In array signal processing, integer linear arrays with sensors placed at multiples of the half-wavelength are standard. In this work, we overcome aperture constraints that often lead to under-utilized sensor resources by using rational arrays that position sensors at rational locations. By formulating direction-of-arrival (DOA) estimation as a joint sparse support recovery (JSSR) problem, we demonstrate that rational arrays can achieve superior performance compared to conventional integer arrays. Notably, rational non-uniform arrays can resolve$\mathcal{O}\left(M^{2}\right)$uncorrelated sources using only$M$sensors, even when the available aperture is limited, a feat that integer non-uniform arrays like nested and coprime configurations cannot attain without large apertures. We derive the performance of these arrays using a sufficient JSSR condition and validate our findings through extensive simulations covering both overdetermined and underdetermined DOA estimation scenarios.

Underdetermined direction of arrival (U-DOA) estimation refers to the ability to estimate the DOA of more sources than the number of sensors in an array. Usually, to perform U-DOA estimation, the difference coarray of the physical array is utilized in techniques like coarray MUSIC. However, existing U-DOA estimation techniques are computationally expensive. To tackle this issue, in this work, we introduce a computationally efficient adaptive filtering technique that is capable of resolving more sources than the number of sensors. The proposed adaptive algorithm utilizes the second-order statistics of the source signals captured by the coarray along with the least mean square (LMS) principle to perform U-DOA estimation. The coarray sensor at the zeroth location is used as a reference coarray sensor and the positive part of the coarray is used as an auxiliary coarray. The auxiliary coarray signal is passed through a linear filter and an error signal of the adaptive process is generated by subtracting the filter output from the reference coarray signal. The error is then minimized iteratively to obtain the final filter weights. The filter is then used to calculate a novel spatial spectrum whose peaks give the estimate of the DOAs. A polynomial rooting version of the proposed algorithm is also introduced. Simulations show the efficacy of the proposed method.

Decentralized systems are appealing due to their reduced complexity and flexibility. A class of decentralized multi-channel active noise control (MCANC) systems has been developed in this paper. In the first part of the study, a modified filtered-x least mean square/fourth (FxLMS/F) algorithm, which offers improved noise reduction performance over the conventional FxLMS/F algorithm, was developed for MCANC. Further, to reduce the computational complexity of the proposed MCANC system, a nearest Kronecker product (NKP) decomposition strategy has been incorporated to develop decentralized versions of FxLMS/F algorithms. The proposed algorithms have been shown to offer enhanced noise reduction at reduced computational complexity when applied for noise control for narrowband noise, bandlimited white noise, traffic noise and wind noise.

Dereverberation and acoustic beamforming is used to capture the speech of a desired speaker in the presence of interfering speakers in a reverberant room using an array of microphones. Traditionally, to perform these two tasks, the desired speech is modelled in the time-frequency domain using a complex Gaussian (CG) prior with time-varying variances. The shape parameter of the prior distribution is fixed at the same value for all time-frequency bins. In this work, we propose to model the inverse of the variance (i.e. the precision parameter) of the CG prior distribution which controls the shape of the distribution as a Gamma distributed random variable. The hyperparameters of the Gamma distribution are then estimated based on the data captured by the microphones. This data-dependent blind estimation of the shape of the prior distribution helps the proposed algorithm to accurately model the desired speech and adapt to different speakers and acoustic scenarios better than algorithms with a fixed shape parameter. We use maximum likelihood techniques to estimate the multi-channel linear prediction (MCLP) dereverberation coefficients and the beamforming weights using the proposed signal model. The stochastically latent precision parameters are obtained by estimating the hyperparameters using the expectation maximization (EM) method. For the online version of the algorithm, a recursive EM method is also proposed for real-time processing. Extensive simulation results show improved dereverberation and interference cancellation performance of the proposed method highlighting the importance of not choosing the shape parameter of the prior distribution manually.

In many practical scenarios, non-Gaussian noise contaminates the desired signal and introduces outliers. The recently proposed logistic distance metric adaptive filter (LDMAF) outperforms the existing algorithms and provides better performance in the presence of such outliers. There is a need for efficient hardware architecture for the implementation of LDMAF. This article proposes an efficient VLSI architecture of LDMAF. The implementation of error-gradient function of LDMAF puts significant implementation problem in terms of delay and cost. We introduce here an efficient tangent-based piecewise linear (TPL) approximation algorithm for implementing the corresponding architecture. The proposed approach improves the power, performance, and area (PPA) metrics over state-of-the-art implementations of other robust algorithms while meeting system performance within an acceptable deviation.

