Sign Subband Adaptive Filter Research Articles

Affine Projection Sign Subband Adaptive Filter Algorithm With Unbiased Estimation Under System Identification

The affine projection sign subband adaptive filter (AP-SSAF) was designed by utilizing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M}$ </tex-math></inline-formula> most recent input samples to further enhance the performance of the traditional SSAF. However, the abovementioned algorithms only concentrate on the noise interferences that exist in the output of system under system identification application. Actually, the input of adaptive filter could contain the noises as well. Thereby the performance of the above algorithms will inevitably deteriorate. Based on the excellent performance of AP-SSAF, in this brief, through incorporating unbiasedness criteria into the AP-SSAF, the bias-compensated AP-SSAF (BC-AP-SSAF) is devised for diminishing the impact of input noises via introduced bias compensation term, with some necessary assumptions. And the convergence is provided. Monte-Carlo simulations certify that the proposed BC-AP-SSAF holds stability under impulsive interferences and decreases the estimated bias markedly.

Statistics Behavior of Individual-Weighting-Factors SSAF Algorithm Under Errors-in-Variables Model

The individual-weighting-factors sign subband adaptive filtering (IWF-SSAF) algorithm has acquired attention due to its quick convergence and brilliant robustness against impulsive interference. However, its statistics behavior has not been investigated under errors-in-variables (EIV) model, which system input and output are all corrupted by noise. Therefore, in this letter, the statistics analysis including transient and steady-state behaviors of IWF-SSAF is derived in mean and mean-square senses by virtue of some frequently-utilized assumptions and Price's theorem. Finally, numerical simulations under system identification scenario manifest that the simulated and theoretical results are in good agreement in different environments, which corroborate the accurateness of the derived theoretical models.

A family of variable step-size sparsity-aware SSAF algorithms with individual-weighting-factors under model-driven method

Recently, the sparsity-aware sign subband adaptive filter algorithm with individual-weighting-factors (S-IWF-SSAF) was devised. To accomplish performance enhancement, the variable parameter S-IWF-SSAF (VP-S-IWF-SSAF) algorithm was developed through optimizing the step-size and penalty factor, respectively. Different from the optimization scheme, we devise a family of variable step-size strategy S-IWF-SSAF (VSS-S-IWF-SSAF) algorithms based on the transient model of algorithms via minimizing the mean-square deviation (MSD) on each iteration with some reasonable and frequently adopted assumptions and Price's theorem. And in order to enhance the tracking capability, an effective reset mechanism is also incorporated into the proposed algorithms. It is worth mentioning that the presented algorithms could acquire lower computational requirements and exhibit higher steady-state estimation accuracy obviously and acceptable tracking characteristic in comparison to the VP-S-IWF-SSAF algorithm. In addition, the stable step-size range in the mean and mean square sense and steady-state performance are concluded. And the computational requirements are exhibited as well. Monte-Carlo simulations for system identification and adaptive echo cancellation applications certify the proposed algorithms acquire superior performance in contrast to other related algorithms within various system inputs under impulsive interference environments.

Sparsity-Aware Logarithmic Hyperbolic Cosine Normalized Subband Adaptive Filter Algorithm With Step-Size Optimization

To enhance the filtering accuracy of the traditional sign subband adaptive filter (SSAF) algorithm and its individual-weighting-factors variant, this brief proposes the logarithmic hyperbolic cosine normalized subband adaptive filter algorithm (LHCNSAF) and its sparsity-aware version through minimizing the LHC cost function. As the combination of mean-square-error and mean-absolute-error criterion, the presented LHCNSAF demonstrates higher filtering accuracy under white Gaussian background noise and impulse noise environments than SSAF-type algorithms, with almost no increase in computational complexity. To tackle the trade-off between filtering accuracy and convergence behavior caused by the fixed step-size, an effective variable step-size scheme is also devised based on the transient model of proposed algorithms through minimizing the mean-square deviation (MSD) at each iteration with some reasonable assumptions. Additionally, the stability and complexity analysis are also provided. Finally, the computer simulations certify the proposed algorithms possess good performance in terms of convergence speed, steady-state error, and tracking capability via contrasting with the considering algorithms under system identification application.

