On steady-state performance of the fixed-point RLS algorithm

This paper presents an analysis of a fixed-point recursive least squares (R LS) algorithm for first-order Markov channel estimation and derives express ions for the mean weight misadjustment. The expressions derived are general in that they take into account the correlation in the input. It is shown t hat correlation amplifies the effect of roundoff error due to the desired s ignal estimate computation and the additive system noise. The misadjustment due to time-varying system weights and the weight update roundoff error be have similarly and are minimally affected by the input correlation. They co ntribute to the total misadjustment in such away that is directly proportio nal to the algorithm's time constant which is a function of the algorithm f orgetting factor; The contributions of system noise and roundoff error due to the desired estimate, on the other hand, are inversely proportional to t he algorithm time constant. Hence, they indicate a tradeoff in the choice o f the forgetting factor to balance the effects of these noise sources. We p resent simulation results which demonstrate very good agreement with the th eory, (C) 1999 Elsevier Science Ltd, All rights reserved.