In the past years, the generalized maximum correntropy criterion (GMCC) has been widely used in adaptive filters to provide robust behavior under non-Gaussian/impulsive noise environments. However, GMCC-based adaptive filters are affected by high steady-state misalignment. In order to enhance the robustness under non-Gaussian noise environments and reduce steady-state misalignment, a generalized modified Blake–Zisserman (GMBZ) robust loss function is introduced in this correspondence. Furthermore, a GMBZ adaptive filter (GMBZ-AF) has been developed that provides improved convergence performance over other existing algorithms. The proposed learning scheme has a computational complexity very similar to that of the GMCC-based adaptive filtering method. In order to further exploit the sparse nature of the system for identifying sparse systems and simultaneously provide robust convergence, two new robust sparse adaptive filters: 1) zero attracting GMBZ-AF (ZA-GMBZ-AF) and 2) reweighted ZA-GMBZ-AF (RZA-GMBZ-AF) have also been proposed. To further enhance the filter convergence performance, a new robust and sparsity-aware loss function called generalized modified dual Blake–Zisserman (GMDBZ) is also introduced in this correspondence and the corresponding GMDBZ adaptive filter (GMDBZ-AF) has been developed.

The order of a three-dimensional wavefield captured by a spherical array is limited by the number of sampling points i.e. the number of sensors in the array. This restricts the source localization performance of existing techniques for a spherical array. In this paper, we introduce the concept of difference coarray to spherical arrays and propose an algorithm which utilises the increased degrees-of-freedom (DOF) provided by the virtual coarray sensors to perform enhanced source localization. We make use of coarray manifold separation in the spherical harmonics domain to generate a Vandermonde structured coarray manifold matrix which allows us to propose a novel subspace-based algorithm, which we call the coarraySH-MUSIC. We also introduce a polynomial rooting version of our algorithm which does not rely on extensive grid searches. The proposed algorithms are evaluated using various simulated experiments on source localization.

Phase-mode array processing which utilizes the spherical harmonics decomposition offers a useful framework for spherical microphone arrays. In the modal domain, one of the major applications of spherical arrays is acoustic beamforming. Usually, beamforming is performed by minimizing the power of the beamformer output with a distortionless constraint towards the look direction. Also, most beamformers model the spectral coefficients of target speech using a Gaussian distribution. In this letter, a beamforming method that minimizes the$\ell _{0}$-norm of the beamformer output in the spherical harmonics domain with a distortionless constraint is proposed. The proposed method assumes a super-Gaussian prior for the target speech and sparsifies the beamformer output which is shown to reduce the residual elements of the interfering speech signals from the beamformer output leading to superior spatial separation. The formulation of the proposed beamformer in the spherical harmonics signal model is presented along with an algorithm to solve it. Simulation results show the effectiveness of the proposed beamformer in spatially filtering the desired speaker signal from the interfering signals using a number of objective measures.

In recent years, correntropy-based algorithms which include maximum correntropy criterion (MCC), generalized MCC (GMCC), kernel MCC (KMCC) and hyperbolic cosine function-based algorithms such as hyperbolic cosine adaptive filter (HCAF), logarithmic HCAF (LHCAF), least lncosh (Llncosh) have been widely utilized in adaptive filtering due to their robustness towards non-Gaussian/impulsive background noises. However, the performance of such algorithms suffers from high steady-state misalignment. To minimize the steady-state misalignment along with having comparable computational complexity, an exponential hyperbolic cosine function (EHCF) based new robust norm is introduced and a corresponding EHCF based adaptive filter called exponential hyperbolic cosine adaptive filter (EHCAF) is developed in this letter. Further, computational complexity and bound on learning rate for stability of the proposed algorithm is also studied. A set of simulation studies has been carried out for system identification scenario to assess the performance of the proposed algorithm. Further, EHCAF algorithm has been extended and the filtered-x EHCAF (Fx-EHCAF) algorithm is proposed for robust room equalization.

In this letter, we propose to exploit the array motion of sparse circular arrays (SCA) on a rotating platform to increase the degrees of freedom (DOF) (i.e. the number of unique spatial lags) associated with the rotating array when compared to the array on a fixed platform. This increases the total number of sources that can be resolved by the rotating SCA with the same amount of physical sensors. The signal model for the combined synthetic array before and after a unit rotation motion is derived together with the closed-form expression for the increase in the DOF of a rotating nested sparse circular array (NSCA). A new modified NSCA is proposed and it is shown that the DOF of the proposed sparse array is higher than the conventional NSCA under motion with the same number of sensors. A simulation study is carried out to estimate the direction of arrival (DOA) of signals in a sensing environment that is assumed to be stationary over array motion of unit rotation and it verifies the effectiveness of array motion to increase the DOF of an SCA. The simulations also show the improved performance of the proposed NSCA.

