A Convex Combination of NLMS and ZA-NLMS for Identifying Systems With Variable Sparsity

Abstract

This brief aims to identify and track a sparse system with time varying sparseness by a convex combination of two adaptive filters, one based on the sparsity unaware normalized least mean square (NLMS) algorithm and the other based on the sparsity aware zero-attracting NLMS (ZA-NLMS) algorithm. An analysis of the proposed combination is carried out, which reveals that while the proposed combination converges to the ZA-NLMS or the NLMS-based filter for systems that are highly sparse or highly non-sparse, respectively (i.e., better of the two under the given sparsity condition), it may, however, lead to a filter that performs better than both the constituent filters in the case of systems that lie between moderately sparse to moderately non-sparse. The same is confirmed via detailed simulation studies under different sparsity conditions.