Convergence analysis of the binormalized data-reusing LMS algorithm

Normalized least mean squares algorithms for FIR adaptive filtering with or without the reuse of past information are known to converge often faster than the conventional least mean squares (LMS) algorithm. This correspondence analyzes an LMS-like algorithm: the binormalized data-reusing least mean squares (BNDR-LMS) algorithm. This algorithm, which corresponds to the affine projection algorithm for the case of two projections, compares favorably with other normalized LMS-like algorithms when the input signal is correlated. Convergence analyses in the mean and in the meansquared are presented, and a closed-form formula for the mean squared error is provided for white input signals as well as its extension to the case of a colored input signal. A simple model for the input-signal vector that imparts simplicity and tractability to the analysis of second-order statistics is fully described. The methodology is readily applicable to other adaptation algorithms of difficult analysis. Simulation results validate the analysis and ensuing assumptions.