Fixed-point roundoff error analysis of the RLS algorithm with time-varying channels

The authors derive the steady-state mean square prediction error expression for the fixed-point RLS (recursive least squares) algorithm for the case of time-varying channel estimation, which is modeled as a first-order Markov tapped delay line. It is shown that the random variable driving the time-varying system taps affects the prediction error in the same way as does the roundoff error term due to weight update. It causes the error to grow linearly with time when the forgetting factor, λ, is chosen as 1. For λ<1, the excess error tends to increase when the data are correlated. However, this effect is not direct as in the cases of the additive noise and the roundoff error due to the desired signal estimate