Convex Combination of Transform Domain LMS and Sparse LMS

Abstract

This work introduces a convex combination of two algorithms, namely, the Transform Domain LMS (TD-LMS) algorithm and its sparse-aware $L_{1}$ version known as the Zero-Attractor Transform Domain LMS (TD-ZA-LMS), to solve the problem of variable sparsity rate under highly correlated input environments. This combination has the ability to converge to the sparse and non-sparse solutions in the case that the system is sparse or dense, respectively. The transform domain algorithms are known also for their ability to reach the steady state condition faster than the LMS algorithm when the input is highly correlated. The analysis of the proposed combination proved that the aggregation is universal, i.e., it performs, at least, as the best of the two algorithms. Simulation results are performed to verify the universality of the combination.