Adaptive equalisation of time varying channels

This thesis is concerned with solving the problem of equalisation of digital signals which have been passed through a time varying channel and corrupted by additive white noise. The approach used in this thesis to solve this problem is by the use of a robust filter structure rather than a tailored adaptation method. The reason for applying this approach is that, most adaptive algorithms such as the least mean square (LMS) and the recursive least squares (RLS) algorithms make the assumption that the input signals are statistically stationary. In the channel condition considered here, this assumption is violated and neither algorithm as a result works particularly well. Traditional attempts to overcome this problem have focused on modelling an assumed underlying dynamics of the channel distortion mechanism. The problem with these structures is that they are not robust in the case where the channel time variations do not match the assumed underlying dynamical model and the algorithms tend to be complex in nature. Consequently, two filter structures have been proposed in this thesis to tackle this problem. One structure known as the order statistic equaliser uses a combination of temporal and order statistic information of the received data sequence. The other structure, which has been named as the amplitude banded equaliser, uses a combination of temporal and amplitude information as opposed to the order statistics of the first structure. Both these structures have the advantage that they do not rely explicitly on the channel model. It has been concluded from the computer simulation studies conducted here that the tracking performance of the order statistic equaliser outperforms the linear equaliser structure when both are operating on the same time varying channel. The new amplitude banded structure, however, outperforms the order statistic equaliser in this situation.