Conference Paper

An improved proportionate NLMS algorithm based on the l0 norm

Telecommun. Dept., Univ. Politeh. of Bucharest, Bucharest, Romania
DOI: 10.1109/ICASSP.2010.5495903 Conference: Acoustics Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on
Source: IEEE Xplore


The proportionate normalized least-mean-square (PNLMS) algorithm was developed in the context of network echo cancellation. It has been proven to be efficient when the echo path is sparse, which is not always the case in real-world echo cancellation. The improved PNLMS (IPNLMS) algorithm is less sensitive to the sparseness character of the echo path. This algorithm uses the l1 norm to exploit sparseness of the impulse response that needs to be identified. In this paper, we propose an IPNLMS algorithm based on the l0 norm, which represents a better measure of sparseness than the l1 norm. Simulation results prove that the proposed algorithm outperforms the original IPNLMS algorithm.

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    • "Furthermore, the l0 norm family algorithms have recently become popular for sparse system identification. A new PNLMS algorithm based on the l0 norm was proposed to represent a better measure of sparseness than the l1 norm in a PNLMS-type algorithm [6]. Benesty demonstrated that PNLMS could be deduced from a basis pursuit perspective [7]. "
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    ABSTRACT: In this paper, a new family of proportionate normalized least mean square (PNLMS) adaptive algorithms that improve the performance of identifying block-sparse systems is proposed. The main proposed algorithm, called block-sparse PNLMS (BS-PNLMS), is based on the optimization of a mixed l2,1 norm of the adaptive filter coefficients. It is demonstrated that both the NLMS and the traditional PNLMS are special cases of BS-PNLMS. Meanwhile, a block-sparse improved PNLMS (BS-IPNLMS) is also derived for both sparse and dispersive impulse responses. Simulation results demonstrate that the proposed BS-PNLMS and BS-IPNLMS algorithms outperformed the NLMS, PNLMS and IPNLMS algorithms with only a modest increase in computational complexity.
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    • "Compared with the IPAPA, the MIPAPA speeded up convergence rate and had a lower-computational complexity. In this Letter, considering the fact that the l 0 -norm can represent an even better measure of sparseness than the l 1 -norm [5], we propose an improved MIPAPA denoted as improved MIPAPA (IMIPAPA) by introducing the l 0 -norm [6] into MIPAPA. Furthermore, it is a simplified version (called SIMIPAPA) with low computations is obtained by the firstorder Taylor series expansion. "
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