects. This results in wide delay spreads and a considerably changing channel for a moving mobile unit. There exist a number of options to overcome the difficulties of heavy multipath propagation.
In this book, the mobile channel is modeled as a linear time variant chan-nel. Further, the issues in the design of the neuro-fuzzy channel equalizer to null the effects of fading are investigated. One of the objectives of this work is to establish the fact that, within an acceptable bound, the mobile cellular channel is LTV. Another major objective of the book is to investigate the suit-ability of neuro-fuzzy models as applicable to the analysis and design of mobile cellular channel equalizers. Three solutions to the channel equalizer problem are investigated in this work. First, a type-2 Fuzzy Adaptive Filter (FAF) for the above purpose is considered. Simulations show that it performs bet-ter than a type-1 FAF or Neural Network Classifier (NNC) equalizer. Then the use of an Adaptive Network-Based Fuzzy Inference System (ANFIS) is investigated. Last, a Compensatory Neuro-Fuzzy Filter (CNFF) for channel equalization is considered. Subsequently, an attempt is made to bring the var-ious equalizer realizations in the study under the generic framework of a radial basis function (RBF) neural network. Further, a novel modular approach for the simulation and design of equalizers for Nonlinear Time-Variant (NL TV) channels is proposed. A suitable model for an Ultra-Wide Band (UWB) chan-nel and its equalization is the last goal.
The contributions of this work are the establishment of the fact that the mobile cellular channel can indeed be modeled as an LTV channel, in general, with a Rayleigh distribution for the channel coefficients. It is shown that FAF-,CNFF-, and ANFIS-based equalizers are capable of achieving desired SNR in the presence of CCI and ACI. It is also shown that the channel equalizers based on type-2 FAF, CNFF, and ANF IS could be brought under the generic framework of RBF Neural Networks. A detailed performance evaluation of the equalizers is made. And, finally, a modular approach for the simulation and modeling of NLTV channels is proposed. In the beginning it was men-tioned that mobile channels are considered to be LTV. However, when the transmitter stages are driven to their nonlinear regions, the channel needs to be modeled as nonlinear (to account for the nonlinearities thus introduced to the transmitted signal) and Time Variant (NLTV). The modular approach in combating ISI is to cascade an adaptive nonlinear preprocessor filter and lin-ear adaptive equalizer, which simplifies the equalizer design. It is also shown that the ANFIS model can be successfully adapted to equalization of UWB channels.
The book is organized thus. Chapter 1 gives a brief introduction to channel equalizers. Chapter 2 begins with a study of the nature of mobile cellular channels with regard to the frequency reuse and the resulting CCI. Several channel models available for mobile cellular channels are considered and the one best suited for our system is selected. It is established that the mobile indoor channel is a Rayleigh fading channel. The channel equalization problem is presented. It is succeeded by a study of various equalizers for mobile cellular channels. It starts with a discussion on conventional equalizers like LE and DFE using a simple LMS algorithm and transversal equalizers. Then channel equalization with neural networks and fuzzy logic is discussed, and various equalizers are classified.
In Chapter 3, the concept of fuzzy logic controllers in noise cancellation problems is considered in detail. This being a relatively new branch of study, the fundamental concepts of neuro-fuzzy systems are given and FAFs that are used in a variety of applications are discussed. Type-2 fuzzy sets are introduced and their advantages in overcoming certain short falls of conventional fuzzy sets (type-1 fuzzy sets) in dealing with real life problems are discussed. The performance of the type-2 fuzzy adaptive filter (FAF-II) is compared with the type-1 fuzzy adaptive filter (FAF-I) and NNC for the same purpose.
In Chapter 4, the ANFIS-based channel equalizer for mobile cellular and UWB channels is treated in detail. Contemporary literature provides sufficient information on the statistical properties of mobile cellular channels. The train-ing of the ANFIS-based channel equalizer is based on the abovementioned statistics. As the ANFIS synergic ally combines the learning capability of the neural network and the decision-making capability (in presence of noise) of the fuzzy system, it can outperform the FAF as well as neural network-based channel equalizers.
In Chapter 5, the CNFF is considered for equalization. It is shown that the performance of the CNFF is well suited for the equalization of nonlinear channels.
A generic framework of RBF neural networks for the three filter structures developed in previous chapters (Chapters 3, 4, and 5) is established in Chapter 6. It is shown that under certain conditions, the type-2 FAF (FAF-II), CNFF, and ANFIS behave as an RBF network. A novel modular approach for the simulation and design of nonlinear time-variant channels is proposed in Chap-ter 7. It is established that the modular approach is the most appropriate one to model transmitter nonlinearities.
In Chapter 8, we discuss orthogonal frequency division multiplexing (OFDM) and spatial diversity techniques. Equalizers used for OFDM channels are considered here. In Chapter 9, the work done is summarized and venues for further research are explored. As mobile cellular technology is fast moving toward higher frequency bands and as there is a lot of scope for Multi-Input Multi-Output (MIMO) systems and Local Multi-Point Distribution System (LMDS) technology, it is expected that the techniques developed in Chapters 4, 5, 6, 7, and 8 can be applied there as well. Pointers on possible extensions of the work done are also given.
All the simulations in this book were written and tested in MATLAB® Version R2012b, and are bug free. For detailed product information on MATLAB®, please contact The Math Works Inc, Corporate Headquarters, United States of America:
The MathWorks, Inc.
3 Apple Hill Drive
Natick, MA 01760-2098 USA
Tel: 508-647-7000
Fax: 508-647-7001
E-mail: info@mathworks.Com
Web: www.mathworks.com

