In this work, to address the fixed step-size problem of the widely linear complex-valued affine projection algorithm (WL-CAPA), we propose a sliding-window step-size (SWSS) selection scheme, which results in the SWSS-WL-CAPA. To devise this scheme, we derive the mean-square deviation (MSD) recursion of WL-CAPA and obtain the optimal step-size at each iteration based on the comparison of MSD trends of the algorithm using two different step-sizes in the sliding-window. Interestingly, the SWSS scheme removes the length limitation of the step-size sequence with iterations, which allows the proposed algorithm to achieve better steady-state behavior. Furthermore, we develop a reset mechanism for enhancing the real-time tracking capability of the algorithm for unknown systems. The efficacy of the proposed algorithm is substantiated through the execution of simulations in scenarios of system identification and stereophonic acoustic echo cancellation.

Compared with the functional link neural network (FLNN) algorithm, the delayless multi-sampled multiband-structured subband FLNN (DMSFLNN) algorithm provides fast convergence when encountering highly auto-correlated input signals, but there is a compromise between convergence and steady-state performances. Therefore, in order to overcome this flaw, we develop an optimal DMSFLNN (ODMSFLNN) algorithm by minimizing the mean square deviation of the weight vector with respect to the subband gain vectors. Interestingly, a vectorized version is also proposed for the ODMSFLNN algorithm, which aims at reducing computational complexity. Additionally, this paper also presents a stability analysis of this algorithm. Then, considering the impulsive noise environment, we develop two robust variants of ODMSFLNN that are the R-ODMSFLNN-I and R-ODMSFLNN-II algorithms, which are based on the specified robust function and the energy constraint of the weight update increment, respectively. Finally, to resolve that the DMSFLNN algorithm may not exploit cross-terms of input samples in nonlinear active noise control scenarios, we further propose the subband second-order Volterra filter (SSOVF) framework in an analogy way and apply the R-ODMSFLNN-II learning principle to obtain the robust optimal SSOVF algorithm. Simulations in several nonlinear scenarios have shown that the proposed algorithms perform better than their competitors.

This paper studies the problem of acoustic source localization in room environments. It presents an improved steered response power (SRP) approach with low-complexity and trade-off prewhitening. This method consists of two steps. In the first one, the linear predictor that is used to model the speech signals is formulated as a bilinear form, and a group of convex-constrained linear prediction sub-models with respect to dual sub-predictors are established to pre-filter microphone signals. The pre-filtered (prewhitened) microphone signals are subsequently used in SRP for speaker localization. Simulation results demonstrate the properties of the presented method: it is robust to reverberation and noise, and is computationally efficient thanks to the bilinear form.

This paper proposes a frequency-domain recursive least-squares (RLS) adaptive filtering algorithm for identifying time-varying acoustic systems in noisy environments. The Kronecker product (KP) is employed to decompose the model filter of the acoustic channel impulse response into two sets of short sub-filters, based on which a generalized frequency-domain signal model and the associated cost function are established. A KP based RLS algorithm is subsequently deduced. In comparison with the conventional frequency-domain RLS adaptive filter, the presented algorithm is not only computationally more efficient, but also has a faster convergence rate for the identification of acoustic systems regardless of whether the excitation is a white sequence or a speech signal.

We propose a novel M-estimate conjugate gradient (CG) algorithm, termed Tukey’s biweight M-estimate CG (TbMCG), for system identification in impulsive noise environments. In particular, the TbMCG algorithm can achieve a faster convergence while retaining a reduced computational complexity as compared to the recursive least-squares (RLS) algorithm. Specifically, the Tukey’s biweight M-estimate incorporates a constraint into the CG filter to tackle impulsive noise environments. Moreover, the convergence behavior of the TbMCG algorithm is analyzed. Simulation results confirm the excellent performance of the proposed TbMCG algorithm for system identification and active noise control applications.

This paper proposes a unified sparsity-aware robust recursive least-squares RLS (S-RRLS) algorithm for the identification of sparse systems under impulsive noise. The proposed algorithm generalizes multiple algorithms only by replacing the specified criterion of robustnessand sparsity-aware penalty. Furthermore, by jointly optimizing the forgetting factor and the sparsity penalty parameter, we develop the jointly-optimized S-RRLS (JO-S-RRLS) algorithm, which not only exhibits low misadjustment but also can track well sudden changes of a sparse system. Simulations in impulsive noise scenarios demonstrate that the proposed S-RRLS and JO-S-RRLS algorithms outperform existing techniques.