Bias-Compensated Sign Subband Adaptive Filter Algorithm With Individual Weighting Factors for Input Noise

To thoroughly exploit the decorrelation property of the traditional sign subband adaptive filter (SSAF), an individual weighting factors SSAF (IWF-SSAF) was presented. However, when the input of the adaptive filter is polluted by white Gaussian noise, the IWF-SSAF will produce estimation bias for unknown system identification. Thus, this brief proposes the bias-compensated IWF-SSAF (BC-IWF-SSAF) for resolving the above trouble. Especially, the unbiased criterion is applied to obtain compensation term for the conventional IWF-SSAF to alleviate the effect of noisy input. The proposed BC-IWF-SSAF both retains stability of impulse noise and decreases the estimated bias. The stable condition of the proposed BC-IWF-SSAF is achieved resorting to Price’s theorem with some reasonable assumptions and theorems. In addition, the complexity is given as well. Finally, simulations confirm the superiority of the proposed BC-IWF-SSAF algorithm.

Normalized Combinations of Proportionate Affine Projection Sign Subband Adaptive Filter

The proportionate affine projection sign subband adaptive filter (PAP-SSAF) has a better performance than the affine projection sign subband adaptive filter (AP-SSAF) when we eliminate the echoes. Still, the robustness of the PAP-SSAF algorithm is insufficient under unknown environmental conditions. Besides, the best balance remains to be found between low steady-state misalignment and fast convergence rate. In order to solve this problem, we propose a normalized combination of PAP-SSAF (NCPAP-SSAF) based on the normalized adaption schema. In this paper, a power normalization adaptive rule for mixing parameters is proposed to further improve the performance of the NCPAP-SSAF algorithm. By using Nesterov’s accelerated gradient (NAG) method, the mixing parameter of the control combination can be obtained with less time consumed when we take the l1-norm of the subband error as the cost function. We also test the algorithmic complexity and memory requirements to illustrate the rationality of our method. In brief, our study contributes a novel adaptive filter algorithm, accelerating the convergence speed, reducing the steady-state error, and improving the robustness. Thus, the proposed method can be utilized to improve the performance of echo cancellation. We will optimize the combination structure and simplify unnecessary calculations to reduce the algorithm’s computational complexity in future research.

Delayless Block Individual-Weighting-Factors Sign Subband Adaptive Filters With an Improved Band-Dependent Variable Step-Size

Delayless individual-weighting-factors sign subband adaptive filter (IWF-SSAF) algorithms with a band-dependent variable step-size (BDVSS) were recently introduced to achieve a robust convergence performance against the impulsive interference and to avoid an undesirable signal path delay in subband systems. In this paper, we develop a block implementation of the delayless IWF-SSAF algorithm designed for an active impulsive noise control (AINC) system. With the block-processing approach, the proposed delayless block IWF-SSAF algorithm can be implemented more efficiently than the original delayless algorithm regardless of number of subbands, which is verified through the computational analysis. Furthermore, an improved BDVSS version (I-BDVSS) is also proposed by using the multiple auxiliary past gradients, which are given for each band by the block-processing. Finally, the simulation results illustrate that the proposed delayless block IWF-SSAF algorithm with the I-BDVSS, even requiring less computational burden, can achieve a better convergence performance than the original delayless algorithm with the BDVSS under severe impulsive noise control environment.

