Proportionate NLMS Algorithm Research Articles

A novel block-sparse proportionate NLMS algorithm based on the l2,0 norm

To ameliorate the performance of the normalized least mean square (NLMS) algorithm applied in identifying block-sparse system, a novel block-sparse proportionate NLMS (BS-PNLMS) algorithm based on the mixed l2,0 norm is presented in this paper. The cost function of proposed algorithm is obtained by introducing the approximated mixed l2,0 norm penalty in the cost function of BS-PNLMS algorithm, which is equivalent to attaching the mixed l2,0 norm zero attraction to the update equation. The proposed algorithm is named as the l2,0-BS-PNLMS algorithm. Futhermore, a variable step-size l2,0-BS-PNLMS is developed to further improve the performance of the l2,0-BS-PNLMS. Simulation results demonstrate the advantages of proposed algorithms.

The Bias-Compensated Proportionate NLMS Algorithm With Sparse Penalty Constraint

For compensating the bias caused by the noisy input which is always ignored by ordinary algorithms, two novel algorithms with zero-attraction (ZA) penalties are proposed in this paper. The first one constructs a bias-compensated term in the updating recursion of the zero-attraction proportionate normalized least mean square (PNLMS) algorithm which is named BC-ZA-PNLMS algorithm. The second one employs the bias-compensated term and the correntropy induced metric (CIM) constraint to renew the updating recursion of the PNLMS algorithm which is named BC-CIM-PNLMS algorithm. Both of these two algorithms are derived on the basis of unbiased criterion. Simulation examples are carried out, and the results indicate that the two newly developed unbiased algorithms outperform the related algorithms previously presented in other literatures for combating noisy input and measurement noises.

Filter proportionate normalized least mean square algorithm for a sparse system

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.

A bias‐compensated proportionate NLMS algorithm with noisy input signals

SummaryThis paper proposes a novel proportionate normalized least‐mean‐squares (PNLMS) algorithm that is robust to input noises. Through compensating for biases due to input noise added at the filter input, the proposed PNLMS algorithm avoids performance deterioration owing to the noisy input signals. Moreover, since the proposed PNLMS algorithm uses a new gain‐distribution matrix, it has a fast convergence rate compared with the existing PNLMS algorithms, even when there is no input noise. The experimental results verify that the proposed PNLMS algorithm enhances the filter performance for sparse system identification in the presence of input noises.

Robust Adaptive Filter Algorithms Against Impulsive Noise

This paper proposes a prefiltered observation-based adaptive filter algorithm that is robust against impulsive noise. Previous impulsive noise rejection algorithms were based on output error stochastic, so there was a trade-off relationship between impulsive noise detection and tracking performances. The proposed rejection algorithm is derived by using the statistics of the observed signal and the inequality such as the Schwarz and Young inequality in the absence of impulsive noise. From this, the proposed algorithm updates the weight vector only when the observed signal is not corrupted by impulsive noise. The proposed algorithm achieves the good tracking performance because it distinguishes between the system change and interruption of impulsive noise. In addition, the proposed algorithm has same performance without impulsive noise, compared with the normalized least-mean-square-type algorithm. Further, the proposed rejection algorithm could expand to various adaptive filtering structures, which suffer the performance degradation with impulsive noise, because it is easy to implement. Hence, the proposed algorithm is combined with the NLMS algorithm for dispersive systems and the proportionate NLMS algorithm for sparse systems. Simulation results show that the proposed algorithm achieves fast convergence rate, good tracking performance, and robustness under the impulsive noise environment.

Cluster-Sparse Proportionate NLMS Algorithm With the Hybrid Norm Constraint

In this paper, an enhanced proportionate normalized least mean square (PNLMS) algorithm with the hybrid ${l_{2,0}}$ -norm constraint is proposed for block-sparse signal processing. The proposed algorithm penalizes a mixed ${l_{2,0}}$ -norm on the PNLMS to fully exploit the sparsity and handle block-sparse signals, which is called the ${l_{2,0}}$ norm constrained PNLMS (L20-PNLMS). The L20-PNLMS is well derived and carefully analyzed. Various experiments have been constructed to verify the effectiveness of the devised L20-PNLMS. The experimental results demonstrate that the devised L20-PNLMS performs better than the previous PNLMS algorithms do in block sparse signal processing.

