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Publication Summary and Abstract

Mitchinson B. (2002), Iterative Kernel Techniques in Application to Channel Equalisation, PhD Thesis, The University of Sheffield.

High data-rate digital transmission is facilitated by accurate equalisation at the receiver. Theoretical results indicate that non-linear receivers may substantially outperform linear receivers. Recent work has highlighted the potential of using Mercer kernels in conjunction with a variety of learning algorithms to perform non-linear regression and classification in a computationally efficient way. In this work, we investigate the performance of a family of kernel-based iterative techniques in application to the channel equalisation problem. In the case of stationary channels, we focus on the Kernel Adaline, a non-linear extension to Widrow's and Hoff's Adaline. For non-stationary channels, the Kernel Least Mean Square (LMS) rule (a closely related algorithm) is more appropriate owing to its ability to learn adaptively in a real-world environment. Owing to its considerable complexity, however, we introduce a reduced complexity approximation to the same, Fast Kernel LMS, and focus on this latter in application to the equalisation problem. For the stationary case, we show that, on short to medium length channels, the Kernel Adaline can perform comparably to the Bayesian Equaliser, which is derived directly from Bayesian decision theory to match the structure of the ideal receiver for the time-dispersive channel model used. For the non-stationary case, we demonstrate that Fast Kernel LMS can outperform adaptive linear equalisers, both in terms of error rate performance and tracking ability. Alongside, we see a strong case being made for the usefulness of both of these algorithms in the wider context of learning problems. Alongside this work, inspired by the investigation, we devote a little space to investigation of a new large margin linear technique which we consider a potential direct replacement for the currently popular LMS algorithm.
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