Normalized Subband Adaptive Filter Research Articles

Normalized Subband Adaptive Filter Algorithm with Combined Step Size for Acoustic Echo Cancellation

A novel normalized subband adaptive filter algorithm with combined step size is proposed for acoustic echo cancellation, which is derived by utilizing a variable mixing parameter to combine a large step size and a small one, thus providing fast convergence rate and small steady-state error. The mixing parameter is indirectly updated by utilizing the stochastic gradient method which minimizes the sum of squared subband errors. Simulation results demonstrate the superiority of the proposed algorithm in terms of the convergence rate and steady-state error as compared to other algorithms mentioned in this paper.

Affine Projection Subband Adaptive Filter With Low Computational Complexity

The affine projection algorithm (APA) and the normalized subband adaptive filter (NSAF) have been proposed to improve the convergence rate of the normalized least mean square algorithm for colored input signals. Recently, the improved multiband-structured subband adaptive filter (IMSAF) has been advanced, combining the APA and NSAF optimization approaches. The use of the IMSAF may result in accelerated convergence rate but at the expense of a large increase in computational complexity. In this brief, a reduced complexity subband adaptive algorithm is proposed, which employs sparse subfilters and a subband APA cost function. A variable-step-size method is developed, thereby providing fast convergence rate while ensuring small steady-state misadjustment.

A joint-optimization NSAF algorithm based on the first-order Markov model

Recently, the normalized subband adaptive filter (NSAF) algorithm has attracted much attention for handling the colored input signals. Based on the first-order Markov model of the optimal tap-weight vector, this paper provides a convergence analysis of the standard NSAF. Following the analysis, both the step size and the regularization parameter in the NSAF are jointly optimized in such a way that minimizes the mean square deviation. The resulting joint-optimization step size and regularization parameter (JOSR-NSAF) algorithm achieves a good tradeoff between fast convergence rate and low steady-state error. Simulation results in the context of acoustic echo cancellation demonstrate good features of the proposed algorithm.

Sparse normalized subband adaptive filter algorithm with l0-norm constraint

In order to improve the filter׳s performance when identifying sparse system, this paper develops two sparse-aware algorithms by incorporating the l0-norm constraint of the weight vector into the conventional normalized subband adaptive filter (NSAF) algorithm. The first algorithm is obtained from the principle of the minimum perturbation; and the second one is based on the gradient descent principle. The resulting algorithms have almost the same convergence and steady-state performance while the latter saves computational complexity. What׳s more, the performance of both algorithms is analyzed by resorting to some assumptions commonly used in the analyses of adaptive algorithms. Simulation results in the context of sparse system identification not only demonstrate the effectiveness of the proposed algorithms, but also verify the theoretical analyses.

Adaptive Combination of Proportionate NSAF with Individual Activation Factors

This paper presents a new proportionate normalized subband adaptive filter (PNSAF) algorithm, called the IAF-PNSAF, which assigns an individual activation factor for each filter coefficient instead of a common one for all filter coefficients as in the standard PNSAF algorithm. This algorithm achieves an improved performance in terms of the convergence rate and tracking capability for identifying a highly sparse system. Moreover, to overcome the trade-off of the fixed-step-size IAF-PNSAF algorithm between the fast convergence rate and small steady-state misalignment, its adaptive combination version is proposed. Simulation results for identifying the impulse response with high sparseness have demonstrated that the proposed algorithms outperform their counterparts.

Adaptive Combination of Proportionate NSAF with the Tap-Weights Feedback for Acoustic Echo Cancellation

To obtain fast convergence rate and low steady-state error in acoustic echo cancellation, a convex combination scheme of the improved proportionate normalized subband adaptive filter algorithm is proposed. Instead of the gradient method in the conventional combination theory, the mixing parameter is adapted by using the normalized gradient method which makes it more robust to the variations of subband error signals. Also, to implement a smooth transition from the fast filter to the accurate filter, a cyclic feedback of the overall tap-weights giving to all component filters is applied.

A band-independent variable step size proportionate normalized subband adaptive filter algorithm

Proportionate-type normalized subband adaptive filter (PNSAF-type) algorithms are very attractive choices for echo cancellation. To further obtain both fast convergence rate and low steady-state error, in this paper, a variable step size (VSS) version of the presented improved PNSAF (IPNSAF) algorithm is proposed by minimizing the square of the noise-free a posterior subband error signals. A noniterative shrinkage method is used to recover the noise-free a priori subband error signals from the noisy subband error signals. Significantly, the proposed VSS strategy can be applied to any other PNSAF-type algorithm, since it is independent of the proportionate principles. Simulation results in the context of acoustic echo cancellation have demonstrated the effectiveness of the proposed method.

