Normalized Subband Adaptive Filter Research Articles

Diffusion Improved Multiband-Structured Subband Adaptive Filter Algorithm With Dynamic Selection of Nodes Over Distributed Networks

In this brief, an improved multiband-structured subband adaptive filter (IMSAF) algorithm is applied in diffusion networks. The introduced diffusion IMSAF (DIMSAF) utilizes the input regressors at each subband to increase the convergence speed of the diffusion normalized subband adaptive filter. This advantage is achieved at the cost of increased computational complexity and steady-state error. Therefore, the DIMSAF with dynamic selection of nodes (DIMSAF-DSN) is proposed. In DIMSAF-DSN, the nodes are dynamically selected according to the largest decrease in mean-square deviation at each iteration. The DIMSAF-DSN has low computational complexity, fast convergence speed, and low steady-state error. Simulation results demonstrate the good performance of the proposed algorithms.

Block‐sparse non‐uniform norm constraint normalised subband adaptive filter

This study proposes a block-sparse non-uniform norm constraint normalised subband adaptive filter (BS-NNCNSAF) for the block-sparse system identification problem, which is obtained by minimising a novel cost function involving the non-uniform mixed l 2, p norm like a constraint. It can achieve better performance compared with the existing algorithms in the block-sparse system identification. To further enhance the performance of the algorithm, the shrinkage BS-NNCNSAF (SH-BS-NNCNSAF) algorithm is proposed. The proposed SH-BS-NNCNSAF algorithm is derived by taking the priori and the posteriori subband errors to achieve the time-varying subband step sizes. Finally, simulations have been carried out to verify the performance of proposed algorithms. The simulation results verify that the proposed algorithms improve the performance of the filter, in terms of system identification in sparse systems.

Zero attracting proportionate normalized subband adaptive filtering technique for feedback cancellation in hearing aids

Acoustic feedback cancelers (AFC) employing normalized subband adaptive filtering (NSAF) in conjunction with proportionate gain allocation strategy (PNSAF) have been utilized to mitigate the effect of acoustic feedback in hearing aids. However, it was found to exhibit fast convergence at the initial stage whereas slowing down the convergence at later phase of the adaptation process. In an endeavor to overcome this, l1 norm-based penalty element is incorporated with the PNSAF algorithm proposing a new zero attracting PNSAF (ZA-PNSAF) based AFC system. Further, re-weighted ZA-PNSAF (RZA-PNSAF) algorithm is newly introduced to address the varying sparsity conditions. The efficacy of the proposed method is demonstrated by higher maximum stable gain (MSG) (3–5 dB) and PESQ (perceptual evaluation of speech quality) values obtained over existing algorithms. In addition, the convergence and mean square deviation (MSD) analysis of the proposed algorithm are also carried out. Analysis of the ZA-PNSAF algorithm is validated through comparison of the simulated and analytical MSD values.

A Normalized Subband Adaptive Filter with Combined Regularization Parameter

Proposed is a novel variable regularization algorithm for normalized subband adaptive filter (NSAF) by employing the mixing parameter to combine a large regularization parameter with a small regularization parameter. The mixing parameter is derived by minimizing the energy of noise-free a posteriori subband error. The combined regularization parameter can vary from a small value to a large value. Therefore, the proposed algorithm exhibits fast convergence rate meanwhile obtains low steady-state misalignment. Experimental simulations demonstrate the effectiveness of our work.

Adaptive regularisation for normalised subband adaptive filter: mean‐square performance analysis approach

The normalised subband adaptive filter (NSAF) is a useful adaptive filter, which improves the convergence rate compared with the normalised least mean-square algorithm. Most analytical results of the NSAF set the regularisation parameter set to zero or present only steady-state mean-square error performance of the regularised NSAF (e-NSAF). This study presents a mean-square performance analysis of e-NSAF, which analyses not only convergence behaviour but also steady-state behaviour. Furthermore, a novel adaptive regularisation for NSAF (AR-NSAF) is also developed based on the proposed analysis approach. The proposed AR-NSAF selects the optimal regularisation parameter that leads to improving the performance of the adaptive filter. Simulation results comparing the proposed analytical results with the results achieved from the simulation are presented. In addition, these results verify that the proposed AR-NSAF outperforms the previous algorithms in a system-identification and acoustic echo-cancellation scenarios.

