Abstract
In this paper, an improved set-membership proportionate normalized least mean square (SM-PNLMS) algorithm is proposed for block-sparse systems. The proposed algorithm, which is named the block-sparse SM-PNLMS (BS-SMPNLMS), is implemented by inserting a penalty of a mixed l 2 , 1 norm of weight-taps into the cost function of the SM-PNLMS. Furthermore, an improved BS-SMPNLMS algorithm (the (BS-SMIPNLMS algorithm) is also derived and analyzed. The proposed algorithms are well investigated in the framework of network echo cancellation. The results of simulations indicate that the devised BS-SMPNLMS and BS-SMIPNLMS algorithms converge faster and have smaller estimation errors compared with related algorithms.
Highlights
Echo cancellation is one of the most typical applications in adaptive filtering scenarios [1,2].Among the many adaptive algorithms, the normalized least mean square (NLMS) is a classical algorithm due to its good performance and easy implementation [3,4]
In order to expand the BS-SMPNLMS to make it more useful for the dispersive application field, we propose an improved BS-SMPNLMS (BS-SMIPNLMS) algorithm
Because of inserting the SM principle, the total numbers of additions of the BS-SMPNLMS and BS-SMIPNLMS are less than 4N − 1 and 4N + B − 1
Summary
Echo cancellation is one of the most typical applications in adaptive filtering scenarios [1,2]. To further exploit the sparse characteristic of the echo path, the proportionate NLMS (PNLMS) and zero-attracting algorithms were proposed [6,7,8,9,10,11,12,13,14,15,16]. The BS-PNLMS algorithm proposed in [26] inserts a penalty of a mixed l2,1 norm to the cost function of the PNLMS algorithm This algorithm further exploits the block-sparsity of the estimated system as compared to the BS-LMS, and it can serve for the multi-clustering case in addition to the single-clustering case. We use the SM principle and the mixed l2,1 norm to devise the block-sparse proportionate adaptive filtering algorithm to improve the estimation performances of the previous block-sparse algorithms.
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