The PNLMS algorithm with unbiasedness criterion in sparse system identification

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.

The proportionate normalized least-mean squares (PNLMS) adaptation algorithm exploits the sparse nature of acoustic impulse responses and assigns adaptation gain proportional to the absolute value of filter coefficients, thereby resulting in faster convergence. In the past it has shown to improve con vergence of acoustic paths in echo-cancellation applications. In this paper, we investigate the use of PNLMS algorithm for blind speech separation and show that with a careful selection of operating parameters the PNLMS algorithm greatly helps promote convergence of the un-mixing filters when compared to the conventional normalized least-mean-squares (NLMS) adaptation. The PNLMS based blind speech separation is suitable for real-time implementation as it promises faster con vergence and requires only a modest increase in complexity as compared to the NLMS algorithm.

Objectives: To enhance the quality of Cardiac Signal for perfect diagnosis by the doctor. Methods/Statistical Analysis: We are introducing some adaptive filter structures for Cardiac Signal (CS) enhancement for the extraction of high resolution cardiac signals and these structures were based on the Proportionate Normalized Least Mean Square (PNLMS) algorithm. The main advantage of PNLMS over the conventional techniques is extraction of sparse coefficients, suitably weighing them and fast convergence. These ANCs are tested using MIT-BIH database to compare the performance. Findings: We consider Signal to Noise Ratio (SNR), Excess Mean Square Error (EMSE), Misadjustment (MSD), convergence curves and residual error plots as performance measures. Among the ANCs tested, PMNSRLMA based ANC is found to be better with reference to the considered performance measures and computational complexity. The average SNRI achieved by this ANC is 18.8856dBs for PLI elimination, 8.7580dBs for BW elimination, 8.5106dBs for MA elimination and 8.5012dBs for EM elimination. From the above results it is clear that in practical biotelemetry applications to minimize the computational complexity of the noise canceller we combine PNLMS with signature algorithms. Again, to reduce the complexity in the denominator of the normalized recursion, we use maximum normalized version of PNLMS. Finally, these variations result in seven algorithms in addition to PNLMS. Based on these algorithms, we develop various Adaptive Noise Cancellers (ANCs) to eliminate artifacts present in the CS and to present best quality signal to the doctor for diagnosis. Application/ Improvement: The standard of Cardiac Signal can be enhanced by improving data acquisition methods.

Several set-membership (SM) based proportionate normalized least-mean-square (PNLMS) using the modified filtered-x (MFx) structures are proposed for active noise control. It is shown by simulations that the proposed algorithms that have a reduced numerical complexity can obtain better performance than MFx-PNLMS for various ANC paths.

The Proportionate Normalized Least Mean Squares (PNLMS) algorithm has been quite successful in combining higher convergence rates with low to moderate complexity that at the same time avoids numerical difficulties in fixed-point implementations. While the algorithm is stable in the mean square and l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -sense for time-invariant matrices, the treatment of time-variant matrices requires additional approximations. These approximations are discarded in this paper which allows us to analyse the robustness in terms of l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -stability for actually time-variant matrix step-sizes. This provides important results, as the algorithm in its variants also occurs in other fields of adaptive filtering such as cascaded filter structures. By simulations as well as by theoretical analysis, we demonstrate that in general, even small variations of the matrix step-size are sufficient for the algorithm to loose its robustness. Only in special cases, where specific constraints are imposed additionally, robustness can be guaranteed.

In this paper, a feedback interference cancellation scheme for digital on-channel repeaters (DOCRs) in terrestrial-digital multimedia broadcasting (TDMB) system is introduced. In order to mitigate the feedback signal in DOCR, an interference cancellation scheme using proportionate normalized least mean squares (PNLMS) algorithm is proposed. Simulation results confirm the RFP performance improvement at the DOCR and the BER performance improvement of T-DMB in time-varying typical urban channel.

This paper incorporates a correntropy-induced metric (CIM)-based sparsity constraint into variable step size normalized least mean square (VSSNLMS) algorithm for identification of sparse system corrupted by additive noise. The proposed CIM-VSSNLMS algorithm makes a good trade-off between convergence characteristics, filter stability, and steady state error. The proposed (CIM-VSSNLMS) algorithm incorporates a variable step size that accelerates the convergence characteristics and lowers the normalized misalignment (NMSA) error with respect to CIM-NLMS with constant value of step size. An expression for variant step size is derived under the stability condition of proposed algorithm. Finally, the implementation of the proposed algorithm is carried out in MATLAB software to manifest the improved estimated behavior in the identification of sparse system.

The newly proposed l 1 norm constraint zero-point attraction least mean square algorithm (ZA-LMS) demonstrates excellent performance on exact sparse system identification. However, ZA-LMS has less advantage against standard LMS when the system is near sparse. Thus, in this study, firstly the near sparse system (NSS) modelling by generalised Gaussian distribution is recommended, where the sparsity is defined accordingly. Second, two modifications to the ZA-LMS algorithm have been made. The l 1 norm penalty is replaced by a partial l 1 norm in the cost function, enhancing robustness without increasing the computational complexity. Moreover, the ZA item is weighted by the magnitude of estimation error which adjusts the ZA force dynamically. By combining the two improvements, Dynamic Windowing ZA-LMS (DWZA-LMS) algorithm is further proposed, which shows better performance on NSS identification. In addition, the mean-square performance of DWZA-LMS algorithm is analysed. Finally, computer simulations demonstrate the effectiveness of the proposed algorithm and verify the result of theoretical analysis.

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.

To address the sparse system identification problem under noisy input and non-Gaussian output measurement noise, two novel types of sparse bias-compensated normalized maximum correntropy criterion algorithms are developed, which are capable of eliminating the impact of non-Gaussian measurement noise and noisy input. The first is developed by using the correntropy-induced metric as the sparsity penalty constraint, which is a smoothed approximation of the norm. The second is designed using the proportionate update scheme, which facilitates the close tracking of system parameter change. Simulation results confirm that the proposed algorithms can effectively improve the identification performance compared with other algorithms presented in the literature for the sparse system identification problem.

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 an ell _1-regularized recursive total least squares (RTLS) algorithm is considered for the sparse system identification. Although recursive least squares (RLS) has been successfully applied in sparse system identification, the estimation performance in RLS based algorithms becomes worse, when both input and output are contaminated by noise (the error-in-variables problem). We proposed an algorithm to handle the error-in-variables problem. The proposed ell _1-RTLS algorithm is an RLS like iteration using the ell _1 regularization. The proposed algorithm not only gives excellent performance but also reduces the required complexity through the effective inversion matrix handling. Simulations demonstrate the superiority of the proposed ell _1-regularized RTLS for the sparse system identification setting.

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

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.

A stochastic conjugate gradient multi-modulus algorithm based on global artificial fish swarm and genetic optimization DNA encoding sequences(GAFS-GDNA-SMMA) is proposed to solve the high computational loads, low convergence rate, and large mean square error(MSE) of the multi-modulus blind equalization algorithm(MMA). In this proposed algorithm, the optimal DNA coding sequence can be found and used as the initial optimal weight vector of the stochastic conjugate gradient MMA(SMMA) after decoding the optimization DNA sequences. The simulation results show that the proposed algorithm has the faster convergence speed and smaller mean square error comparison with MMA, SMMA, GA-DNA-SMMA(Genetic algorithm and DNA optimization based SMMA)