Performance comparison of RLS and LMS algorithms for tracking a first order Markov communications channel

Abstract
The performances of recursive-least-squares (RLS) and least-mean-square (LMS) adaptive algorithms for tracking a first-order Markov tapped delay line model of a communications channel whose output is observed in a white Gaussian noise background are studied. The model includes the errors due to the finite memory of the channel. A rigorous analytical evaluation of the misadjustment errors of both RLS and LMS is presented. The misadjustment errors are individually minimized over the RLS forgetting factor and the LMS step size. It is shown that the misadjustment factors are nearly equal (RLS is slightly superior) whether the bandwidth of the channel tap fluctuations is greater than or less than the bandwidth of the adaptation algorithm. Conditions are presented for when the adaptation process should be turned off.

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