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.

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.

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.

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.

Blind multichannel identification is a challenging problem in many domains. The normalized multichannel frequency-domain least-mean-square (NMCFLMS) algorithm was developed to blindly identify a single-input multiple-output acoustic system, which can yield good performance in noise-free environments. However, the robustness of this algorithm to noise has been shown to be problematic. One way to improve the robustness is by applying a constraint on the spectral flatness of the channel impulse responses, which led to the development of the so-called robust normalized multichannel frequency-domain least-mean-square (RNMCFLMS) algorithm. This spectral flatness constraint, however, may not be always proper or reasonable in realistic acoustic environments. In this paper, we develop an ℓp-norm constraint based robust normalized multichannel frequency-domain least-mean-square (ℓp-RNMCFLMS) algorithm. The ℓp-norm constraint is introduced into the NMCFLMS algorithm to control the effect of different ℓp-norm penalties on the adaptive filter for the impulse responses with different degrees of sparseness. Numerical and realistic experiments justify the effectiveness of the proposed ℓp-RNMCFLMS algorithm.

Time delay estimation (TDE) plays an important role in localizing and tracking radiating acoustic sources. Although many efforts have been devoted to this problem in the literature, the robustness of TDE with respect to noise and reverberation remains a great challenge for practical systems. In this paper, we investigate the TDE problem in acoustic single-input/multiple-output (SIMO) systems in reverberant and noisy environments. We first define a Cauchy estimator in the frequency domain, which is robust in dealing with speech as the SIMO system's excitation. This robust estimator is then used to construct a cost function, from which a robust multichannel frequency-domain adaptive filter is deduced. This adaptive algorithm is subsequently employed to blindly identify the acoustic impulse responses between the source and the microphones. Finally, the time difference of arrival is determined from the identified channel responses.

Noise and reverberation can significantly affect the performance of time delay estimation (TDE) in room acoustic environments. The multichannel cross-correlation coefficient (MCCC) algorithm, which extends the traditional cross-correlation method from two to multiple channels, can exploit the spatial information among multiple microphones to improve the robustness of TDE with respect to environmental noise; but this algorithm is not robust to reverberation. The multichannel spatiotemporal prediction (MCSTP) algorithm uses both the spatial and temporal information provided by the array. This algorithm improves significantly the robustness of TDE with respect to reverberation; however, it is found sensitive to noise. In this paper, we develop a multichannel spatiotemporal sparse prediction (MCSTSP) algorithm for TDE. This algorithm obtains a good compromise between robustness of TDE to noise and that to reverberation through making a tradeoff between pre-whitening and non-prewhitening. This is achieved via adjusting a regularization parameter, which is solved by an augmented Lagrangian alternating direction method of multipliers (ADMM). The property of this developed algorithm is justified with numerical experiments in both noisy and reverberant environments.

To localize sound sources in room acoustic environments, time differences of arrival (TDOA) between two or more microphone signals must be determined. This problem is often referred to as time delay estimation (TDE). The multichannel cross-correlation-coefficient (MCCC) algorithm, which is an extension of the traditional cross-correlation method from two- to multiple-channel cases, exploits spatial information among multiple microphones to improve the robustness of TDE. In this paper, we propose a multichannel spatio-temporal prediction (MCSTP) algorithm, which can be viewed as a generalization of the MCCC principle from using only spatial information to using both spatial and temporal information. A recursive version of this new algorithm is then developed, which can achieve similar performance as MCSTP, but is computationally more efficient. Experimental results in reverberant and noisy environments demonstrate the advantages of this new method for TDE.

To overcome the limitations of the existing algorithms for active impulsive noise control, an algorithm based on minimizing the squared logarithmic transformation of the error signal is proposed in this correspondence. The proposed algorithm is more robust for impulsive noise control and does not need the parameter selection and thresholds estimation according to the noise characteristics. These are verified by theoretical analysis and numerical simulations.