Adaptive Combination of l0 LMS Adaptive Filters for Sparse System Identification in Fluctuating Noise Power

Recently, the l0-least mean square (l0-LMS) algorithm has been proposed to identify sparse linear systems by employing a sparsity-promoting continuous function as an approximation of l0 pseudonorm penalty. However, the performance of this algorithm is sensitive to the appropriate choice of the some parameter responsible for the zero-attracting intensity. The optimum choice for this parameter depends on the signal-to-noise ratio (SNR) prevailing in the system. Thus, it becomes difficult to fix a suitable value for this parameter, particularly in a situation where SNR fluctuates over time. In this work, we propose several adaptive combinations of differently parameterized l0-LMS to get an overall satisfactory performance independent of the SNR, and discuss some issues relevant to these combination structures. We also demonstrate an efficient partial update scheme which not only reduces the number of computations per iteration, but also achieves some interesting performance gain compared with the full update case. Then, we propose a new recursive least squares (RLS)-type rule to update the combining parameter more efficiently. Finally, we extend the combination of two filters to a combination of M number adaptive filters, which manifests further improvement for M > 2.