Evolving Optimal IIR and Adaptive Filters

Abstract

In this thesis, current digital filter design techniques are critically reviewed and problems associated with computational cost, complexity, frequency response and speed of convergence, identified. Based on this, a globally optimal, fine- tuned and efficient evolutionary hybrid technique has been developed to automate and optimise infinite impulse response (HR) and adaptive filter design. The proposed hybrid design approach employs an evolutionary algorithm (EA) as a global search tool and a least mean square (LMS) algorithm, whenever appropriate, as a fine-tuner. This permits optimal and real-time tracking of time varying changes in nonstationary environments as widely encountered in telecommunications. In the development, various improvements on existing algorithms are made, including those on components of EAs, LMS algorithm and the filter structures. The aims are to be able to evolve direct form HR structures using simple stability monitoring techniques, to improve local hue-tuning performance and to avoid premature convergence. To evolve complex phenotype chromosomes that are needed by complex HR. filters, a novel method of crossover operation is developed. This is a variation of the standard uniform crossover in which the split points are considered to combine uniquely as indivisible floating-point complex valued genes. The split-point crossover operation produces more new members than the standard crossover operation, and hence provides a faster rate of convergence and avoids premature convergence. The EAs have been particularly designed for small population sizes and to reduce premature convergence, a new operator is designed to introduce new members into the population during evolution. Two techniques are investigated in the design of linear adaptive HR digital filters, namely, the pole design method and the coefficient design method. The pole design method provides filter stability throughout the genetic search without requiring a variety of stability monitoring techniques. The coefficient design method uses simple stability guaranteeing techniques, which also improves the rate of convergence of the EAs. With the hybrid technique, complex-coefficient filters have been designed successfully and globally optimal and adaptive filters have been achieved. The developed methodologies and designs are verified using higher order complex HR systems and, for adaptation, inverse system modelling that is synonymous with channel equalising filters operating in multipath environments. Here adaptive complex parameters become possible to equalise amplitude and phase distortions of the received signals. Various stability-ensuring techniques are investigated extensively and their convergence performances are compared with the proposed method. The proposed hybrid, global and fine design technique is applied to solve adaptive channel equalisation and noise cancellation problems commonly existing in telecommunications