An Improved μ-law Proportionate NLMS Algorithm for Estimating Block-Sparse Systems

An improved μ-law proportionate normalized least mean square (MPNLMS) algorithm is presented and analyzed for giving an estimation of block-sparse systems, which is also named as block-sparse MPNLMS (BS-MPNLMS). The proposed BS-MPNLMS algorithm introduces a hybrid $l_{2,1}$-norm into the MPNLMS’s cost function to create a penalty. The devised new BS-MPNLMS is derived in detail and is analyzed for estimating the network echo signals whose response has a typical block-sparse characteristic. Numerical simulation results show that the devised algorithm has better convergence and stability performance for handling the block-sparse systems compared with related algorithms.