Algorithm For Sparse System Identification Research Articles

Proportionate recursive maximum correntropy criterion adaptive filtering algorithms and their performance analysis

The maximum correntropy criterion (MCC) has been employed to design outlier-robust adaptive filtering algorithms, among which the recursive MCC (RMCC) algorithm is a typical one. Motivated by the success of our recently proposed proportionate recursive least squares (PRLS) algorithm for sparse system identification, we propose to introduce the proportionate updating (PU) mechanism into the RMCC, leading to two sparsity-aware RMCC algorithms: the proportionate recursive MCC (PRMCC) algorithm and the combinational PRMCC (CPRMCC) algorithm. The CPRMCC is implemented as an adaptive convex combination of two PRMCC filters. For PRMCC, its stability condition and mean-square performance were analyzed. Based on the analysis, optimal parameter selection in nonstationary environments was obtained. Performance study of CPRMCC was also provided and showed that the CPRMCC performs at least as well as the better component PRMCC filter in steady state. Numerical simulations of sparse system identification corroborate the advantage of proposed algorithms as well as the validity of theoretical analysis.

A Scaled LMS Algorithm for Sparse System Identification with Impulsive Interference

A Scaled LMS Algorithm for Sparse System Identification with Impulsive Interference

Convex Combination of Nonlinear Filters using Improved Proportionate Least Mean Square/Fourth Algorithm for Sparse System Identification

Convex Combination of Nonlinear Filters using Improved Proportionate Least Mean Square/Fourth Algorithm for Sparse System Identification

A two-gain NLMS algorithm for sparse system identification

This paper introduces a modified normalized least-mean-square (NLMS) algorithm for sparse system identification. The proposed approach is in line with the proportionate NLMS (PNLMS)-type algorithms in the sense that different gains are considered in the coefficient update equation. However, in contrast to the PNLMS-type algorithms, the proposed approach considers only two different gains, one related to the active coefficients and other related to the inactive ones. Such an approach allows obtaining closed-form expressions for both gains without relying on proportionality functions and activation factors. As a result of the proposed strategy, the new algorithm, termed here two-gain NLMS (TG-NLMS), leads to both fast convergence and low computational complexity. Simulation results are shown aiming to confirm the effectiveness of the proposed algorithm.

A reweighted l0-norm-constraint LMS algorithm for sparse system identification

The l0-norm-constraint algorithm is widely used in sparse system identification due to its attractive performance. However, the algorithm is sensitive to the tuning parameters and its convergence speed can be further improved due to the small attraction range of the zero attractor. This paper proposes a reweighted l0-norm-constraint Least Mean Square (l0-RLMS) algorithm which expands the attraction range of the zero attractor to accelerate the convergence with even lower mean-square deviation (MSD) value and lower sensitivity to the tuning parameters. The theoretical analysis of the proposed algorithm, along with numerical simulations and comparisons with the latest sparse algorithms, is carried out. The analysis and simulations show that the l0-RLMS algorithm has lower steady-state MSD, lower sensitivity of tuning parameters and lower complexity than the l0-norm-constraint algorithm.

An Optimized Zero-Attracting LMS Algorithm for the Identification of Sparse System

This paper introduces an optimized zero-attractor to improve the performance of least mean square (LMS)-based algorithms for the identification of sparse system. Compared with previous LMS-based algorithms for sparse system identification, the performance of the proposed optimized zero-attracting LMS (OZ-LMS) is much less sensitive to the tuning parameters and measurement noise power, and performs much better for sparse system. Comprehensive performance analysis of the mean-square deviation (MSD) of OZ-LMS is derived in detail. Moreover, the parameter selection rules for optimal steady-state MSD are discussed. Simulation results, using white Gaussian noise and speech input signals, show improved performance over existing methods. Furthermore, we show that the numerical results of OZ-LMS agree with the theoretical predictions.

Improved multiband structured subband adaptive filter algorithm with L0-norm regularization for sparse system identification

The improved multiband structured subband adaptive filter (IMSAF) algorithm improves the performance of normalized subband adaptive filter (NSAF) algorithm by employing the recent regressors at each subband. The present study introduces the IMSAF algorithm for sparse system identification. The L0-norm regularization term is applied to the proposed cost function of IMSAF and the L0-IMSAF is established. The L0-IMSAF has significantly better convergence speed than conventional IMSAF. In the following, the theoretical steady-state performance analysis of the L0-IMSAF is presented. To reduce the computational complexity of the L0-IMSAF, the selective regressor (SR) and the dynamic selective regressor (DSR) strategies are utilized and L0-SR-IMSAF and L0-DSR-IMSAF are proposed. The approaches in L0-SR-IMSAF and L0-DSR-IMSAF algorithms are based on the selection of the regressors at each subband. The L0-SR-IMSAF and L0-DSR-IMSAF have good convergence speed, low steady-state error, and low computational complexity features. The good performances of the proposed algorithms are demonstrated through several simulation results in sparse system identification.

