A Low Delay and Fast Converging Improved Proportionate Algorithm for Sparse System Identification

In acoustic signal processing, the improved proportionate normalized least mean square (IPNLMS) is known as an effective adaptive algorithm for sparse impulse response systems. And it is known that the subband adaptive filter provides fast convergence rate, because of its data prewhitening characteristic. In this paper, we propose a subband blind adaptive algorithm for multi-inputs multi-outputs (MIMO) systems. The proposed algorithm (subband IPNLMS) combines subband filtering technique with IPNLMS algorithm. In this approach, subband adaptive filtering is employed to overcome the problems in long adaptive filters such as computational complexity and slow convergence rate. Simulation results show that the subband IPNLMS performs better than the subband NLMS, when the blind channel impulse response is sparse.

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 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.

In this paper, we derive a new improved proportionate normalized least mean square (IPNLMS) algorithm with unconventional minimization criterion that minimizes the summation of each squared Euclidean norm of difference between the currently updated coefficient vector and past coefficient vectors, which is called the improved IPNLMS (I-IPNLMS) algorithm. Simulation results demonstrate that the proposed I-IPNLMS algorithm has the superiority of the lower misalignment than the conventional IPNLMS algorithm in the context of sparse system identification with a low signal-noise-ratio (SNR).

A convex combination LMS (least mean square) algorithm based on Krylov subspace transform is proposed in this paper. In this approach, impulse response of the unknown system is firstly transformed into Krylov subspace, in which the system structure is changed into sparse. Then an improved proportionate normalized LMS (IPNLMS) algorithm and a variable tap-length normalized LMS (VTNLMS) algorithm are combined. Simulations are performed to show the convergence performance of the combined algorithm. The results show that both a fast convergence rate and small steady state mean square deviation (MSD) are obtained.

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.

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

High-rate underwater acoustic (UWA) channels often demonstrate long, time-varying and sparse impulse responses. Classical and most used adaptive algorithms such as the recursive least-squares (RLS) algorithm and the normalized least-mean-square (NLMS) algorithm do not take sparseness into account when they try to match the channel. Thus, performance improvement of these algorithms is possible. Sparse adaptive algorithms developed for acoustic echo cancellation, such as the improved proportionate normalized least-mean-square (IPNLMS) algorithm and the improved proportionate affine projection algorithm (IPAPA), have shown better performance than the NLMS algorithm without any essential cost in computational complexity. In this work, we apply IPNLMS, IPAPA, RLS and NLMS in both channel estimation and decision feedback equalization (DFE) of a short-range, shallow water acoustic link. Our results confirm the superior performance of the sparse algorithms (IPAPA being the best) when the channel becomes sparse. In addition, it is shown that both IPAPA and IPNLMS have robust performance (similar to RLS) when the channel is non-sparse.

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.

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.

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.

SummaryIn this paper, the proportionate normalized least mean square (PNLMS) and its modifications, such as improved PNLMS (IPNLMS) and μ‐law PNLMS (MPNLMS) algorithms, developed for a sparse system, are analyzed for a compressed input signal. This analysis is based on a comparative study of the steady‐state error and convergence time for the original signal and the compressed signal. Further, in this paper, a filter PNLMS (FPNLMS) algorithm that is a modification of the IPNLMS algorithm is proposed. The FPNLMS algorithm uses a step size varying in time to adapt to the sparse system. Simulations are carried out to compare the proposed FPNLMS algorithm for different signal‐to‐noise ratio for a compressed input signal with existing algorithms, ie, PNLMS, MPNLMS, and IPNLMS algorithms. The FPNLMS algorithm achieves a better steady‐state and convergence time compared with other existing algorithms in both low and high SNRs. The FPNLMS algorithm is further simulated for a real transfer function to show its robustness compared with existing algorithms.

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 ...