Improving the Performance of the PNLMS Algorithm Using Norm Regularization

The proportionate normalized least mean square (PNLMS) algorithm and its variants are by far the most popular adaptive filters that are used to identify sparse systems. The convergence speed of the PNLMS algorithm, though very high initially, however, slows down at a later stage, even becoming worse than sparsity agnostic adaptive filters like the NLMS. In this paper, we address this problem by introducing a carefully constructed $l_1$ norm (of the coefficients) penalty in the PNLMS cost function which favors sparsity. This results in certain zero attracting terms in the PNLMS weight update equation which help in the shrinkage of the coefficients, especially the inactive taps, thereby arresting the slowing down of convergence and also producing lesser steady state excess mean square error (EMSE). A rigorous convergence analysis of the proposed algorithm is presented that expresses the steady state mean square deviation of both the active and the inactive taps in terms of a zero attracting coefficient of the algorithm. The analysis reveals that further reduction of the EMSE is possible by deploying a variable step size (VSS) simultaneously with a variable zero attracting coefficient in the weight update process. Simulation results confirm superior performance of the proposed VSS zero attracting PNLMS algorithm over existing algorithms, especially in terms of having both higher convergence speed and lesser steady state EMSE simultaneously.

Proportionate Adaptive Filtering for Block-Sparse System Identification

In this paper, a new family of proportionate normalized least mean square (PNLMS) adaptive algorithms that improve the performance of identifying block-sparse systems is proposed. The main proposed algorithm, called block-sparse PNLMS (BS-PNLMS), is based on the optimization of a mixed l2,1 norm of the adaptive filter coefficients. It is demonstrated that both the NLMS and the traditional PNLMS are special cases of BS-PNLMS. Meanwhile, a block-sparse improved PNLMS (BS-IPNLMS) is also derived for both sparse and dispersive impulse responses. Simulation results demonstrate that the proposed BS-PNLMS and BS-IPNLMS algorithms outperformed the NLMS, PNLMS and IPNLMS algorithms with only a modest increase in computational complexity.

An improved proportionate normalized least mean square algorithm for sparse impulse response identification

In this paper after analyzing the adaptation process of the proportionate normalized least mean square (PNLMS) algorithm, a statistical model is obtained to describe the convergence process of each adaptive filter coefficient. Inspired by this result, a modified PNLMS algorithm based on precise magnitude estimate is proposed. The simulation results indicate that in contrast to the traditional PNLMS algorithm, the proposed algorithm achieves faster convergence speed in the initial convergence state and lower misalignment in the stead stage with much less computational complexity.

Adaptive Sub‐Band Acoustic Echo Cancellation Algorithms for Echo Paths Involving Nonlinear Amplifiers and Transducers

AbstractThis paper examines the normalized least‐mean‐squares (NLMS) algorithm, the proportionate normalized least‐mean‐squares (PNLMS) algorithm, and the affine projection algorithm (APA) applied to the linear and nonlinear sub‐band acoustic echo canceller (AEC). The AEC aims at reducing the acoustic echo generated from a loudspeaker‐enclosure‐microphone (LEM) system. In order to enhance the efficacy of echo cancellation, the AEC utilizes sub‐band structure in conjunction with the PNLMS algorithm and the APA. To cope with nonlinear distortions from low‐cost transducers, the AEC is augmented with nonlinear processors based on second‐order Volterra filters and a Hammerstein nonlinear model. The proposed AEC was verified through extensive simulations and experiments. The results have shown that the proposed system achieved improved echo cancellation performance over conventional systems and met the telecom standard ITU‐T Rec. G.168.

Mean-square error and stability analysis of a subband structure for the rapid identification of sparse impulse responses

In a context of supervised adaptive filtering, the sparsity of the impulse response to be identified can be employed to accelerate the convergence rate of the algorithm. This idea was first explored by the so-called proportionate NLMS (PNLMS) algorithm, where the adaptation step-sizes are made larger for the coefficients with larger magnitudes. Whereas fast initial adaptation convergence rate is obtained with the PNLMS algorithm for white-noise input, slow convergence is observed for colored input signals. The combination of the PNLMS approach and a subband structure results in an algorithm with better convergence rate for sparse systems and colored input signals. In this paper, the steady-state mean-square error (MSE) and the maximum value of the step-size @b that allows convergence of the subband PNLMS-type algorithm are analyzed. Theoretical results are confirmed by simulations.

A PNLMS Algorithm With Individual Activation Factors

This paper presents a proportionate normalized least-mean-square (PNLMS) algorithm using individual activation factors for each adaptive filter coefficient, instead of a global activation factor as in the standard PNLMS algorithm. The proposed individual activation factors, determined in terms of the corresponding adaptive filter coefficients, are recursively updated. This approach leads to a better distribution of the adaptation energy over the filter coefficients than the standard PNLMS does. Thereby, for impulse responses exhibiting high sparseness, the proposed algorithm achieves faster convergence, outperforming both the PNLMS and improved PNLMS (IPNLMS) algorithms.