Steady-state mean-square deviation analysis of improved ℓ0-norm-constraint LMS algorithm for sparse system identification

The ℓ0-norm-constraint LMS (ℓ0-LMS) algorithm is one of the widely used sparse LMS algorithms for the identification of sparse system, and its performance is quite attractive compared to other precursors. However, ℓ0-LMS is still confronted with some limitations on the optimal parameter selection and the estimated coefficient accuracy of sparse system identification. In this paper, we proposed an improved ℓ0-LMS (ℓ0-ILMS) algorithm to address these limitations. The convergence condition and the parameter selection rules for optimal steady-state mean-square deviation (MSD) of ℓ0-ILMS are discussed. Compared with ℓ0-LMS, the steady-state MSD of ℓ0-ILMS is lower and less sensitive to the tuning parameters and measurement noise power. Numerical simulations comparing the performance of standard LMS, ℓ0-LMS and ℓ0-ILMS demonstrate the effectiveness of ℓ0-ILMS.

Bias-Compensated Minimum Error Entropy Algorithms With Polynomial Sparsity Penalty Constraints

This brief proposes a polynomial bias-compensated adaptive filtering algorithm for sparse system identification under minimum error entropy criterion, which outperforms in a sparse environment with noisy input and impulsive output noise. In previous studies, the minimum error entropy criterion (MEE) has been widely used in lots of works to develop adaptive filtering algorithms, which show better performance than the traditional algorithms under impulsive noise. However, the MEE algorithm not only has the essential assumption of no-noise input, but also loses the ability to identify the sparse system. To address above two issues, a bias-compensated vector is introduced into the previous traditional MEE algorithm and propose a bias-compensated adaptive filtering algorithm under minimum error entropy criterion named BCMEE algorithm, which compensates the bias caused by the input noise. By taking advantage of the capability of the sparse penalty term in sparse system identification, an attempt has been made to design a polynomial sparse BCMEE algorithm, named PZA-BCMEE algorithm. Simulation results prove the excellent performance of the proposed algorithms.

L1 Norm Penalized Bias Compensated Linear Constrained Affine Projection Algorithm

This paper presents an l1-norm penalized bias compensated linear constrained affine projection (l1-BC-CAP) algorithm for sparse system identification having linear phase aspectin the presence of noisy colored input. The motivation behind the development of the proposed algorithm is formulated on the concept of reusing the previous projections of input signal in affine projection algorithm (APA) that makes it suitable for colored input. At First, l1-CAP algorithm is derived by adding zero attraction based on l1-norm into constrained affine projection (CAP) algorithm. Then, the proposed l1-BC-CAP algorithm is derived by addinga bias compensator into the filter coefficient update equation of l1-norm constrained affine projection (l1-CAP) algorithm to alleviate the adverse consequence of input noise on the estimation performance. Hence, the resulting l1-BC-CAP algorithm excels the estimation performance when applied to linear phase sparse system in the existence of noisy colored input. Further, this work also examines the stability concept of the proposed algorithm

A Partial Update Adaptive Algorithm for Sparse System Identification

A sparse partial update (SPU) algorithm and its improved version improved SPU (ISPU) algorithm, are proposed in this paper for sparse system identification. The SPU first categorizes its filter coefficients into active and inactive coefficients. Then all the active coefficients are included in each adaptation, while only a small portion of the inactive coefficients is periodically chosen to be included in the adaptation. The SPU emphasizes convergence of the active coefficients by updating them at every adaptation, while the periodical adaptation of the inactive coefficients ensures its robustness and tracking capability. By eliminating most of the inactive coefficients from adaptation, the SPU significantly reduces the number of adapting coefficients in each adaptation. The decline in the number of adapting coefficients eventually leads to improvement in both computation and convergence speed. To avoid performance degradation in the case of identifying a dispersive system, an ISPU is further proposed by making modifications to the SPU. The simulation results demonstrate that the ISPU not only outperforms other sparse adaptive algorithms in identifying a sparse system but also performs at least as well as the NLMS algorithm in identifying a dispersive system.