In this paper, we propose a general robust subband adaptive filtering (GR-SAF) scheme against impulsive noise by minimizing the mean square deviation under the random-walk model with individual weight uncertainty. Specifically, by choosing different scaling factors such as from the M-estimate and maximum correntropy robust criteria in the GR-SAF scheme, we can easily obtain different GR-SAF algorithms. Importantly, the proposed GR-SAF algorithm can be reduced to a variable regularization robust normalized SAF algorithm, thus having fast convergence rate and low steady-state error. Simulations in the contexts of system identification with impulsive noise and echo cancellation with double-talk have verified that the proposed GR-SAF algorithms outperforms its counterparts.

To identify acoustic systems (which are low-rank in nature) in non-Gaussian and Gaussian noise, a robust recursive least M-estimate adaptive filtering algorithm is developed in this paper by applying the nearest Kronecker product to decompose the acoustic impulse response. Two M-estimators, i.e., the Cauchy and Welsch estimators, are employed to define the cost function of the adaptive filter, leading to a class of numerically stable adaptive filtering algorithms, which are robust to non-Gaussian noise. The effectiveness of the developed algorithm is validated in acoustic environments with both Gaussian and non-Gaussian noise.

In this paper, we propose a novel normalized subband adaptive filter algorithm suited for sparse scenarios, which combines the proportionate and sparsity-aware mechanisms. The proposed algorithm is derived based on the proximal forward-backward splitting and the soft-thresholding methods. We analyze the mean and mean square behaviors of the algorithm, which is supported by simulations. In addition, an adaptive approach for the choice of the thresholding parameter in the proximal step is also proposed based on the minimization of the mean square deviation. Simulations in the contexts of system identification and acoustic echo cancellation verify the superiority of the proposed algorithm over its counterparts.

To identify acoustic systems in non-Gaussian and Gaussian noises, a robust frequency-domain recursive least M-estimate (FRLM) adaptive filtering algorithm is proposed. The cost function of the adaptive filter is defined by using a robust time-domain M-estimator, while its update equation is derived from the normal equation in the frequency domain. As compared to the frequency-domain recursive least-squares adaptive filter, the FRLM algorithm obtains the robustness to non-Gaussian and Gaussian noises. The performance of the proposed algorithm is validated in simulated acoustic environments.

This article studies the mean and mean-square behaviors of the M-estimate based normalized subband adaptive filter algorithm (M-NSAF) with robustness against impulsive noise. Based on the contaminated-Gaussian noise model, the stability condition, transient and steady-state results of the algorithm are formulated analytically. These analysis results help us to better understand the M-NSAF performance in impulsive noise. To further obtain fast convergence and low steady-state estimation error, we derive a variable step size (VSS) M-NSAF algorithm. This VSS scheme is also generalized to the proportionate M-NSAF variant for sparse systems. Computer simulations on the system identification in impulsive noise and the acoustic echo cancellation with double-talk are performed to demonstrate our theoretical analysis and the effectiveness of the proposed algorithms.

This work develops a robust diffusion recursive least squares algorithm to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. This algorithm minimizes an exponentially weighted least-squares cost function subject to a time-dependent constraint on the squared norm of the intermediate estimate update at each node. With the help of side information, the constraint is recursively updated in a diffusion strategy. Moreover, a control strategy for resetting the constraint is also proposed to retain good tracking capability when the estimated parameters suddenly change. Simulations show the superiority of the proposed algorithm over previously reported techniques in various impulsive noise scenarios.

In order to improve the performances of recently presented improved normalised subband adaptive filter (INSAF) and proportionate INSAF algorithms for highly noisy system, this study 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.

An individual-activation-factor memory proportionate affine projection algorithm (IAF-MPAPA) is proposed for sparse system identification in acoustic echo cancellation (AEC) scenarios. By utilizing an individual activation factor for each adaptive filter coefficient instead of a global activation factor, as in the standard proportionate affine projection algorithm (PAPA), the adaptation energy over the coefficients of the proposed IAF-MPAPA can achieve a better distribution, which leads to an improvement of the convergence performance. Moreover, benefiting from the memory characteristics of the proportionate coefficients, its computational complexity is less than the PAPA and improved PAPA (IPAPA). In the context of AEC and stereophonic AEC (SAEC) for highly sparse impulse responses, simulation results indicate that the proposed IAF-MPAPA outperforms the PAPA, IPAPA, and memory IPAPA (MIPAPA) in terms of the convergence rate and tracking capability when the unknown impulse response suddenly changes.