Convergence analysis of the zero-attracting variable step-size LMS algorithm for sparse system identification

Jahromi, Mohammad N. S.; Salman, Mohammad Shukri; Hocanin, Aykut; Kükrer, Osman

doi:10.1007/s11760-013-0580-9

Cited by 22 publications

(14 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[11,12,25] that the fourthorder moment of a Gaussian variable is three times the variance squared and that S(n) is symmetric, and under the Assumption 3, we get…”

Section: −ρ(G(n) − E[g(n)])mentioning

confidence: 96%

“…[11,12,25]. The Assumption 3 is valid when the weight vector w(n) lies in the neighbourhood of the optimal solution w * (n).…”

Section: Assumption 5 the Expectation E[ F (E(∞))] Is Upper Boundedmentioning

confidence: 99%

“…This conclusion is the same as that in Refs. [11,12,25] when the sparsity penalty term g(n) is chosen as the l 1 -norm or logarithmic penalty term. The CIM penalty term is also bounded because the negative exponential term can reach its maximum value.…”

Section: (32) E[w(n)] Converges [See (25)] and C(n) Is Bounded And mentioning

confidence: 99%

“…Well-known examples include zeroattracting LMS (ZALMS) [7], reweighted zero-attracting LMS (RZALMS) [7], sparse RLS [8] and l 0 -LMS [9]. Other variations of sparse LMS algorithm can be found in [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Sparse least mean p-power algorithms for channel estimation in the presence of impulsive noise

Chen

et al. 2015

SIViP

View full text Add to dashboard Cite

The least mean p-power (LMP) is one of the most popular adaptive filtering algorithms. With a proper p value, the LMP can outperform the traditional least mean square ( p = 2), especially under the impulsive noise environments. In sparse channel estimation, the unknown channel may have a sparse impulsive (or frequency) response. In this paper, our goal is to develop new LMP algorithms that can adapt to the underlying sparsity and achieve better performance in impulsive noise environments. Particularly, the correntropy induced metric (CIM) as an excellent approximator of the l 0 -norm can be used as a sparsity penalty term. The proposed sparsity-aware LMP algorithms include the l 1 -norm, reweighted l 1 -norm and CIM penalized LMP algorithms, which are denoted as ZALMP, RZALMP and CIMLMP respectively. The mean and mean square convergence of these algorithms are analysed. Simulation results show that the proposed new algorithms perform well in sparse channel estimation under impulsive noise environments. In particular, the CIMLMP with suitable kernel width will outperform other algorithms significantly due to the superiority of the CIM approximator for the l 0 -norm. B Wentao Ma

show abstract

“…[11,12,25] that the fourthorder moment of a Gaussian variable is three times the variance squared and that S(n) is symmetric, and under the Assumption 3, we get…”

Section: −ρ(G(n) − E[g(n)])mentioning

confidence: 96%

“…[11,12,25]. The Assumption 3 is valid when the weight vector w(n) lies in the neighbourhood of the optimal solution w * (n).…”

Section: Assumption 5 the Expectation E[ F (E(∞))] Is Upper Boundedmentioning

confidence: 99%

Section: (32) E[w(n)] Converges [See (25)] and C(n) Is Bounded And mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Sparse least mean p-power algorithms for channel estimation in the presence of impulsive noise

Chen

et al. 2015

SIViP

View full text Add to dashboard Cite

show abstract

“…After that, zero-attracting techniques have been introduced into the proportionate adaptive filter algorithms [5,16,18], leaky least mean square [19] and normalized least mean square algorithms [7] to form desired zero attractors [6,11,17]. Their convergence characteristics are analyzed in [10,22]. Recently, a smooth approximation l 0 -norm method has been introduced into the cost function of the conventional LMS and AP algorithms to further improve the estimation performance, and these are known as l 0 -LMS and l 0 -AP algorithms [8,9,12,13].…”

Section: Introductionmentioning

confidence: 99%

Low-Complexity Non-Uniform Penalized Affine Projection Algorithm for Sparse System Identification

Zhang

Wang

2015

Circuits Syst Signal Process

View full text Add to dashboard Cite

In this paper, an improved sparse-aware affine projection (AP) algorithm for sparse system identification is proposed and investigated. The proposed sparse AP algorithm is realized by integrating a non-uniform norm constraint into the cost function of the conventional AP algorithm, which can provide a zero attracting on the filter coefficients according to the value of each filter coefficient. Low complexity is obtained by using a linear function instead of the reweighting term in the modified AP algorithm to further improve the performance of the proposed sparse AP algorithm. The simulation results demonstrate that the proposed sparse AP algorithm outperforms the conventional AP and previously reported sparse-aware AP algorithms in terms of both convergence speed and steady-state error when the system is sparse.

show abstract

Recursive Generalized Maximum Correntropy Criterion Algorithm with Sparse Penalty Constraints for System Identification

Duan

Chen

et al. 2016

Asian Journal of Control

View full text Add to dashboard Cite

To address the sparse system identification problem in a non‐Gaussian impulsive noise environment, the recursive generalized maximum correntropy criterion (RGMCC) algorithm with sparse penalty constraints is proposed to combat impulsive‐inducing instability. Specifically, a recursive algorithm based on the generalized correntropy with a forgetting factor of error is developed to improve the performance of the sparsity aware maximum correntropy criterion algorithms by achieving a robust steady‐state error. Considering an unknown sparse system, the l1‐norm and correntropy induced metric are employed in the RGMCC algorithm to exploit sparsity as well as to mitigate impulsive noise simultaneously. Numerical simulations are given to show that the proposed algorithm is robust while providing robust steady‐state estimation performance.

show abstract

Convergence analysis of the zero-attracting variable step-size LMS algorithm for sparse system identification

Cited by 22 publications

References 8 publications

Sparse least mean p-power algorithms for channel estimation in the presence of impulsive noise

Sparse least mean p-power algorithms for channel estimation in the presence of impulsive noise

Low-Complexity Non-Uniform Penalized Affine Projection Algorithm for Sparse System Identification

Recursive Generalized Maximum Correntropy Criterion Algorithm with Sparse Penalty Constraints for System Identification

Contact Info

Product

Resources

About