Augmented complex-valued normalized subband adaptive filter: Algorithm derivation and analysis

In this paper, a novel augmented complex-valued normalized subband adaptive filter (ACNSAF) algorithm is proposed for processing the noncircular complex-valued signals. Based on the augmented statistics, the proposed algorithm is derived by computing a constraint cost function. Due to contain all second-order statistical properties, the ACNSAF algorithm can process the circular and noncircular complex-valued signals simultaneously. Moreover, the stability and mean square steady-state analysis of the proposed algorithm is derived by using the energy conservation principle. Computer simulation experiments on complex-valued system identification, prediction and noise cancelling show that the proposed algorithm achieves the improved mean square deviation and prediction gain compared to the ACNLMS algorithm. And the simulation results are consistent with the analysis results.

Combined-Step-Size Normalized Subband Adaptive Filter With a Variable-Parametric Step-Size Scaler Against Impulsive Interferences

The variable step-size normalized subband adaptive filter (NSAF) with a fixed parametric step-size scaler (SSS) results in a tradeoff between the fast convergence rate and small steady-state error, and needs to reset the algorithm to improve the tracking in abrupt change scenarios. Thus, a combined-step-size NSAF with a variable-parametric SSS (VPSSS) is proposed in this brief to address these problems. In the proposed algorithm, an adaptive parameter with respect to the smallest ${L} _{\mathbf{1}}$ -norm of the subband error vectors in a window is proposed for the VPSSS and then two different step sizes are adaptively combined by a modified sigmoidal activation function, in which this modified sigmoidal activation function is updated by using the gradient descent method to minimize the ${L} _{\mathbf{1}}$ -norm of the subband error vector. Simulation results have verified that the proposed algorithm yields improved transient behavior and tracking performance as compared to the compared algorithms.

Sparsity-aware subband adaptive algorithms with adjustable penalties

We propose two sparsity-aware normalized subband adaptive filter (NSAF) algorithms by using the gradient descent method to minimize a combination of the original NSAF cost function and the l1-norm penalty function on the filter coefficients. This l1-norm penalty exploits the sparsity of a system in the coefficients update formulation, thus improving the performance when identifying sparse systems. Compared with prior work, the proposed algorithms have lower computational complexity with comparable performance. We study and devise statistical models for these sparsity-aware NSAF algorithms in the mean square sense involving their transient and steady-state behaviors. This study relies on the vectorization argument and the paraunitary assumption imposed on the analysis filter banks, and thus does not restrict the input signal to being Gaussian or having another distribution. In addition, we propose to adjust adaptively the intensity parameter of the sparsity attraction term. Finally, simulation results in sparse system identification demonstrate the effectiveness of our theoretical results.

A Sequential Selection Normalized Subband Adaptive Filter with Variable Step-Size Algorithms

This letter proposes a sequential selection normalized subband adaptive filter (SS-NSAF) in order to reduce the computational complexity. In addition, a variable step-size algorithm is also proposed using the mean-square deviation analysis of the SS-NSAF. To enhance the performance in terms of the convergence speed, we propose an improved variable step-size SS-NSAF using a two-stage concept. The simulation results show the low computational complexity and low misalignment errors using the proposed algorithm.

A low computational complexity normalized subband adaptive filter algorithm employing signed regressor of input signal

ᅟIn this paper, the signed regressor normalized subband adaptive filter (SR-NSAF) algorithm is proposed. This algorithm is optimized by L1-norm minimization criteria. The SR-NSAF has a fast convergence speed and a low steady-state error similar to the conventional NSAF. In addition, the proposed algorithm has lower computational complexity than NSAF due to the signed regressor of the input signal at each subband. The theoretical mean-square performance analysis of the proposed algorithm in the stationary and nonstationary environments is studied based on the energy conservation relation and the steady-state, the transient, and the stability bounds of the SR-NSAF are predicated by the closed form expressions. The good performance of SR-NSAF is demonstrated through several simulation results in system identification, acoustic echo cancelation (AEC) and line EC (LEC) applications. The theoretical relations are also verified by presenting various experimental results.

