Sparse Adaptive Filtering by an Adaptive Convex Combination of the LMS and the ZA-LMS Algorithms

In practice, one often encounters systems that have a sparse impulse response, with the degree of sparseness varying over time. This paper presents a new approach to identify such systems which adapts dynamically to the sparseness level of the system and thus works well both in sparse and non-sparse environments. The proposed scheme uses an adaptive convex combination of the LMS algorithm and the recently proposed, sparsity-aware zero-attractor LMS (ZA-LMS) algorithm. It is shown that while for non-sparse systems, the proposed combined filter always converges to the LMS algorithm (which is better of the two filters for non-sparse case in terms of lesser steady state excess mean square error (EMSE)), for semi-sparse systems, on the other hand, it actually converges to a solution that produces lesser steady state EMSE than produced by either of the component filters. For highly sparse systems, depending on the value of a proportionality constant in the ZA-LMS algorithm, the proposed combined filter may either converge to the ZA-LMS based filter or may produce a solution which, like the semi-sparse case, outperforms both the constituent filters. A simplified update formula for the mixing parameter of the adaptive convex combination is also presented. The proposed algorithm requires much less complexity than the existing algorithms and its claimed robustness against variable sparsity is well supported by simulation results.