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A block-based convex combination of NLMS and ZA-NLMS for identifying sparse systems with variable sparsity

This paper presents a novel block based convex combination of two adaptive filters — the sparsity unaware NLMS and the sparsity aware zero-attracting NLMS (ZA-NLMS) for identifying and tracking a sparse system with variable sparsity. The proposed scheme partitions the system impulse response blockwise. As most often in practice, sparse systems exhibit sparseness in blocks, such partitioning renders inactive blocks fully or almost fully sparse and active blocks highly non-sparse. For active and inactive blocks, the proposed convex combination switches respectively to the NLMS and the ZA-NLMS based filters, with the latter not suffering any performance degradation due to zero-attraction on active taps as the inactive blocks are almost fully sparse. The combined effect of this on the overall filter is a greatly reduced steady state excess mean square error, which is also corroborated by simulation studies.