List of Figures xiii

List of Tables xv

Preface xvii

Acknowledgments xxi

List of Abbreviations xxiii

1 Introduction 1

1.1 Introduction 1

1.2 Need for Equalizers 2

1.3 Review of Contemporary Literature 3

1.4 Major Contributions of the Book 5

Further Reading 5

2 Overview of Mobile Channels and Equalizers 9

2.1 Introduction 9

2.2 Mobile Cellular Communication System 9

      2.2.0.1 Call Initiation 10

      2.2.0.2 Frequency Reuse 11

      2.2.1 Co-Channel Interference and System Capacity 12

      2.2.2 Adjacent Channel Interference 14

      2.2.3 Digital Modulation Types and Relative Efficiencies 15

2.3 Fading Characteristics of Mobile Channels 16

      2.3.0.1 Tapped Delay Line (TDL) Channel Model 17

      2.3.0.2 Rayleigh and Ricean Fading Models 17

2.4 Channel Models 18

      2.4.1 Suburban Path Loss Model 18

      2.4.2 Urban (Alternative Flat Suburban) Path Loss Model 19

      2.4.2.1 Multipath Delay Profile 20

      2.4.2.2 RMS Delay Spread 21

      2.4.2.3 Fade Distribution, K-Factor 21

      2.4.2.4 Doppler Spectrum 22

      2.4.2.5 Spatial Characteristics, Coherence Distance 22

      2.4.2.6 CCI 23

      2.4.3 Multiple Input Multiple Output (MIMO) Matrix Models 23

      2.4.4 Modified Stanford University Interim (SUI) Channel Models 23

      2.4.5 FCC Model 25

      2.4.6 ITU-R Models 25

      2.4.7 Free Space Model 26

      2.4.8 Two-Ray or Dual Slope Model 26

      2.4.9 Wideband Tapped Delay Line Channel Model 26

      2.4.10 Conclusions on Model Selection 26

2.5 Classification of Equalizers 27

      2.5.1 A Note on Historical Development 27

      2.5.2 Classification of Adaptive Equalizers 28

      2.5.2.1 Nonlinear Equalizers 30

      2.5.3 Optimal Symbol-by-Symbol Equalizer 30

      2.5.4 Symbol-by-Symbol Linear Equalizers 32

      2.5.5 Block FIR Decision Feedback Equalizers 34

      2.5.6 Symbol-by-Symbol Adaptive Nonlinear Equalizer 35

      2.5.6.1 RBF Equalizer 35

      2.5.6.2 Fuzzy Adaptive Equalizer (FAE) 37

      2.5.6.3 Equalizer Based on Feedforward Neural Networks 38

      2.5.6.4 A Type-2 Neuro Fuzzy Adaptive Filter 39

      2.5.7 Equalizer Based on the Nearest Neighbor Rule 39

2.6 Conclusion 40

Further Reading 40

3 Neuro-Fuzzy Equalizers for Cellular Channels 45

3.1 Introduction to Neuro-Fuzzy Systems 45

      3.1.1 Fuzzy Systems and Type-1 Fuzzy Sets 46

      3.1.2 Type-2 Fuzzy Sets 46

      3.1.2.1 Extension Principle 46

      3.1.3 Operations on Type-2 Fuzzy Sets 48

3.2 Type-2 Fuzzy Adaptive Filter 49

      3.2.1 TE for Time-Varying Channels 51

      3.2.1.1 Designing the Type-2 FAF 55

      3.2.1.2 Simulations 56

      3.2.1.3 Observations 56

      3.2.2 DFE for Time-Varying Channel Using a Type-2 FAF 59

      3.2.2.1 Design of a DFE Based on a Type-2 FAF 5

      3.2.2.2 Simulations 62

      3.2.2.3 Observations 62

      3.2.3 Inferences 62

3.3 Adaptation of the Type-2 FAF for the Indoor Environment 65

      3.3.1 Log–Distance Path Loss Model 65

      3.3.2 Ericsson Multiple Breakpoint Model 65

      3.3.3 Attenuation Factor Model 65

      3.3.4 DFE for an Indoor Mobile Radio Channel 66

      3.3.4.1 Channel Equation 66

      3.3.5 Co-Channel Interference Suppression 69

3.4 Conclusion 69

Further Reading 70

4 ANFIS-Based Channel Equalizer 73

4.1 Introduction 73

4.2 Methods of Channel Equalizer Analysis and Design 74

      4.2.0.1 FIS 75

      4.2.0.2 ANFIS 77

      4.2.1 ANFIS Architecture and Functional Layers 78

      4.2.1.1 Node Functions 79

4.3 Mobile Channel Equalizer Based on ANFIS 80

      4.3.1 Simulation of a Channel Equalizer Using MATLAB® 80

