Analysis of the QR-RLS algorithm for colored-input signals

The recursive least squares (RLS) algorithms for FIR adaptive filtering are particularly attractive due to their fast convergence, especially for correlated input signals. A detailed analysis of the QR-RLS algorithm in finite and infinite precision implementations is presented, emphasizing the case where the input signal samples are correlated. The expressions for the mean square values of all internal variables in a steady state are first derived. These expressions are the key used to determine the dynamic range of the internal signals, and to derive the analytical expressions for the mean square values of the deviations in the output variables of the algorithm in finite wordlength implementations. Previous works address this problem considering the input signal a white noise, a situation not so often encountered in practice. The accuracy of all analytical results are verified through a number of computer simulations