Robust Variable Step-Size Reweighted Zero-Attracting Least Mean M-Estimate Algorithm for Sparse System Identification

The reweighted zero-attracting least mean square (RZA-LMS) algorithm has good performance in sparse system identification. However, the convergence performance of the RZA-LMS algorithm degrades in the impulsive noise environment. In this brief, a reweighted zero-attracting least mean M-estimate (RZA-LMM) algorithm is proposed to address the issue. The RZA-LMM algorithm employs the M-estimate cost function with a sparsity-aware penalty term and is derived by using the unconstrained minimization method. In order to further enhance the convergence speed and reduce the steady-state error of the RZA-LMM algorithm, a variable step-size reweighted zero-attracting least mean M-estimate (VSSRZA-LMM) algorithm is proposed. The variable step-size scheme, which adopts the M-estimate cost function with a sparsity-aware penalty term and a constrained term of the step-size, is obtained by using the constrained minimization method. Besides, the mean-square stability is analyzed to obtain the range of the step-size, which guarantees the stabilization of the proposed algorithms. The computer simulation results show that the proposed RZA-LMM algorithm achieves better convergence performance than the RZA-LMS algorithm, and the proposed VSSRZA-LMM algorithm exhibits better convergence performance in terms of convergence speed and steady-state normalized mean square deviation (NMSD) than the RZA-LMM algorithm for sparse system identification in the impulsive noise environment.

A Polynomial Zero Attracting Affine Projection Algorithm for Sparse System Identification

A polynomial zero attracting affine projection algorithm is prosed in this work for sparse system identification. The existing zero attracting algorithms based on affine projection algorithm for sparse system identification, consider an objective function which is a combination of an l2-norm and an approximation of l0-norm. The difference between these algorithms is the approximation of the l0-norm. In order to further improve the zero attraction capability of sparse adaptive algorithms based on affine projection algorithm, a polynomial is used to approximate the l0-norm. Simulation results verify that the proposed algorithm is effective for sparse system identification.

Algorithm and VLSI Architecture Design of Proportionate-Type LMS Adaptive Filters for Sparse System Identification

Proportionate-type normalized LMS (Pt-NLMS) family of adaptive filtering algorithms for sparse system identification pose significant implementation challenges due to their high computational complexity especially for real-time applications like network echo cancelation. In this paper, we make the first attempt to implement Pt-NLMS algorithms in hardware. Several reformulations are proposed to simplify the original Pt-NLMS algorithms, thereby making them amenable to real-time VLSI implementations and the reformulated algorithms referred as delayed $\mu $ -law proportionate LMS (DMPLMS) algorithm for white input and delayed wavelet MPLMS (DWMPLMS) for colored input are then implemented in hardware. Simulation studies demonstrate that the performance loss is very small for the proposed reformulations. We implemented the proposed designs considering 16-bit fixed point representation in hardware, and synthesis results show that the DMPLMS architecture with ${\approx } 30\%$ increase in hardware over the state-of-the-art conventional delayed LMS architecture achieves $3\times $ improvement in convergence rate for white input and the DWMPLMS architecture with ${\approx } 70\%$ increase in hardware achieves $10\times $ improvement in convergence rate for correlated input conditions.

DEVELOPMENT OF ADAPTIVE ALGORITHM FOR SPARSE SYSTEM IDENTIFICATION.

28May 2018 DEVELOPMENT OF ADAPTIVE ALGORITHM FOR SPARSE SYSTEM IDENTIFICATION. Pooja Pawar and Dr. K. B. Khanchandani. Electronics and Telecommunication Department, Shri Sant Gajanan Maharaj college of engineering Shegaon, Buldana.

Bias compensated zero attracting normalized least mean square adaptive filter and its performance analysis

This paper presents a new normalized least mean square (NLMS) algorithm for sparse system identification where the input signal is corrupted by white measurement noise. The proposed algorithm, which is called bias-compensated zero attracting NLMS (BC-ZA-NLMS) algorithm, introduces the bias-compensation vector to get rid of the bias resulting from noisy input and introduces an l1-norm penalty in the cost function of the NLMS algorithm to make full use of the special property of the sparse system. In addition, to address the time variant sparsity, the bias-compensated reweight ZA-NLMS (BC-RZA-NLMS)) algorithm is also proposed, where the l1-norm penalty in the cost function of BC-ZA-NLMS algorithm is replaced by a log-sum function. Owing to the zero attractors in update equation, the proposed algorithms are superior to the conventional NLMS and bias-compensated NLMS (BC-NLMS) algorithms in the application of identifying the sparse system. A transient analysis of the proposed algorithms is also derived, which is able to accurately predict the behaviors of proposed algorithms. In addition, a stability analysis is introduced. Monte Carlo (MC) simulations are conducted to demonstrate the advantage of the proposed algorithms and to validate the theoretical results.

