Error Gradient-based Variable-Lp Norm Constraint LMS Algorithm for Sparse System Identification

Sparse adaptive filtering has gained much attention due to its wide applicability in the field of signal processing. Among the main algorithm families, sparse norm constraint adaptive filters develop rapidly in recent years. However, when applied for system identification, most priori work in sparse norm constraint adaptive filtering suffers from the difficulty of adaptability to the sparsity of the systems to be identified. To address this problem, we propose a novel variable p-norm constraint least mean square (LMS) algorithm, which serves as a variant of the conventional Lp-LMS algorithm established for sparse system identification. The parameter p is iteratively adjusted by the gradient descent method applied to the instantaneous square error. Numerical simulations show that this new approach achieves better performance than the traditional Lp-LMS and LMS algorithms in terms of steady-state error and convergence rate.Comment: Submitted to 41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2016), 5 pages, 2 tables, 2 figures, 15 equations, 15 reference

Performance Analysis of l_0 Norm Constraint Least Mean Square Algorithm

As one of the recently proposed algorithms for sparse system identification, $l_0$ norm constraint Least Mean Square ($l_0$-LMS) algorithm modifies the cost function of the traditional method with a penalty of tap-weight sparsity. The performance of $l_0$-LMS is quite attractive compared with its various precursors. However, there has been no detailed study of its performance. This paper presents all-around and throughout theoretical performance analysis of $l_0$-LMS for white Gaussian input data based on some reasonable assumptions. Expressions for steady-state mean square deviation (MSD) are derived and discussed with respect to algorithm parameters and system sparsity. The parameter selection rule is established for achieving the best performance. Approximated with Taylor series, the instantaneous behavior is also derived. In addition, the relationship between $l_0$-LMS and some previous arts and the sufficient conditions for $l_0$-LMS to accelerate convergence are set up. Finally, all of the theoretical results are compared with simulations and are shown to agree well in a large range of parameter setting.Comment: 31 pages, 8 figure

An Improved Variable Step-size Zero-point Attracting Projection Algorithm

This paper proposes an improved variable step-size (VSS) scheme for zero-point attracting projection (ZAP) algorithm. The proposed VSS is proportional to the sparseness difference between filter coefficients and the true impulse response. Meanwhile, it works for both sparse and non-sparse system identification, and simulation results demonstrate that the proposed algorithm could provide both faster convergence rate and better tracking ability than previous ones.Comment: 5 pages, ICASSP 2015. arXiv admin note: substantial text overlap with arXiv:1312.261

Reweighted l1-norm Penalized LMS for Sparse Channel Estimation and Its Analysis

A new reweighted l1-norm penalized least mean square (LMS) algorithm for sparse channel estimation is proposed and studied in this paper. Since standard LMS algorithm does not take into account the sparsity information about the channel impulse response (CIR), sparsity-aware modifications of the LMS algorithm aim at outperforming the standard LMS by introducing a penalty term to the standard LMS cost function which forces the solution to be sparse. Our reweighted l1-norm penalized LMS algorithm introduces in addition a reweighting of the CIR coefficient estimates to promote a sparse solution even more and approximate l0-pseudo-norm closer. We provide in depth quantitative analysis of the reweighted l1-norm penalized LMS algorithm. An expression for the excess mean square error (MSE) of the algorithm is also derived which suggests that under the right conditions, the reweighted l1-norm penalized LMS algorithm outperforms the standard LMS, which is expected. However, our quantitative analysis also answers the question of what is the maximum sparsity level in the channel for which the reweighted l1-norm penalized LMS algorithm is better than the standard LMS. Simulation results showing the better performance of the reweighted l1-norm penalized LMS algorithm compared to other existing LMS-type algorithms are given.Comment: 28 pages, 4 figures, 1 table, Submitted to Signal Processing on June 201

Adaptive Sparse Channel Estimation for Time-Variant MIMO-OFDM Systems

Accurate channel state information (CSI) is required for coherent detection in time-variant multiple-input multipleoutput (MIMO) communication systems using orthogonal frequency division multiplexing (OFDM) modulation. One of low-complexity and stable adaptive channel estimation (ACE) approaches is the normalized least mean square (NLMS)-based ACE. However, it cannot exploit the inherent sparsity of MIMO channel which is characterized by a few dominant channel taps. In this paper, we propose two adaptive sparse channel estimation (ASCE) methods to take advantage of such sparse structure information for time-variant MIMO-OFDM systems. Unlike traditional NLMS-based method, two proposed methods are implemented by introducing sparse penalties to the cost function of NLMS algorithm. Computer simulations confirm obvious performance advantages of the proposed ASCEs over the traditional ACE.Comment: 6 cages,10 figures, conference pape

