Abstract
This paper presents an analysis of a fixed-point recursive least squares (RLS) algorithm for first-order Markov channel estimation and derives expressions for the mean weight misadjustment. The expressions derived are general in that they take into account the correlation in the input. It is shown that correlation amplifies the effect of roundoff error due to the desired signal estimate computation and the additive system noise. The misadjustment due to time-varying system weights and the weight update roundoff error behave similarly and are minimally affected by the input correlation. They contribute to the total misadjustment in such a way that is directly proportional to the algorithm's time constant which is a function of the algorithm forgetting factor. The contributions of system noise and roundoff error due to the desired estimate, on the other hand, are inversely proportional to the algorithm time constant. Hence, they indicate a tradeoff in the choice of the forgetting factor to balance the effects of these noise sources. We present simulation results which demonstrate very good agreement with the theory.
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