A Block-sparse Set-Membership PNLMS Algorithm Based on Hybrid Zero-Attraction Penalty

In some practical communication systems, the channel impulse responses whose values are large but just account for a small fraction distributed in clusters. Hybrid norm l
_2,
0
is employed as a zero-attraction penalty to build the cost function (CF) of the proportional normalized least mean square (PNLMS) algorithm. In addition, the set-membership (SM) criterion is also used to reduce the computing complexity and to get good tracking performance by presetting a thresh-old of error. The novel method named l
_2,
0
-set-membership PNLMS (l
_2,
0
-SMPNLMS) algorithm not only has fast initial convergence speed inheriting from the PNLMS algorithm, but also has good performance to deal with block-sparse signals. Numerical simulations have been conducted and the result shows the superiority of the proposed algorithm compared with the related algorithms.