      4.3.2 Description of the ANFIS-Based Channel Equalizer 82

      4.3.3 Results of Simulations 85

      4.3.4 Interpretation of Results and Observations 102

4.4 Equalization of UWB Systems Using ANFIS 103

      4.4.1 Introduction to UWB 103

      4.4.2 Conventional Channel Models for UWB 104

      4.4.2.1 The Modified SV/IEEE 802.15.3a Model 105

      4.4.2.2 The 802.15.4a Model for High Frequencies (4a HF) 105

      4.4.2.3 The 802.15.4a Model for Low Frequencies (4a LF) 105

      4.4.2.4 Channel Covariance Matrix (CCM) Formulation 106

      4.4.2.5 Simulation of an ANFIS Equalizer for UWB Based on CCM 107

      4.4.3 Conclusions on an ANFIS-Based Equalizer for UWB 110

4.5 Conclusion 110

Further Reading 111

5 Compensatory Neuro-Fuzzy Filter (CNFF) 113

5.1 Introduction 113

5.2 CNFF 114

      5.2.1 Outline of the CNFF 114

      5.2.2 Details of Compensatory Operations 115

5.3 Structure of CNFFs 117

      5.3.1 Online Learning Algorithm 118

      5.3.1.1 Structure Learning Algorithm 118

      5.3.1.2 Parameter Learning Algorithm 119

      5.3.1.3 A Digital Communication System with AWGN and CCI 119

      5.3.1.4 Channel Models and Simulation 121

      5.3.2 Simulation Results 121

5.4 Conclusion 122

Further Reading 123

6 Radial Basis Function Framework 125

6.1 Introduction 125

6.2 RBF Neural Networks 126

      6.2.1 Review of Previous Work 126

      6.2.1.1 Motivation for the Unified Framework 127

6.3 Type-2 FAF Equalizer 128

6.3.0.1 A Simplified Mathematical Formulation for FAF-II 129

6.4 CNFF 129

6.4.0.1 A Mathematical Formulation of CNFF 131

6.5 ANFIS-Based Channel Equalizer 131

      6.5.0.1 A Mathematical Formulation of the ANFIS Equalizer 132

      6.5.0.2 Simulations 133

6.6 Conclusion 140

Further Reading 141

7 Modular Approach to Channel Equalization 143

7.1 Introduction 143

7.2 Nonlinear Channel Models 145

7.3 Nonlinear Channel Equalizers 146

      7.3.1 Nonlinear Equalizers Based on RBF Neural Network 146

      7.3.2 Nonlinear Equalizers Based on MLPs 163

      7.3.3 Nonlinear Equalizers Based on FAFs 164

7.4 A Modular Approach for Nonlinear Channel Equalizers 164

7.5 Simulation Results 165

7.6 Conclusion 165

Further Reading 166

8 OFDM and Spatial Diversity 169

8.1 Introduction 169

8.2 CDMA 170

      8.2.1 Processing Gain of CDMA Systems 171

      8.2.2 Generation of CDMA 171

      8.2.3 CDMA Forward Link Encoding 172

      8.2.4 CDMA Reverse Link Decoding 173

8.3 COFDM 173

      8.3.1 OFDM Transmission and Reception 174

      8.3.1.1 Adding a Guard Period to OFDM 175

8.4 Conclusion 176

Further Reading 177

9 Conclusion 179

9.1 Introduction 179

9.2 Major Achievements of the Work 180

9.3 Limitations of the Work 181

9.4 Scope for Further Research 181

Further Reading 182

Index 183

K.C. Raveendranathan holds a bachelor’s degree in electronics and communication engineering, masters in electrical communication engineering, and Ph.D. in computer science and engineering. He worked in BEL Bangalore prior to joining College of Engineering Trivandrum, as a faculty. Now he is working as principal and professor in LBS Institute of Technology for Women Poojappura, Trivandrum, Kerala, India. Raveendranathan has over 25 years of teaching experience in various reputed government engineering colleges in Kerala. He has published over 12 papers in national/international conferences and journals and guided over a dozen UG and PG theses. He has also authored three textbooks. He is a life member of ISTE, Life Fellow of IETE, Life Fellow and Chartered Engineer of IE (India), and a senior member of IEEE.

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