Robust Proportionate Normalized Least Mean M-Estimate Algorithm for Block-Sparse System Identification

Abstract

In practical applications, the impulse responses (IRs) of some network echo paths are blocksparse (BS), while the traditional proportionate and zero attraction algorithms do not consider the prior sparsity of the BS system, so they do not perform well in the block-sparse system identification (BSSI). In addition, most of the current BS filtering algorithms are based on the assumption of Gaussian noise, so the performance will deteriorate seriously in the background of impulse noise. To overcome the shortcoming, we use the mixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2,1} $ </tex-math></inline-formula> norm of the filter weight vector to fully tap the sparsity of the BS system, and combine the anti impulse noise characteristic of the M-estimate function to design and derive the BS proportionate normalized least mean M-estimate (BSPNLMM) algorithm from the perspective of basis pursuit (BP), which well realizes the BSSI in the presence of impulse noise. Then, we analyze the mean performance of the BSPNLMM algorithm in detail and give the stable step size bound. Finally, the superiority of the proposed BSPNLMM algorithm is verified by numerical simulations