Non-Uniform Norm Constraint LMS Algorithm for Sparse System Identification

Abstract:A group-constrained maximum correntropy criterion (GC-MCC) algorithm is proposed on the basis of the compressive sensing (CS) concept and zero attracting (ZA) techniques and its estimating behavior is verified over sparse multi-path channels. The proposed algorithm is implemented by exerting different norm penalties on the two grouped channel coefficients to improve the channel estimation performance in a mixed noise environment. As a result, a zero attraction term is obtained from the expected l 0 and l 1 penalty techniques. Furthermore, a reweighting factor is adopted and incorporated into the zero-attraction term of the GC-MCC algorithm which is denoted as the reweighted GC-MCC (RGC-MMC) algorithm to enhance the estimation performance. Both the GC-MCC and RGC-MCC algorithms are developed to exploit well the inherent sparseness properties of the sparse multi-path channels due to the expected zero-attraction terms in their iterations. The channel estimation behaviors are discussed and analyzed over sparse channels in mixed Gaussian noise environments. The computer simulation results show that the estimated steady-state error is smaller and the convergence is faster than those of the previously reported MCC and sparse MCC algorithms.

Section: The Proposed Group-constrained Sparse MCC Algorithmsmentioning

confidence: 99%

“…For the "large" group, l 0 -norm penalty is used to count the number of active channel coefficients, and l 1 -norm penalty is adopted to uniformly attract inactive coefficients to zero for the "small" group. To effectively integrate these two groups into (23), we define [37] …”

Section: The Proposed Group-constrained Sparse MCC Algorithmsmentioning

confidence: 99%

Group-Constrained Maximum Correntropy Criterion Algorithms for Estimating Sparse Mix-Noised Channels

Wang

Albu

et al. 2017

“…Many algorithms have been developed to solve the problem in (3) in the literature [12][13][14][15][16][17][18][19][20], where the mean square error (MSE) [21] criterion based on second-order statistics has been employed for these algorithms, which show their optimality when e is Gaussian noise. In practical applications, however the transmitted signals are distorted by not only Gaussian noise, but also other kinds of noise, such as burst noise and high noise.…”

Section: Introductionmentioning

confidence: 99%

Sparse Coding Algorithm with Negentropy and Weighted ℓ1-Norm for Signal Reconstruction

Zhao

Liu

Wang

et al. 2017

Abstract:Compressive sensing theory has attracted widespread attention in recent years and sparse signal reconstruction has been widely used in signal processing and communication. This paper addresses the problem of sparse signal recovery especially with non-Gaussian noise. The main contribution of this paper is the proposal of an algorithm where the negentropy and reweighted schemes represent the core of an approach to the solution of the problem. The signal reconstruction problem is formalized as a constrained minimization problem, where the objective function is the sum of a measurement of error statistical characteristic term, the negentropy, and a sparse regularization term, p -norm, for 0 < p < 1. The p -norm, however, leads to a non-convex optimization problem which is difficult to solve efficiently. Herein we treat the p -norm as a serious of weighted 1 -norms so that the sub-problems become convex. We propose an optimized algorithm that combines forward-backward splitting. The algorithm is fast and succeeds in exactly recovering sparse signals with Gaussian and non-Gaussian noise. Several numerical experiments and comparisons demonstrate the superiority of the proposed algorithm.

“…In general, a sparse adaptive filtering algorithm can be derived by incorporating a sparsity penalty term (SPT), such as the l0-norm, into a traditional adaptive algorithm. Typical examples of sparse adaptive filtering algorithms include sparse least mean square (LMS) [1][2][3][4], sparse affine projection algorithms (APA) [5], sparse recursive least squares (RLS) [6], and their variations [7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Minimum Error Entropy Algorithms with Sparsity Penalty Constraints

Peng

et al. 2015

Abstract:Recently, sparse adaptive learning algorithms have been developed to exploit system sparsity as well as to mitigate various noise disturbances in many applications. In particular, in sparse channel estimation, the parameter vector with sparsity characteristic can be well estimated from noisy measurements through a sparse adaptive filter. In previous studies, most works use the mean square error (MSE) based cost to develop sparse filters, which is rational under the assumption of Gaussian distributions. However, Gaussian assumption does not always hold in real-world environments. To address this issue, we incorporate in this work an l1-norm or a reweighted l1-norm into the minimum error entropy (MEE) criterion to develop new sparse adaptive filters, which may perform much better than the MSE based methods, especially in heavy-tailed non-Gaussian situations, since the error entropy can capture higher-order statistics of the errors. In addition, a new approximator of l0-norm, based on the correntropy induced metric (CIM), is also used as a sparsity penalty term (SPT). We analyze the mean square convergence of the proposed new sparse adaptive filters. An energy conservation relation is derived and a sufficient condition is obtained, which ensures the mean square convergence. Simulation results confirm the superior performance of the new algorithms. OPEN ACCESSEntropy 2015, 17 3420 Keywords: sparse estimation; minimum error entropy; correntropy induced metric; mean square convergence; impulsive noise MSC Codes: 62B10