Set‐membership improved normalised subband adaptive filter algorithms for acoustic echo cancellation

In order to improve the performances of recently-presented improved normalized subband adaptive filter (INSAF) and proportionate INSAF algorithms for highly noisy system, this paper proposes their set-membership versions by exploiting the theory of set-membership filtering. Apart from obtaining smaller steady-state error, the proposed algorithms significantly reduce the overall computational complexity. In addition, to further improve the steady-state performance for the algorithms, their smooth variants are developed by using the smoothed absolute subband output errors to update the step sizes. Simulation results in the context of acoustic echo cancellation have demonstrated the superiority of the proposed algorithms.

Memorized error and varying error bound for extending adaptiveness for normalized subband adaptive filtering

This paper extends the adaptive normalized sub-band adaptive filtering (NSAF) by introducing variable error bound and memorizing the error convergence. The variable error bound attempts to vary the updating point of the filter coefficients. The error memory aids in updating the point based on the history of error rather than the previous error. The extended adaptiveness significantly improved NSAF in terms of convergence, complexity and noise robustness. The algorithm is also proved for its stability though the step-size is varied. The characteristics of the step-size are also investigated to determine its significance and nature on minimizing the error. The superiority of the MVS-SNSAF algorithm is proved against conventional algorithm using the aforesaid analysis.

Diffusion normalized subband adaptive algorithm for distributed estimation employing signed regressor of input signal

This paper presents a novel diffusion subband adaptive filtering algorithm for distributed estimation over networks. To achieve the low computational load, the signed regressor (SR) approach is applied to normalized subband adaptive filter (NSAF) and two algorithms for diffusion networks are established. The diffusion SR-NSAF (DSR-NSAF) and modified DSR-NSAF (MDSR-NSAF) have fast convergence speed and low steady-state error similar to the conventional DNSAF. In addition, the proposed algorithms have lower computational complexity than DNSAF due to the signed regressor of the network input signals at each node. Also, based on the spatial-temporal energy conservation relation, the mean-square performance of DSR-NSAF is analyzed and the expressions for the theoretical learning curve and steady-state error are derived. The good performance of these algorithms and the validity of the theoretical results are demonstrated by presenting several simulation results.

A Variable Step-Size Normalized Subband Adaptive Filter With a Step-Size Scaler Against Impulsive Measurement Noise

This brief introduces a variable step-size (VSS) normalized subband adaptive filter (NSAF) using a step-size scaler to improve the robustness against impulsive measurement noise. When impulsive measurement noise appears, the step size of the proposed VSS NSAF is scaled down by the step-size scaler, which is suitable for application in the NSAF. This removes a possibility of updating weight estimates based on defective information of the subband output errors due to impulsive measurement noise. In the proposed VSS NSAF, the equations for updating the step size are constructed by interpreting the behavior of the mean square deviation of the conventional NSAF and applying the step-size scaler. The step-size scaler utilizes the sum of the subband output errors, which can be influenced by impulsive measurement noise. Simulations using the proposed VSS NSAF show an excellent transient and steady-state behavior with colored input in impulsive-noise environments.

A family of diffusion normalized subband adaptive filter algorithms over distributed networks

SummaryThis paper solves the problem of distributed estimation in the diffusion networks based on the family of normalized subband adaptive filters (NSAFs). The diffusion NSAF (DNSAF), the diffusion selective partial update NSAF (DSPU‐NSAF), the diffusion fix selection NSAF (DFS‐NSAF), and the diffusion dynamic selection NSAF (DDS‐NSAF) are established based on the general formalism. In DSPU‐NSAF, the weight coefficients are partially updated rather than the entire weights at each node during the adaptation. The DFS‐NSAF selects a subset of subbands and uses them to update the weights. The dynamic selection of subbands is performed in DDS‐NSAF at each node during the weigh coefficients update. In comparison with DNSAF, the DSPU‐NSAF, the DFS‐NSAF, and the DDS‐NSAF have lower computational complexity while the convergence speed of them is close to the DNSAF. Also, by combination of SPU with FS and DS approaches, the DSPU‐FS‐NSAF and the DSPU‐DS‐NSAF are established, which are computationally efficient. In the following, based on the spatial‐temporal energy conservation relation, a unified framework for mean‐square performance analysis of the family of DNSAF algorithms in stationary and nonstationary environments is presented, and the theoretical expressions for learning curve and steady‐state error are derived for entire network. The validity of the theoretical results and the good performance of introduced algorithms are demonstrated by several computer simulations.

