A Mixed (2,p-like)-Norm Penalized Least Mean Squares Algorithm for Block-Sparse System Identification


This work presents a new mixed (2,p-like)-norm penalized least mean squares (LMS) algorithm for block-sparse system identifications where the nonzero coefficients in the impulse response vector of unknown systems are structured in a single cluster or multiple clusters. The new algorithm divides the tap-weight vector into groups of equal-sized sub-vectors and then introduces a mixed l2,p-like-norm constraint on the filter tap-weight vector in addition to the original mean-square-error cost function. The parameter p in the l2,p-like-norm constraint takes any value between zero and two, thus improving the identification performance of the block-sparse systems. The effect of the parameter p and the group size on the performance of the proposed algorithm is studied, and general guidelines for choosing these two parameters are provided to facilitate practical use. The advantage of the proposed scheme is that no comparison operations are required while algebraic operations are of the same order as the block-sparse LMS algorithm. Numerical simulations show that the proposed (2 , p-like) -norm penalized LMS algorithm outperforms the existing l2,0- and l2,1-norm-based block-sparsity-aware algorithms and single-norm penalized LMS strategies.


Electrical and Computer Engineering

Keywords and Phrases

Adaptive filtering; l2,p-like norm; LMS algorithm; Block-sparse system identifications

International Standard Serial Number (ISSN)

0278-081X; 1531-5878

Document Type

Article - Journal

Document Version


File Type





© 2018 Springer Verlag, All rights reserved.

Publication Date

01 Oct 2018