Exploiting sparsity in adaptive filters

This paper studies a class of algorithms called natural gradient (NG) algorithms. The least mean square (LMS) algorithm is derived within the NG framework, and a family of LMS variants that exploit sparsity is derived. This procedure is repeated for other algorithm families, such as the constant modulus algorithm (CMA) and decision-directed (DD) LMS. Mean squared error analysis, stability analysis, and convergence analysis of the family of sparse LMS algorithms are provided, and it is shown that if the system is sparse, then the new algorithms will converge faster for a given total asymptotic MSE. Simulations are provided to confirm the analysis. In addition, Bayesian priors matching the statistics of a database of real channels are given, and algorithms are derived that exploit these priors. Simulations using measured channels are used to show a realistic application of these algorithms.