Robust Novel Affine Projection Sign Subband Adaptive Filter Algorithm

This paper presents a novel affine projection sign subband adaptive filter (NAPSSAF) which could achieve better performance than the conventional APSSAF. The proposed NAPSSAF is obtained by solving the optimal problems regarding the l1-norm of the subband a posteriori error vectors rather than overall a posteriori error vector, which fully uses the subband adaptive filter’s inherent decorrelating property. However, since the NAPSSAF algorithm uses the fixed step size, it has an inherent trade-off between low steady-state error and fast convergence rate. Thus, we also propose a combined step size NAPSSAF (CSS-NAPSSAF) to further improve the performance of the NAPSSAF. Finally, simulations are carried out to exhibit the advantages of the NAPSSAF and CSS-NAPSSAF algorithms. The results of simulations demonstrate that the NAPSSAF is superior to the existing algorithms. Besides, the results of simulations also exhibit the improved performance of the CSS-NAPSSAF compared to NAPSSAF.

An Improved Variable Regularization Parameter for Sign Subband Adaptive Filter

This paper proposes an improved variable regularization parameter (VRP) for sign subband adaptive filter, which is derived on the basis of the mean-square deviation (MSD) analysis. Since it is difficult to get access to the exact values of some quantities in the MSD, the VRP is calculated by minimizing the upper bound of a certain term which is employed to update the MSD. Moreover, a re-initialization mechanism that can enhance the tracking capability is developed. We also discuss the computational complexity of our finding. The proposed scheme enjoys more merits than several prior algorithms, which is illustrated by sufficient simulations designed for both the system identification and acoustic echo cancelation applications in the presence of impulsive noise.

Variable step-size sign subband adaptive filter with subband filter selection

Abstract This letter proposes a novel sign subband adaptive filtering (SSAF) algorithm with a subset selection for subband filters, called the SS-SSAF. The proposed algorithm achieves the fast convergence performance and reduces the computational complexity by a proposed sufficient condition. The condition associated with each subband immediately ensures the decrease of the mean square deviation (MSD) value at every iteration. Furthermore, we suggest the variable step-size algorithm for SS-SSAF to achieve both fast convergence speed and small steady-state errors. Simulation results show that the proposed algorithm with fixed step-size performs better than the conventional SSAF and the other improved SSAF algorithms in terms of the convergence rate. In addition, the performance of proposed variable step-size algorithm is demonstrated in the system identification compared with recent variable step-size SSAFs.

Delayless Individual-Weighting-Factors Sign Subband Adaptive Filter With Band-Dependent Variable Step-Sizes

Sign subband adaptive filter algorithms with individual weighting factors (IWF-SSAF) were recently proposed to achieve improved convergence performance in impulsive noise environments by fully utilizing the decorrelating property of subband adaptive filters. However, such sign subband adaptive filter (SSAF) algorithms may have an inherent signal path delay problem for real-time applications, and thus, can be restrictively applied. In this paper, a delayless IWF-SSAF with band-dependent variable step-sizes (BD-VSS), robust in impulsive noise environments, is proposed for real-time applications, whereby two delayless filter structures developed for the $\ell _2$ -norm-based SAF are employed along with the IWF-SSAF. In particular, a BD-VSS algorithm is also introduced for better convergence by applying the recent $\ell _1$ -norm minimization technique to respective subband. Finally, the performance of the proposed delayless IWF-SSAF with BD-VSS is verified in various impulsive interference environments such as system identification with impulsive noise, acoustic echo cancellation in a double-talk scenario, and active impulsive noise control.

Steady‐state mean‐square deviation analysis of the sign subband adaptive filter

The steady-state mean-square deviation (MSD) analysis of the sign subband adaptive filter is proposed. The proposed analysis is derived by the update recursion of the MSD using Price's theorem and chi-distribution in stationary environments. Experimental results show that the proposed analysis is very close to simulated results not only for white input but also for coloured input signals.

