A reweighted l0-norm-constraint LMS 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.

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

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

Long impulse response system identification presents two challenges for standard normalized least mean square (NLMS) filtering method: heavy computational load and slow convergence. When the response is sparse, partial update algorithms can reduce the computational complexity, but most often at the expense of performance. This paper discusses the tap selection rule for partial update NLMS algorithm in the case of white Gaussian input. We consider output mean square error (MSE) minimization based on gradient analysis and propose an algorithm that switches tap selection criterion between the one based on filter coefficient magnitudes and the one based on input magnitudes. We show that for identifying sparse systems, the new algorithm can outperform standard NLMS significantly with a reduced computational load.

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.

Sparse constraint Least Mean Square (LMS) is a recently proposed efficient adaptive algorithm for sparse system identification. However, its computational complexity is quite high especially when the filter length is long and convergence is slow for colored input signal. This paper extends the idea of sparse constraint into multidelay frequency adaptive filter (MDF) algorithm and proposes the sparse MDF algorithm for echo cancellation. The proposed algorithm perserves both the advantage of sparse LMS which has fast convergence performance for sparse system and MDF algorithm which has temporal decorrelation effect with lower implementation complexity. Two typical sparse constraints, l 1 -norm and an approximate l 0 -norm, are employed. And their performances of various aspects are simulated. Experiments show they have better performance than existing algorithms.

A sparse system identification algorithm for network echo cancellation is presented. This new approach exploits both the fast convergence of the improved proportionate normalized least mean square (IPNLMS) algorithm and the efficient implementation of the multidelay adaptive filtering (MDF) algorithm inheriting the beneficial properties of both. The proposed IPMDF algorithm is evaluated using impulse responses with various degrees of sparseness. Simulation results are also presented for both speech and white Gaussian noise input sequences. It has been shown that the IPMDF algorithm outperforms the MDF and IPNLMS algorithms for both sparse and dispersive echo path impulse responses. Computational complexity of the proposed algorithm is also discussed.

For sparse system identification, a μ-law memorised improved proportionate affine projection algorithm (MMIPAPA) can achieve faster convergence rate than the standard affine projection algorithm. However, the MMIPAPA with constant regularisation parameter requires a tradeoff between fast convergence speed and low steady-state error. To address the problem, proposed are two kinds of variable non-identity regularisation matrices for the MMIPAPA with a negligible additional computational cost and a stability condition for the step-size choice. Simulation results show the good misalignment performance of the proposed algorithms for both coloured and speech input.

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.

System identification has wide applications in adaptive echo/feedback cancellation, active noise control, adaptive channel equalization, etc. When the system is sparse, recently, a μ-law memorised improved proportionate affine projection algorithm (MMIPAPA) has been proposed to improve the misalignment performance remarkably. However, the MMIPAPA with constant step-size has the conflicting requirement of fast convergence rate and low steady-state error. To solve this problem, a variable step-size version of the MMIPAPA (VSS-MMIPAPA) has been extended by setting each component of the a posterior error energy vector equal the system noise energy. Furthermore, through an alternative method to compute the variable step-size, when the estimated component of the a prior error energy vector is smaller than the system noise energy, further lower steady-state misalignment is achieved. This method leads to an improved VSS-MMIPAPA (IVSS-MMIPAPA). The computational complexity of the IVSS-MMIPAPA is O(P2L), which may ...

摘要: 该文研究和改进了l0-LMS算法以提高对稀疏系统进行辨识的性能。首先依据均方误差反映出的收敛深度信息动态调节步长，提高了算法的收敛速度；其次利用估计误差绝对值加权修正零吸引函数，减小了稳态失调误差。然后定性分析了改进算法中各个参数的取值对收敛速度和稳态性能的影响。最后，计算机仿真验证了新算法的性能明显优于原l0-LMS算法和若干现有稀疏系统辨识的方法。 关键词: 信号处理 / 稀疏系统辨识 / l0-LMS / 变步长 / 零吸引

Proportionate normalized subband adaptive filter algorithms for sparse system identification

In this paper, we introduce a two dimensional version of the zero-attracting variable step size LMS (ZA-VSSLMS) adaptive filter for image deconvolution. ZA-VSSLMS was proposed to improve the performance of the VSSLMS algorithm when the system is sparse. We design a new 2-D adaptive filter that not only updates its coefficients in both horizontal and vertical directions but more importantly improves the performance of the filter when the the point spread function (PSF) in an image deconvolution problem has a sparse structure. This is achieved by adding an ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm penalty function into the original cost function of the VSSLMS algorithm. The simulation results show improved PSNR compared to 2-D VSSLMS algorithm.

A general zero attraction (GZA) proportionate normalized maximum correntropy criterion (GZA-PNMCC) algorithm is devised and presented on the basis of the proportionate-type adaptive filter techniques and zero attracting theory to highly improve the sparse system estimation behavior of the classical MCC algorithm within the framework of the sparse system identifications. The newly-developed GZA-PNMCC algorithm is carried out by introducing a parameter adjusting function into the cost function of the typical proportionate normalized maximum correntropy criterion (PNMCC) to create a zero attraction term. The developed optimization framework unifies the derivation of the zero attraction-based PNMCC algorithms. The developed GZA-PNMCC algorithm further exploits the impulsive response sparsity in comparison with the proportionate-type-based NMCC algorithm due to the GZA zero attraction. The superior performance of the GZA-PNMCC algorithm for estimating a sparse system in a non-Gaussian noise environment is proven by simulations.

in this paper we studied the performance of several distributed adaptive algorithms for non-stationary sparse system identification. Non-stationarity is a feature that is introduced to adaptive networks recently and makes the performance of them degraded. The performance analyses are carried out with the steady-state mean square deviation (MSD) criterion of adaptive algorithms. Some sparsity aware algorithms are considered in this paper which tested in non-stationary systems for the first time. It is presented and proved that the performance of incremental least means square/forth (ILMS/F) algorithm surpasses all other algorithms as non-stationarity grows. We hope that this work will inspire researchers to look for other advanced algorithms against systems that are both non-stationary and sparse.