Fast ℓ1-recursive total least squares algorithm for sparse system identification

ℓ1-RTLS has been successfully applied to the identification of a sparse system whose input and output are contaminated by noise (the error-in-variables problem). This paper proposes a fast ℓ1-regularized recursive total least squares (fast ℓ1-RTLS) algorithm for sparse system identification. The proposed algorithm is based on the minimization of the ℓ1-regularized Rayleigh quotient by the line search method and the application of the fast gain vector (FGV). Simulation results show that the proposed algorithm requires less complexity than existing ℓ1-RTLS algorithms and that the estimation performance is also equivalent to existing ℓ1-RTLS algorithms in mean square deviation (MSD).

A family of gain-combined proportionate adaptive filtering algorithms for sparse system identification

The classical proportionate adaptive filtering (PAF) algorithms achieve a fast initial convergence for sparse impulse response. But the small coefficients receive very little gain so that the time needed to reach steady-state misalignment is increased. In addition, the PAF algorithms converge much slower than the original adaptive filtering (OAF) algorithms when the impulse response is dispersive. In order to address these problems, this paper proposes a family of gain-combined PAF (GC-PAF) algorithms. The gain-combined matrix of the proposed GC-PAF algorithms is implemented by using a sigmoidal activation function to adaptively combine the proportionate matrix and identity matrix, which can retain the advantages of both the PAF algorithms in the context of sparse impulse response and the OAF algorithms in the context of dispersive impulse response. Meanwhile, to be also applicable to the family of sign algorithms against impulsive noise, a general framework for the update of the sigmoidal activation function is obtained by using the gradient descent method to minimize the L1-norm of the system output error. Simulations in the contexts of three different sparsity impulse responses have shown that the proposed GC-PAF algorithms perform much better than the OAF, PAF and improved PAF (IPAF) algorithms.

L 0 ‐norm penalised shrinkage linear and widely linear LMS algorithms for sparse system identification

In this study, the authors propose an l 0-norm penalised shrinkage linear least mean squares (l 0-SH-LMS) algorithm and an l 0-norm penalised shrinkage widely linear least mean squares (l 0-SH-WL-LMS) algorithm for sparse system identification. The proposed algorithms exploit the priori and the posteriori errors to calculate the varying step-size, thus they can adapt to the time-varying channel. Meanwhile, in the cost function they introduce a penalty term that favours sparsity to enable the applicability for sparse condition. Moreover, the l 0-SH-WL-LMS algorithm also makes full use of the non-circular properties of the signals of interest to improve the tracking capability and estimation performance. Quantitative analysis of the convergence behaviour for the l 0-SH-WL-LMS algorithm verifies the capabilities of the proposed algorithms. Simulation results show that compared with the existing least mean squares-type algorithms, the proposed algorithms perform better in the sparse channels with a faster convergence rate and a lower steady-state error. When channel changes suddenly, a filter with the proposed algorithms can adapt to the variation of the channel quickly.

Proportionate Minimum Error Entropy Algorithm for Sparse System Identification

Sparse system identification has received a great deal of attention due to its broad applicability. The proportionate normalized least mean square (PNLMS) algorithm, as a popular tool, achieves excellent performance for sparse system identification. In previous studies, most of the cost functions used in proportionate-type sparse adaptive algorithms are based on the mean square error (MSE) criterion, which is optimal only when the measurement noise is Gaussian. However, this condition does not hold in most real-world environments. In this work, we use the minimum error entropy (MEE) criterion, an alternative to the conventional MSE criterion, to develop the proportionate minimum error entropy (PMEE) algorithm for sparse system identification, which may achieve much better performance than the MSE based methods especially in heavy-tailed non-Gaussian situations. Moreover, we analyze the convergence of the proposed algorithm and derive a sufficient condition that ensures the mean square convergence. Simulation results confirm the excellent performance of the new algorithm.