Tracking performance of RLS algorithms in WSSUS channels

Abstract

Adaptive algorithms are widely used for estimation of linear time-varying systems, such as communication channels. Their tracking performance depends on the level of noise, characteristics of time variations, and the algorithm parameters. Optimizing these parameters and predicting the algorithm performance is an important task. In this paper, we present an approach for analysing the tracking performance of recursive least squares (RLS) adaptive algorithms in channels with time variations described as wide-sense stationary uncorrelated scattering (WSSUS) random processes characterised by a power spectral density (PSD). We focus on exponential RLS and sliding-window RLS (SRLS) algorithms, for which general formulas for the mean square deviation (MSD) as a measure of the tracking performance are obtained in terms of spectral moments of the PSD. As examples, they are specified for random processes with uniform, Jakes' and autoregressive PSDs. These results are further generalized to RLS algorithms with delays, e.g. processing delays or delays introduced in non-causal adaptive RLS algorithms, and to the SRLS-L algorithm with approximation of channel time variations using Legendre polynomials. Numerical examples show good match between the analytical MSD and simulation results.

12 pages, 8 figures