Efficient adaptive complex filtering algorithm with application to channel equalisation

Abstract

The paper describes a means of efficiently implementing an adaptive complex transversal filter. Three real-coefficient filter sections are used to realise each transversal filter section of the complex equaliser, thus using one less filter than a conventional realisation. An adaptive algorithm is developed, in a manner similar to the least mean square algorithm, which allows the three filters to be trained independently and in parallel using real valued arithmetic. In this way, throughput can be maintained, whilst reducing the number of multipliers in both the filter and coefficient update sections by 25%. Using independence theory, it is demonstrated that the three filters converge to a solution consistent with the optimal Wiener-Hopf solution. The convergence speed is characterised in terms of the complex input data stream. The transient behaviour of the algorithm is examined using a simulation of a channel equaliser and is supported by analysis.