Two Novel Arctangent Normalized Subband Adaptive Filter Algorithms Against Impulsive Interferences

In this paper, two arctangent-based normalized subband adaptive filter (Arc-NSAF) algorithms are proposed, which are derived from two different forms of arctangent cost function and their difference is the order of the arctangent computation and the summation operation of the normalized subband error signal. Benefiting from the excellent property of the arctangent function for suppressing impulsive interferences, the proposed Arc-NSAF algorithms not only possess good robustness against impulsive interferences, but also obtain faster convergence rate for the colored input signals. To further improve the convergence performance of the Arc-NSAFs when identifying sparse system, the proportionate versions of the Arc-NSAF algorithms are also proposed. Simulation results have demonstrated the superiority of the proposed algorithms in impulsive interferences environments as compared to their respective competitors.

Proportionate NSAF algorithms with sparseness-measured for acoustic echo cancellation

In acoustic echo cancellation (AEC), the sparseness of impulse responses can vary over time or/and context. For such scenario, the proportionate normalized subband adaptive filter (PNSAF) and μ-law (MPNSAF) algorithms suffer from performance deterioration. To this end, we propose their sparseness-measured versions by incorporating the estimated sparseness into the PNSAF and MPNSAF algorithms, respectively, which can adapt to the sparseness variation of impulse responses. In addition, based on the energy conservation argument, we provide a unified formula to predict the steady-state mean-square performance of any PNSAF algorithm, which is also supported by simulations. Simulation results in AEC have shown that the proposed algorithms not only exhibit faster convergence rate than their competitors in sparse, quasi-sparse and dispersive environments, but also are robust to the variation in the sparseness of impulse responses.

Improved affine projection subband adaptive filter for high background noise environments

For high background noise environment, an improved affine projection subband adaptive filter (IAPSAF) is proposed, which is derived by minimizing the sum of the squared Euclidean norms of the differences between the updated tap-weight vector and past tap-weight vectors. Due to the use of the past tap-weight vectors, the IAPSAF can achieve lower steady-state misalignment relative to the improved multiband-structured subband adaptive filter (IMSAF). Furthermore, a combined step size IAPSAF (CSS-IAPSAF) is developed to improve the performance of the IAPSAF. Simulation results in an acoustic echo cancellation (AEC) context show that the IAPSAF achieves lower steady-state misalignment than the existing algorithms, such as normalized subband adaptive filter (NSAF), IMSAF, and improved NSAF (INSAF). The improvement of the CSS-IAPSAF is also demonstrated in terms of convergence rate and steady-state misalignment.

A novel variable step-size normalized subband adaptive filter based on mixed error cost function

A novel variable step-size algorithm is proposed for normalized subband adaptive filter. The proposed algorithm is based on the mixed error cost function. By assuming the time-averaging estimate of the priori and posteriori errors equals the variance of subband noise, the step-size is obtained. Therefore, the proposed algorithm has more effective approach to the optimum solution. The power of noise-free subband priori error is obtained by using the shrinkage denoising method. Using the energy conservation method, the mean-square convergence performance analysis is presented. The analysis result shows this algorithm is stable and effective. The simulation results demonstrate the performance of proposed algorithm distinctly outperforms other conventional variable step-size algorithms in both steady-state error and abrupt tracking performance.

Performance analysis of the deficient length NSAF algorithm and a variable step size method for improving its performance

In all presented analyses of the normalized subband adaptive filter (NSAF) algorithm, there is a common assumption that the length of the adaptive filter is equal to that of the unknown system. In many practices, however, the adaptive filter usually works in an under-modeling situation. Namely, the length of the adaptive filter is less than that of the unknown system. Therefore, for this case, the existing analysis results for the NSAF algorithm are not applicable. In this paper, we analyze the performance of the deficient length NSAF algorithm based on some reasonable assumptions and approximations. More precisely, the expressions that characterize the transient-state and steady-state mean-square behavior of the algorithm are presented. Simulation results in various scenarios support our theoretical expressions. In addition, based on our analyses, a variable step size NSAF algorithm suitable for the under-modeling case is developed, which improves the performance.