Sparse LMS with segment zero attractors for adaptive estimation of sparse signals

Adaptive sparse signal estimation is needed for obtaining accurate channel knowledge in communication systems where the system response can be assumed to contain many near-zero coefficients. For sparse filter design, the zero-attracting LMS (ZA-LMS) incorporates the l₁ norm penalty function into the quadratic LMS cost function to promote the sparseness during the adaptation process. The reweighted ZA-LMS (RZA-LMS) is developed using reweighted zero attractors with better performance. In this paper, we propose two new sparse LMS algorithms with segment zero attractors, referred as Segment RZA-LMS and Discrete Segment RZA-LMS. The Segment RZA-LMS outperforms RZA-LMS by using a piece-wise approximation of the reciprocal in the iterative algorithm of RZA-LMS. The Discrete Segment RZA-LMS is further developed to achieve faster convergence speed and lower steady state error performance than Segment RZA-LMS.