Robust variable step-size sign subband adaptive filter algorithm against impulsive noise

The main drawback of the sign subband adaptive filter algorithm (SSAF) is its large steady-state error and poor tracking capability. A robust variable step-size SSAF algorithm is presented to improve the performance, which uses the optimal step-size for each subband by minimizing the mean square deviation. Since the step-size contains the variance of noise-free priori error, the shrinkage denoising method is used to estimate the noise-free error signal. With the step-size adaptation influenced by the variance of error signal for each subband, the proposed algorithm is shown to achieve a significant improvement in both the convergence rate and the steady-state error than the SSAF algorithms. Besides, the proposed algorithm offers robust performance with respect to impulsive noise and good ability of tracking unknown system. Finally, simulation results demonstrate that these features of the proposed algorithm in system identification and echo-cancellation applications.

Novel combination schemes of individual weighting factors sign subband adaptive filter algorithm

AbstractTo improve the performance of the recently presented individual weighting factors sign subband adaptive filter (IWF‐SSAF) algorithm, its 2 combination algorithms using different step sizes are proposed. The first algorithm is to convexly combine the weight vectors of a large step‐size IWF‐SSAF filter and a small step‐size one; and the second algorithm is to obtain a time‐varying step size for the IWF‐SSAF by combining a large step size and a small one. The minimization of the sum of the l1‐norm of subband errors is used to indirectly update the mixing parameters in these 2 algorithms through a modified sigmoidal function. Moreover, in the first algorithm, to implement a smooth transition from the large step‐size IWF‐SSAF filter to the small step‐size one, the component filters receive a cyclic feedback of the combined weight vector. Both proposed algorithms have almost the same convergence performance, but the second algorithm saves computational cost. Simulation results in impulsive noise scenarios demonstrate the superiority of our proposed algorithms.

Adaptive combination of affine projection sign subband adaptive filters for modeling of acoustic paths in impulsive noise environments

The affine projection sign subband adaptive filter (APSSAF) algorithm has attracted much attention because of its fast convergence rate and robustness against impulsive interference. However, a drawback of this algorithm is that the step size implies a compromise between the convergence speed and steady-state error. To solve this problem, a new adaptive combination of the APSSAFs based on convex combination scheme is proposed for modeling of acoustic paths under impulsive noise environments. Moreover, a weight transfer approach is applied to further improve the performance. Simulation results demonstrate that the proposed algorithm achieves improved performance than existing algorithms when applied to modeling sparse/dispersive systems.

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.

Novel sign subband adaptive filter algorithms with individual weighting factors

This paper presents a new sign subband adaptive filter (SSAF) algorithm with an individual-weighting-factor (IWF) for each subband, instead of a common weighting factor in the original SSAF algorithm, called the IWF-SSAF. Each individual weighting factor only depends on the corresponding subband input signal power. Compared with the SSAF algorithm, the proposed approach fully utilizes the inherent decorrelating property of subband adaptive filter for colored inputs, leading to a better convergence performance. After that, to further enhance the performance of the IWF-SSAF in a sparse system, an improved proportionate IWF-SSAF (IWF-IPSSAF) algorithm is proposed. The proposed algorithms not only inherit the good robustness of sign algorithm against impulsive interferences, but also obtain a significant improvement in the performance as compared to their counterparts (i.e., SSAF and IPSSAF), in terms of the convergence rate and tracking capability. Besides, the IWF-IPSSAF algorithm has faster convergence rate than the IWF-SSAF algorithm for sparse impulse responses. Finally, the performances of two proposed algorithms are demonstrated in the system identification and the acoustic echo cancellation with double-talk.

Steady-state mean-square-deviation analysis of the sign subband adaptive filter algorithm

Recently, the sign subband adaptive filter (SSAF) algorithm has obtained great attention, due to its robustness against impulsive noises and decorrelating property for correlated input signals. However, the performance of the algorithm in the steady-state is not analyzed. In this paper, we study the steady-state mean-square-deviation (MSD) behavior of the SSAF algorithm by using energy conservation relation, Price׳s theorem and some reasonable assumptions. Simulation results in different system identification scenarios (including the input signals, tap lengths, impulsive noises, number of subbands, and step sizes) are provided to support our theoretical analysis.

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.