Adaptive Combination of l0 LMS Adaptive Filters for Sparse System Identification in Fluctuating Noise Power

Recently, the l0-least mean square (l0-LMS) algorithm has been proposed to identify sparse linear systems by employing a sparsity-promoting continuous function as an approximation of l0 pseudonorm penalty. However, the performance of this algorithm is sensitive to the appropriate choice of the some parameter responsible for the zero-attracting intensity. The optimum choice for this parameter depends on the signal-to-noise ratio (SNR) prevailing in the system. Thus, it becomes difficult to fix a suitable value for this parameter, particularly in a situation where SNR fluctuates over time. In this work, we propose several adaptive combinations of differently parameterized l0-LMS to get an overall satisfactory performance independent of the SNR, and discuss some issues relevant to these combination structures. We also demonstrate an efficient partial update scheme which not only reduces the number of computations per iteration, but also achieves some interesting performance gain compared with the full update case. Then, we propose a new recursive least squares (RLS)-type rule to update the combining parameter more efficiently. Finally, we extend the combination of two filters to a combination of M number adaptive filters, which manifests further improvement for M > 2.Comment: 15 pages, 15 figure

Sparsity Aware Normalized Least Mean p-power Algorithms with Correntropy Induced Metric Penalty

For identifying the non-Gaussian impulsive noise systems, normalized LMP (NLMP) has been proposed to combat impulsive-inducing instability. However, the standard algorithm is without considering the inherent sparse structure distribution of unknown system. To exploit sparsity as well as to mitigate the impulsive noise, this paper proposes a sparse NLMP algorithm, i.e., Correntropy Induced Metric (CIM) constraint based NLMP (CIMNLMP). Based on the first proposed algorithm, moreover, we propose an improved CIM constraint variable regularized NLMP(CIMVRNLMP) algorithm by utilizing variable regularized parameter(VRP) selection method which can further adjust convergence speed and steady-state error. Numerical simulations are given to confirm the proposed algorithms.Comment: 5 pages, 4 figures, submitted for DSP201

Study of Distributed Spectrum Estimation Using Alternating Mixed Discrete-Continuous Adaptation

This paper proposes a distributed alternating mixed discrete-continuous (DAMDC) algorithm to approach the oracle algorithm based on the diffusion strategy for parameter and spectrum estimation over sensor networks. A least mean squares (LMS) type algorithm that obtains the oracle matrix adaptively is developed and compared with the existing sparsity-aware and conventional algorithms. The proposed algorithm exhibits improved performance in terms of mean square deviation and power spectrum estimation accuracy. Numerical results show that the DAMDC algorithm achieves excellent performance.Comment: 11 pages, 5 figure

Convergence Analysis of l0-RLS Adaptive Filter

This paper presents first and second order convergence analysis of the sparsity aware l0-RLS adaptive filter. The theorems 1 and 2 state the steady state value of mean and mean square deviation of the adaptive filter weight vector

Improved adaptive sparse channel estimation using mixed square/fourth error criterion

Sparse channel estimation problem is one of challenge technical issues in stable broadband wireless communications. Based on square error criterion (SEC), adaptive sparse channel estimation (ASCE) methods, e.g., zero-attracting least mean square error (ZA-LMS) algorithm and reweighted ZA-LMS (RZA-LMS) algorithm, have been proposed to mitigate noise interferences as well as to exploit the inherent channel sparsity. However, the conventional SEC-ASCE methods are vulnerable to 1) random scaling of input training signal; and 2) imbalance between convergence speed and steady state mean square error (MSE) performance due to fixed step-size of gradient descend method. In this paper, a mixed square/fourth error criterion (SFEC) based improved ASCE methods are proposed to avoid aforementioned shortcomings. Specifically, the improved SFEC-ASCE methods are realized with zero-attracting least mean square/fourth error (ZA-LMS/F) algorithm and reweighted ZA-LMS/F (RZA-LMS/F) algorithm, respectively. Firstly, regularization parameters of the SFEC-ASCE methods are selected by means of Monte-Carlo simulations. Secondly, lower bounds of the SFEC-ASCE methods are derived and analyzed. Finally, simulation results are given to show that the proposed SFEC-ASCE methods achieve better estimation performance than the conventional SEC-ASCE methods. 1Comment: 21 pages, 10 figures, submitted for journa