CODING AND EQUALISATION FOR FIXED-ACCESS WIRELESS SYSTEMS A Thesis presented for the degree of Doctor of Philosophy . In Electrical and Electronic Engineering at the University of Canterbury Christchurch, New Zealand by Katharine Ormond Holdsworth, B.E.(Hons), M.E. January 2000 ENGINEERING LIBRARY iK 5/ .1\728 ;; For my Parents 3 1 MAY 20aa ABSTRACT This Thesis considers the design of block coded signalling formats employing spectrally efficient modulation schemes. They are intended for high-integrity, fixed-access, wireless systems on line-of-sight microwave radio channels. Multi­ dimensional multilevel block coded modulations employing quadrature ampli­ tude modulation are considered. An approximation to their error performance is described and compared to simulation results. This approximation is shown to be a very good estimate at moderate to high signal-to-noise ratio. The effect of parallel transitions is considered and the trade-off between distance and the error coefficient is explored. The advantages of soft- or hard-decision decoding of each component code is discussed. A simple approach to combined decoding and equalisation of multilevel block coded modulation is also developed. This approach is shown to have better performance than conventional independent equalisation and decoding. The proposed structure uses a simple iterative scheme to decode and equalise multilevel block coded modulations based on decision feedback. System per­ formance is evaluated via computer simulation. It is shown that the combined decoding and equalisation scheme gives a performance gain of up to 1 dB at a bit error rate of 10-4 over conventional, concatenated equalisation and decoding. v VI CONTENTS ABSTRACT v ACKNOWLEDGEMENTS ri LIST OF FIGURES xiii LIST OF TABLES xvii GLOSSARY OF ABBREVIATIONS xix GLOSSARY OF MATHEMATICAL TERMS xxi Chapter 1 INTRODUCTION 1 1.1 General Introduction 1 1.2 System Goals . 8 1.3 Thesis Contents . 11 1.4 Thesis Contributions 12 1.4.1 Contributions to Multilevel Coding 13 1.4.2 Contributions to Combined Equalisation and Decoding 14 Chapter 2 BACKGROUND INFORMATION 15 2.1 Introduction.................. 15 2.2 Quadrature Amplitude Modulation (QAM) . 17 2.3 Pulse Shaping . 20 2.4 Channel Models. 24 VII 2.4.1 Additive White Gaussian Noise (AWGN) Channel. 25 2.4.2 Multipath Fading Channel . 27 2.4.3 Signal-to-Noise Ratio (SNR) 30 2.5 Equalisation ............ 32 2.6 Error Correcting Coding Principles 36 2.7 Linear Block Codes ........ 40 2.7.1 Reed-Muller Codes .... 46 2.7.2 Decoding Reed-Muller Codes 49 2.8 Coded Modulation . 52 2.8.1 Ungerboeck Set Partitioning. 54 2.8.2 Multidimensional Signal Constellations 57 2.8.3 Shaping Codes for Multidimensional Constellations 59 2.9 Literature Review ............... 62 2.9.1 Multilevel Coding Techniques .... 62 .2.9.2 Combined Equalisation and Decoding. 66 2.10 Summary ............ 69 Chapter 3 MULTILEVEL CODING 71 3.1 Introduction ........... 71 3.2 Multilevel Codes ........ 72 3.3 Encoding a Multilevel Block Code. 77 3.4 Decoding a Multilevel Block Code. 82 3.4.1 Decoding the First Level Block Code 83 3.4.2 Decoding Higher Level Block Codes. 86 3.5 Summary .................. 87 Chapter 4 PERFORMANCE EVALUATION: AWGN CHANNEL 89 4.1 Introduction................... 89 4.2 Performance of 96-QAM using Alternative Decoding Schemes 90 4.3 Approximation to Error Performance . 94 4.4 Analytical versus Simulated Performance . 96 4.4.1 96-QAM, 80-QAM and 64-QAM Constellations 97 Vlll 4.4.2 192-QAM and 128-QAM Constellations. 104 4.4.3 48-QAM and 32-QAM Constellations 106 4.4.4 24-QAM and 16-QAM Constellations 109 4.5 Summary ............ , .... , . 113 Chapter 5 COMBINED EQUALISATION AND DECODING 115 5.1 Introduction ............... 115 5.2 Conventional Equalisation and Decoding 116 5.3 Combined Equalisation and Decoding. 121 5.4 Summary . 126 Chapter 6 PERFORMANCE EVALUATION: COMBINED EQUALISATION AND DECODING 129 6.1 Introduction............................ 129 6.2 Performance of Conventional Equalisation and Decoding . .. 132 6.3 Performance of 64-QAM, 80-QAM and 96-QAM Constellations with Proposed Combined Equalisation and Decoding . .. 132 6.4 Alternative 64-QAM Scenarios using Combined Equalisation and Decoding . .. 138 6.5 Alternative 96-QAM and 80-QAM Scenarios using Combined Equalisation and Decoding. 141 6.6 Performance of the Alternative System Models. 146 6.7 Soft-Decision Decoding Higher Level Codes. 148 6.8 Performance using Alternative Channel Coefficients 152 6.9 Summary ....... 154 Chapter 7 CONCLUSIONS 157 7.1 Introduction ...... 157 7.2 Thesis Conclusions .. 