On the effect of input signal correlation on weight misadjustment in the RLS algorithm

New expressions are derived for the mean weight misadjustment in the recursive least squares (RLS) algorithm for first-order Markov channel estimation. The expressions derived are general in that they take into account the correlation in the input. It is shown that the additive system noise is amplified by a correlation amplification factor that is defined as a function of the input autocorrelation matrix eigenvalues. However, input correlation has almost no effect on the misadjustment due to time-varying system weights. These results are checked by simulations demonstrating excellent agreement with the theory.>