A shrinkage variable step size for normalized subband adaptive filters

The conventional normalized subband adaptive filter (NSAF) using a constant step-size generally faces an inherent trade-off between the steady-state misalignment and the convergence rate. We propose herein a variable step-size NSAF algorithm by minimizing the mean-square deviation (MSD) between the optimal weight vector and the weight vector estimate with the utilization of the shrinkage denoising technique. With the estimation error involved in the step-size adaptation for each subband individually, the proposed algorithm is capable of tracking non-stationary environments. Without the explicit whitening assumption of the input signal in each subband, the proposed algorithm exhibits low steady-state MSD even when the input signal of each subband is colored. Simulation results validate the low misalignment and good tracking ability of the proposed algorithm in system identification application.

Bias-Compensated Normalized Subband Adaptive Filter Algorithm

A bias-compensated normalized subband adaptive filter (BC-NSAF) algorithm is proposed for system identification. In the proposed algorithm, a bias-compensation vector is derived to eliminate the bias caused by the noisy input signals. To estimate the input noise variance, a new estimation method is proposed, which does not require the input-output variance ratio in advance. Simulation results show that the proposed algorithm obtains better convergence performance than the existing algorithms in the presence of noisy input signals.

A novel subband adaptive filter algorithm against impulsive noise and it's performance analysis

The main drawback of the sign subband adaptive filter algorithm (SSAF) is its large steady-state error. To improve the performance, this paper proposes a novel normalized logarithmic subband adaptive filter algorithm (NLSAF), which is derived from a new normalized logarithmic cost function. Due to possess the advantages of the normalized subband adaptive filter (NSAF) and SSAF algorithms in the proposed NLSAF algorithm, it achieves a low steady-state error and the robustness performance against impulsive noise. Then, by using the energy conservation method, the mean-square convergence performance of the proposed NLSAF algorithm is presented. Simulations on system identifications demonstrate that the proposed subband adaptive filter performs better than the conventional SSAF algorithm in an impulsive-noise scenario.

Two Improved Normalized Subband Adaptive Filter Algorithms with Good Robustness Against Impulsive Interferences

To improve the robustness of subband adaptive filter (SAF) against impulsive interferences, we propose two modified SAF algorithms with an individual scale function for each subband, which are derived by maximizing correntropy-based cost function and minimizing logarithm-based cost function, respectively, called MCC-SAF and LC-SAF. Whenever the impulsive interference happens, the subband scale functions can sharply drop the step size, which eliminate the influence of outliers on the tap-weight vector update. Therefore, the proposed algorithms are robust against impulsive interferences, and exhibit the faster convergence rate and better tracking capability than the sign SAF (SSAF) algorithm. Besides, in impulse-free interference environments, the proposed algorithms achieve similar convergence performance as the normalized SAF (NSAF) algorithm. Simulation results have demonstrated the performance of our proposed algorithms.

A new normalized subband adaptive filter under minimum error entropy criterion

A new normalized subband adaptive filter based on the minimum error entropy criterion (MEE-NSAF) is proposed for identifying a highly noisy system. The MEE-NSAF utilizes a kernel function and a number of past errors in adaptation, whereas the classical NSAF relies only on the current error signal. Moreover, the stability of the MEE-NSAF is analyzed. To further improve the performance of the MEE-NSAF under the sparse impulse responses, an improved proportionate MEE-NSAF (MEE-IPNSAF) algorithm is proposed. Simulation results show that the proposed algorithms can achieve improved performance as compared with the conventional NSAF when noise gets severe.

Normalized Subband Adaptive Filtering Algorithm With Reduced Computational Complexity

Subband structures are suitable for improving convergence properties of adaptive filtering algorithms, particularly for colored input signals. This brief proposes a new subband adaptive algorithm with sparse adaptive subfilters, which employs the principle of minimal disturbance with multiple-constraint optimization. A performance analysis is carried out, resulting in an expression for the steady-state mean-square error. It is shown that the proposed algorithm, under some particular parameter choices, presents the same performance as that of the normalized subband adaptive filter, but with reduced computational complexity.