A Variable Step-Size Proportionate NLMS Algorithm for Identification of Sparse Impulse Response

Recently, proportionate adaptive algorithms have been proposed to speed up convergence in the identification of sparse impulse response. Although they can improve convergence for sparse impulse responses, the steady-state misalignment is limited by the constant step-size parameter. In this article, based on the principle of least perturbation, we first present a derivation of normalized version of proportionate algorithms. Then by taking the disturbance signal into account, we propose a variable step-size proportionate NLMS algorithm to combine the benefits of both variable step-size algorithms and proportionate algorithms. The proposed approach can achieve fast convergence with a large step size when the identification error is large, and then considerably decrease the steady-state misalignment with a small step size after the adaptive filter reaches a certain degree of convergence. Simulation results verify the effectiveness of the proposed approach.

Krylov-Proportionate Adaptive Filtering Techniques Not Limited to Sparse Systems

This paper proposes a novel adaptive filtering scheme named the Krylov-proportionate normalized least-mean-square (KPNLMS) algorithm. KPNLMS exploits the benefits (i.e., fast convergence for sparse unknown systems) of the proportionate NLMS algorithm, but its applications are not limited to sparse unknown systems. A set of orthonormal basis vectors is generated from a certain Krylov sequence. It is proven that the unknown system is sparse with respect to the basis vectors in case of fairly uncorrelated input data. Different adaptation gain is allocated to a coefficient of each basis vector, and the gain is roughly proportional to the absolute value of the corresponding coefficient of the current estimate. KPNLMS enjoys i) fast convergence, ii) linear complexity per iteration, and iii) no use of any a priori information. Numerical examples demonstrate significant advantages of the proposed scheme over the reduced-rank method based on the multistage Wiener filter (MWF) and the transform-domain adaptive filter (TDAF) both in noisy and silent situations.

Proportionate adaptive algorithms for network echo cancellation

By analyzing the coefficient adaptation process of the steepest descent algorithm, the condition under which the fastest overall convergence will be achieved is obtained and the way to calculate optimal step-size control factors to satisfy that condition is formulated. Motivated by the results and using the stochastic approximation paradigm, the /spl mu/-law PNLMS (MPNLMS) algorithm is proposed to keep, in contrast to the proportionate normalized least-mean-square (PNLMS) algorithm, the fast initial convergence during the whole adaptation process in the case of sparse echo path identification. Modifications of the MPNLMS algorithm are proposed to lower the computational complexity.

Improving convergence of the PNLMS algorithm for sparse impulse response identification

A proportionate normalized least mean square (PNLMS) algorithm has been proposed for sparse impulse response identification. It provides fast initial convergence, but it begins to slow down dramatically after the initial period. In this letter, we analyze the coefficient adaptation process of the steepest descent algorithm and derive how to calculate the optimal proportionate step size in order to achieve the fastest convergence. The results bring forward a novel view of the concept of proportion. We propose a /spl mu/-law PNLMS (MPNLMS) algorithm using an approximation of the optimal proportionate step size. Line segment approximation and partial update techniques are discussed to bring down the computational complexity.

A Fast Converging Algorithm for Network Echo Cancelation

The letter presents a novel method for network echo cancellation, based on a combination of normalized least mean square (NLMS) and proportionate NLMS (PNLMS) adaptive filtering algorithms. First, based on a rough analysis of PNLMS adaptation, it is indicated why, after PNLMS initial fast convergence, it slows down. Then, the method used to overcome this deficiency is presented. Last, by showing some of the simulations, its improvement over the PNLMS algorithm is shown.

Double-talk robust fast converging algorithms for network echo cancellation

There is a need for echo cancelers for echo paths with long impulse responses (/spl ges/64 ms). This in turn creates a need for more rapidly converging algorithms in order to meet the specifications for network echo cancelers. Faster convergence, however, in general implies a higher sensitivity to near-end disturbances, especially Previously, a fast converging algorithm has been proposed called proportionate normalized least mean squares (PNLMS) algorithm. This algorithm exploits the sparseness of the echo path and has the advantage that no detection of active coefficients is needed. In this paper we propose a method for making the PNLMS algorithm more robust against double-talk. The slower divergence rate of these algorithms in combination with a standard Geigel double-talk detector improves the performance of a network echo canceler considerably during double-talk. The principle is based on a scaled nonlinearity which is applied to the residual error signal. This results in the robust PNLMS algorithm which diverges much slower than PNLMS and standard NLMS. Tradeoff between convergence and divergence rate is easily adjusted with one parameter and the added complexity is about seven instructions per sample which is less than 0.3% of the total load of a PNLMS algorithm with 512 filter coefficients. A generalization of the robust PNLMS algorithm to a robust proportionate affine projection algorithm (APA) is also presented. It converges very fast, and unlike PNLMS, is not as dependent on the assumption of a sparse echo path response. The complexity of the robust proportionate APA of order two is roughly the same as that of PNLMS.