158 7.3 Suggestions for Future Research 161 BIBLIOGRAPHY 165 IX j j j j j j j j j j j j j j j j j j j j j j j j x j j j j ACKNOWLEDGEMENTS I wish to thank the many people who have supported and encouraged me throughout my time as a Ph.D. student and for their contribution to my re­ search - both directly and indirectly. It has been my privilege to take part in this doctoral program. I am indebted to,· and would especially like to acknowledge, Professor Desmond P. Taylor, my supervisor at the University of Canterbury, who fa­ cilitated and guided my research. I very much appreciate his time, effort and unfailing enthusiasm, as well as his attentive proof-reading of this Thesis and the interim material. Professor Taylor also provided the funding to attend the following conferences - for which I am grateful: Globecom'98, Sydney, Australia; ISWC'99, Victoria, Canada; and ICC'99, Vancouver, Canada. My utmost thanks must also be given to my co-supervisor, Dr. Royce T. Pullman, Vice President Research and Development, Digital Microwave Corporation (DMC), Wellington - formally MAS Technology Ltd - for his guidance and careful editing of successive drafts of research papers and this Thesis. I am also grateful to Neville Jordan, who originally seeded the idea of undertaking a Ph.D. in conjunction with MAS Technology Ltd, for his ongoing interest. xi I wish to acknowledge and thank both the Foundation for Research, Science and Technology for providing me with a Graduates in Industry Fel­ lowship (GRIF) as well as DMC for their financial support. I am also grateful for the time I have spent based at DMC as part of the GRIF scheme - for the resources they provided and the interest and encouragement from my colleagues. My thanks must also go to two visitors to the Electrical and Electronic Engineering Department at the University of Canterbury: Professor Bill H. Tranter, visiting Erskine Fellow, for his initial guidance, encouragement and interesting technical discussions at the beginning of my work; and Dr. Wolf­ gang Gerstacker, visiting Post-Doctoral Fellow in the last few weeks of my research, whose infectious enthusiasm for this topic and technical discussions were invaluable. I would also like to thank the post-graduates and staff at the University of Canterbury with whom I have been associated, for helping to provide the stimulating environment in which to work. Finally, I would like to thank my family and friends - especially my wonderful parents who also proof-read my Thesis - for their ongoing support, love and encouragement. Katharine O. Holdsworth Xll LIST OF FIGURES 2.1 Block diagram of a communications system. .. .. 16 2.2 Square signal space constellations for several QAM schemes.. 19 2.3 Raised cosine filter characteristics for different roll-off factors. 22 2.4 AWGN channel or free space propagation model . 26 2.5 Block diagram of the AWGN channel. 26 2.6 Fixed-access line-of-sight multipath fading channel model. 27 2.7 Transmitter and channel block diagram. .......... 29 2.S Block diagram of a decision-feedback equaliser. 34 2.9 Trellis construction of the Reed-Muller block code R(l, 3). 51 2.10 Trellis constructions of two Reed-Muller block codes. 51 2.11 Set partitioning for a two-dimensional constellation. 56 2.12 Set partitioning for a four-dimensional constellation. 59 2.13 Two-dimensional constellations: 96-QAM, SO-QAM, 64-QAM. 61 2.14 A previously proposed joint coding and DFE receiver model.. 69 3.1 Block diagram of staged encoder structure for a multilevel code. 74 3.2 Block diagram of staged decoder structure for a multilevel code. S3 4.1 Performance of 96-QAM: variations in methods for decoding C 1 . 92 4.2 Performance of 96-QAM: soft-decision trellis decoding C1 and C2 • 93 4.3 Performance of coded 96-QAM, SO-QAM and 64-QAM. .. 99 4.4 Performance of 96-QAM utilising alternative component codes. 100 4.5 Performance of SO-QAM utilising alternative component codes. 102 4.6 Performance of 64-QAM utilising alternative component codes. 103 X111 4.7 Performance of 192-QAM and 12S-QAM utilising alternative component codes. .. 105 4.S Performance of 4S-QAM and 32-QAM utilising alternative com­ ponent codes. .. lOS 4.9 Ungerboeck set partitioning of 24-QAM. .. 110 4.10 Performance of 24-QAM and 16-QAM utilising alternative com­ ponent codes. .. 112 5.1 Block diagram of conventional, concatenated equalisation and hard-decision decoding. ., 117 5.2 Block diagram of conventional, concatenated equalisation and soft-decision decoding. .. l1S 5.3 Block diagram of an iterative combined DFE and multilevel block decoding structure. .. 122 6.1 Performance of 64-QAM: unequalised and coded; equalised and uncoded; conventionally equalised and soft-decision decoded.. 133 6.2 Performance of coded 64-QAM using iterative combined equal­ isation and decoding. Case one component codes. .. 134 6.3 Performance of coded SO-QAM using iterative combined equal­ isation and decoding. Case one component codes. ., 136 6.4 Performance of coded 96-QAM using iterative combined equal­ isation and decoding. Case one component codes. .. 137 6.5 Performance of coded 64-QAM using iterative combined equal- isation/ decoding.