A robust band-dependent variable step size NSAF algorithm against impulsive noises

Proposed is a new subband adaptive filter (SAF) algorithm by minimizing Huber’s cost function that is robust to impulsive noises. Generally, this algorithm works in the mode of the normalized SAF (NSAF) algorithm, while it behaves like the sign SAF (SSAF) algorithm only when the impulsive noises appear. To further improve the robustness of this algorithm against impulsive noises, the subband cutoff parameters are updated in a recursive way. Moreover, the proposed algorithm can be interpreted as a variable step size NSAF algorithm, thus it exhibits faster convergence rate and lower steady-state error than the NSAF. Simulation results, using different colored input signals in both impulsive and free-impulsive noise environments, show that the proposed algorithm works better than some existing algorithms.

A New Normalized Subband Adaptive Filter Algorithm with Individual Variable Step Sizes

Proposed is a novel variable step size normalized subband adaptive filter algorithm, which assigns an individual step size for each subband by minimizing the mean square of the noise-free a posterior subband error. Furthermore, a noniterative shrinkage method is used to recover the noise-free priori subband error from the noisy subband error signal. Simulation results using the colored input signals have demonstrated that the proposed algorithm not only has better tracking capability than the existing subband adaptive filter algorithms, but also exhibits lower steady-state error.

Steady-state mean-square deviation analysis of improved normalized subband adaptive filter

A new minimization criterion for the normalized subband adaptive filter (NSAF), which is called improved NSAF (INSAF), was introduced recently to improve the performance of the steady-state mean-square deviation (MSD). However, the steady-state MSD analysis of the INSAF was not studied. Therefore, this paper proposes a general solution of steady-sate MSD analysis of the INSAF algorithm, which is based on the substitution of the past weight error vector in the weight error vector. The simulation shows that our theoretical results correspond closely with the computer simulation results in various environments.

Variable regularization for normalized subband adaptive filter

To overcome the performance degradation of least mean square (LMS)-type algorithms when input signals are correlated, the normalized subband adaptive filter (NSAF) was developed. In the NSAF, the regularization parameter influences the stability and performance. In addition, there is a trade-off between convergence rate and steady-state mean square deviation (MSD) according to the change of the parameter. Therefore, to achieve both fast convergence rate and low steady-state MSD, the parameter should be varied. In this paper, a variable regularization scheme for the NSAF is derived on the basis of the orthogonality between the weight-error vector and weight vector update, and by using the calculated MSD. The performance of the variable regularization algorithm is evaluated in terms of MSD. Our simulation results exhibit fast convergence and low steady-state MSD when using the proposed algorithm.

The New Normalized Subband Adaptive Filter Algorithms with Variable Step-Size

This paper presents a new variable step-size normalized subband adaptive filter (VSS-NSAF) algorithm. In the proposed VSS-NSAF, the step-size changes in order to have largest decrease in the mean square deviation (MSD) for sequential iterations. To reduce the computational complexity of VSS-NSAF, the variable step-size selective partial update normalized subband adaptive filter (VSS-SPU-NSAF) is proposed. In this algorithm the filter coefficients are partially updated in each subband at every iteration. Simulation results show the good performance of the proposed algorithms in convergence speed and steady-state MSD.

A Variable Step Size for Acoustic Echo Cancellation Using Normalized Sub band Adaptive Filter

Numerous various step size normalized least mean square (VSS-NLMS)Algorithms have been derived to solve the problem of fast convergence rate and low mean square error.Here we find out the ways to control the step size. A normalized subband adaptive filter algorithm uses a fixed and variable step size, which is chosen as a trade-off between the steady-state error and the convergence rate. A variable step size for normalized subband adaptive filter is derived by minimizing the mean-square deviation between the optimal weight vector and the estimated weight vector at each instant of time. The variable step size is presented in terms of error variance. Therefore, we verify thedifferent algorithmseither they are capable of tracking in stationary and non-stationary environments. The results show good tracking ability and low misalignment of the algorithm in system identification. Parameters are tracking, steady state errors, and misalignment, environment, step size.

Steady-state mean-square error analysis of regularized normalized subband adaptive filters

The normalized subband adaptive filter (NSAF) has faster convergence rate than the normalized least-mean-square (NLMS) algorithm for colored input signals. Regularization of the NSAF is of importance in practical applications. In this paper, we analyze the steady-state mean-square error (MSE) of regularized NSAFs. The analysis is carried out based on the derivation of a variable regularization matrix NSAF (VRM-NSAF). Theoretical expressions for the steady-state MSE of two regularized NSAFs are derived under some assumptions. Simulation results are given to support the theoretical analysis.