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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Available from: Silviu Ciochina
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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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    • "where µ > 0 is the step size and ε > 0 is a correction to prevent stability issues or to compensate for the presence of noise in the input x n [15]. Despite the increasing awareness [8]– [11] captured by these modern adaptive rules, the methodology employed in their derivation (plain gradient analysis [14]) is not the most appropriate for non-linear and non-convex cost functions, such as the ℓ p -norm (in the range 0 < p ≤ 1). "
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    ABSTRACT: This letter presents the exact normalized least-mean-square (NLMS) algorithm for the lp-norm-regularized square error, a popular choice for the identification of sparse systems corrupted by additive noise. The resulting exact lp-NLMS algorithm manifests differences to the original one, such as an independent update for each weight, a new sparsity-promoting compensated update, and the guarantee of stable convergence for any configuration (regardless the choice of lp norm and sparsity-tradeoff constant). Simulation results show that the exact lp-NLMS is stable and it outperforms the original one, thus validating the optimality of the proposed methodology.
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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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    ABSTRACT: An efficient MIP-APSA (EMIP-APSA) is proposed via incorporating l 0-norm as a better measure of sparseness into a recently presented memory-improved proportionate affine projection sign algorithm (MIP-APSA) to enhance performance for sparse system identification. Also, to reduce computational complexity of EMIP-APSA, we achieve a simple implementation of the EMIP-APSA (SEMIP-APSA) while maintaining the consistent performance in terms of convergence rate and steady-state misalignment. Simulation results demonstrate that the proposed EMIP-APSA and SEMIP-APSA obtain a lower steady-state misalignment in comparison with the MIP-APSA for sparse system identification in the impulsive noise environment.
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