| Summary: | This thesis describes the use of methods derived from Bayesian statistics on the problem of blind equalisation of communications channels, although much of this work is applicable to the more general problem of blind deconvolution. In order to allow general models to be incorporated, numerical methods are used; the focus is on <I>Markov chain Monte Carlo </I>(MCMC) methods for processing of blocks of data and the use of <I>particle filters </I>for sequential processing. In order to obtain the best performance using MCMC, the choice of the Markov chain needs tailoring to the application in hand. The use of joint sampling of all the states (transmitted data sequence) and reversible jump moves to combat delay ambiguity are proposed. The use of particle filters is still in its infancy, and much of the focus is on the development of strategies to improve its applicability to real problems. It is well known that fixed-lag methods may be used to great effect on Markovian models where later observations can provide information about states in the recent past. Methods of performing fixed-lag simulation for incorporation into particle filters are described. The use of data windowing on fixed parameter systems allows regeneration of the parameters at each time-step without having excessive demands on storage requirements. In certain cases it is difficult to perform the updating when a new data point is received in a single step. The novel concept of introducing intermediate densities in a manner akin to simulated annealing between time steps is described. This improves robustness and provides a natural method for initialisation. All of these techniques are demonstrated in simulations based upon standard models of communications systems, along with favourable comparisons to more conventional techniques.
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