An Optimized Differential Step-Size LMS Algorithm

Abstract

Adaptive algorithms with differential step-sizes (related to the filter coefficients) are well known in the literature, most frequently as “proportionate” algorithms. Usually, they are derived on a heuristic basis. In this paper, we introduce an algorithm resulting from an optimization criterion. Thereby, we obtain a benchmark algorithm and also another version with lower computational complexity, which is rigorously valid for less correlated input signals. Simulation results confirm the theory and outline the performance of the algorithms. Unfortunately, the good performance is obtained by an important increase in computational complexity. Nevertheless, the proposed algorithms could represent useful benchmarks in the field.