Adaptive Filters and Equalisers

The Kalman Filter as an IIR Equaliser and Limitations and Further Work, Appendix A The Fast Kalman Algorithm, The RLS Lattice Algorithm and Appendix C Circular and Linear Convolution.

Abstract

1 Introduction.- 1.1 Adaptive Signal Processing.- 1.2 The Adaptive Filter.- 1.3 Modes of Operation.- 1.4 Application of Adaptive Filters.- 1.5 Summary.- 2 Adaptive Fir Filter Algorithms.- 2.1 Introduction.- 2.2 Optimum Linear Estimation.- 2.2.1 The Optimum FIR Filter.- 2.2.2 FIR System Identification.- 2.3 Sampled Matrix Inversion.- 2.4 Least Squares Estimation.- 2.4.1 Recursive Least Squares.- 2.4.2 Data Windows.- 2.4.3 Fast Algorithms.- 2.4.4 Properties of the Least Squares Estimate.- 2.5 Stochastic Gradient Methods.- 2.5.1 The Least Mean Squares Algorithm.- 2.5.2 The Block Least Mean Squares Algorithm.- 2.6 Self-Orthogonalising Algorithms.- 2.6.1 The Sliding DFT Adaptive Filter.- 2.7 Summary and Complexity Comparison.- 3 Performance Comparisons.- 3.1 Introduction.- 3.2 System Identification.- 3.3 Channel Equalisation.- 3.4 Summary and Conclusions.- 4 A Self-Orthogonalising Block Adaptive Filter.- 4.1 Introduction.- 4.2 Theoretical Development.- 4.2.1 Comparison of Theory with Simulation.- 4.3 A Practical Algorithm.- 4.4 Computational Complexity.- 4.5 Simulation Results.- 4.6 Conclusions.- 5 The Infinite Impulse Response Linear Equaliser.- 5.1 Introduction.- 5.2 The Linear Equaliser.- 5.2.1 Structure of an IIR Equaliser.- 5.3 FIR and IIR Equaliser Performance.- 5.4 System Identification.- 5.4.1 Adaptive IIR Solutions.- 5.5 Conclusions.- 6 An Adaptive IIR Equaliser.- 6.1 Introduction.- 6.2 The Kalman Filter.- 6.3 The Kalman Filter as an IIR Equaliser.- 6.4 An Adaptive Kalman Equaliser.- 6.4.1 System Identification.- 6.4.2 Model Uncertainty.- 6.4.3 Verification of Compensation Technique.- 6.4.4 Comparison with an RLS FIR Equaliser.- 6.4.5 Computational Complexity.- 6.5 RLS System Identification.- 6.6 Conclusions.- 7 Conclusions.- 7.1 Summary.- 7.2 Limitations and Further Work.- Appendix A The Fast Kalman Algorithm.- Appendix B The RLS Lattice Algorithm.- Appendix C Circular and Linear Convolution.- References.