A set of algorithms linking NLMS and block RLS algorithms

A set of block processing algorithms that contains as extremal cases the normalized least mean squares (NLMS) and the block recursive least squares (BRLS) algorithms is described. These algorithms use small block lengths, thus allowing easy implementation and small input-output delay. It is shown that these algorithms require a smaller number of arithmetic operations than the classical LMS algorithm, while converging much faster. A precise evaluation of the arithmetic complexity is provided, and the adaptive behavior of the algorithm is analyzed. A simulation shows that the tracking characteristics of the new algorithm compared with the NLMS algorithm are also improved. Another simulation shows that, even in the case where noise is added to the reference signal, the proposed algorithm allows a faster convergence and a lower residual error than the NLMS algorithm.<>