Decision-feedback equalisation with fixed-lag smoothing in nonlinear channels.

Abstract

This thesis is concerned with an aspect of the field of digital signal processing, namely, the application of fixed-lag smoothing (FLS) to decision-feedback equalisation (DFE). The resultant algorithm was introduced in a recent paper and is termed herein the Fixed-Lag-Smoothing Decision-Feedback Equalisation (FLSDFE) algorithm. The motivation for studying the FLSDFE algorithm is that it may potentially improve the performance of a standard DFE algorithm, providing more reliable digital communication and data storage. This thesis extends previous results by applying the FLSDFE algorithm to linear and nonlinear channels, of minimum- or nonminimum-phase. In chapter 2 the FLSDFE formulae are derived for two classes of nonlinear digital communication channel, both described by truncated Volterra series. Section 2.3 treats the case of MPSK and MQAM signalling, and section 2.4 treats the case of BPSK signalling. The discrete probability distribution function of the FLSDFE output estimator is given in each case. Chapter 3 introduces state space models that capture the exact transient dynamics of the FLSDFE algorithm. The atomic model was introduced by other authors earlier, but a suboptimal aggregation of the atomic model is given that is closely linked to an existing steady-state model. Connections are shown between the state space models and the theory of integer partitions, as well as between linear recurrence relations that generalise that of the Fibonacci series. Examples of the performance of the FLSDFE algorithm are provided in chapter 4. Two underwater-acoustic communication channels are simulated, and it is shown that the FLSDFE performs well there, giving lower bit error rates than the DFE alone. Generic channel models, both linear and cubic, minimum- and nonminimum-phase, were then simulated. These showed some peculiar characteristics of the FLSDFE algorithm's behaviour. In particular, using the steady-state models of chapter 3, we observe a pseudo-resonance with increasing SNR (that is, the existence of an optimum SNR) - this is related to the presence of previous equalisation errors. As a caveat to the blind use of the FLSDFE over the DFE, we illustrate that it may be necessary to determine the optimum smoothing lag to use before applying the FLSDFE algorithm, especially on difficult nonlinear channels. On such channels, increasing the lag beyond this optimum may produce worse equalisation performance than at the optimum lag. Despite this word of caution, however, the FLSDFE seems to provide a robust improvement over the DFE across a broad range of channels.