A linear-in-the-parameters nonlinear filter consists of a functional expansion block, which expands the input signal to a higher dimensional space nonlinearly, followed by an adaptive weight network. The number of weights to be updated depends on the type and order of the functional expansion used. When applied to a nonlinear system identification task, as the degree of the nonlinearity of the system is usually not known a priori, linear-in-the-parameters nonlinear filters are required to update a large number of coefficients to effectively model the nonlinear system. However, all the weights of the nonlinear filter may not contribute significantly to the identified model. We show via simulation experiments that, the weight vector of a linear-in-the-parameters nonlinear filter usually exhibits a low-rank nature. To take advantage of this observation, this paper proposes a class of linear-in-the-parameters nonlinear filters based on the nearest Kronecker product decomposition. The performance of the proposed filters is superior in terms of convergence behaviour as well as tracking ability in comparison to their traditional linear-in-the-parameters nonlinear filter counterparts, when tested for nonlinear system identification. Furthermore, the proposed nearest Kronecker product decomposition-based linear-in-the-parameters nonlinear filters has been shown to provide improved noise mitigation capabilities in a nonlinear active noise control scenario.

The adaptive exponential functional link network (AEFLN) is a recently introduced novel linear-in-the-parameters nonlinear filter and is used in numerous nonlinear applications, including system identification, active noise control, and echo cancellation. The improved modeling accuracy offered by AEFLN for different nonlinear applications can be attributed to the exponentially varying sinusoidal basis functions used for nonlinear expansion. Even though AEFLN has been widely used for the identification of nonlinear systems, no theoretical analysis of AEFLN is available in the literature. Hence, in this article, a theoretical performance analysis of AEFLN trained using an adaptive exponential least mean square (AELMS) algorithm under the Gaussian input assumption is discussed. Expressions describing the mean as well as mean square behavior of the weight vector and adaptive exponential parameter are derived. Computer simulations are carried out, and the derived theoretical expressions show a close correspondence with simulation results.

Recently, nearest Kronecker product (NKP) decomposition based Wiener filter and Recursive Least Squares (RLS) have been proposed and was found to be a good candidate for system identification and echo cancellation and was shown to offer better tracking performance along with lower computational complexity, especially for identification of low-rank systems. In this paper, we derive the Least Mean Square (LMS) versions of adaptive algorithms which take advantage of NKP decomposition, namely NKP-LMS and NKP Normalized LMS (NKP-NLMS) algorithms. We compare the convergence and tracking performance along with computational complexity between standard NLMS, standard RLS, NKP based RLS (RLS-NKP), the standard Affine Projection Algorithm (APA) and NKP-NLMS algorithm, to evaluate the efficacy of NKP-NLMS algorithm in the context of system identification. Simulation results show that NKP-NLMS can be a good candidate for system identification, especially for sparse/low rank systems.

Robust adaptive signal processing algorithms based on a generalized maximum correntropy criterion (GMCC) suffers from high steady state misalignment. In an endeavour to achieve lower steady state misalignment, in this letter we propose a generalized hyperbolic secant function (GHSF) as a robust norm and derive the generalized hyperbolic secant adaptive filter (GHSAF). The new algorithm is seen to offer robust system identification performance over the conventional GMCC algorithm. To further improve the convergence performance under non-Gaussian noise environments, we propose the nearest Kronecker product decomposition based GMCC and GHSAF algorithms. Extensive simulation study show the improved convergence performance provided by the proposed algorithms for system identification.

Zero-attraction-based adaptive filters are widely used for sparse system identification, where a suitable penalty function is integrated with the least mean square (LMS) framework to improve the convergence behavior of the identification process. In this brief, we have made an attempt to implement some of the most popular zero-attracting algorithms in hardware. The complexity of realization associated with these algorithms is investigated in detail. Following the above analysis, several architectural simplifications are proposed for the reduced-complexity implementation of their penalty functions. We then use these realizations to develop a set of novel design strategies for the efficient implementation of these algorithms. Simulation results show that the performance loss for the proposed algorithms is minimal compared to their standard versions. A detailed synthesis study is also carried out to validate the proposed structures, which demonstrates that the hardware overhead in the proposed designs is marginal compared to the existing delayed LMS architecture.

Distributed arithmetic (DA) based architectures are popularly used for inner-product computation in various applications. Existing literature shows that the use of approximate DA-architectures in error resilient applications provides a significant improvement in the overall efficiency of the system. Based on precise error analysis, we find that the existing methods introduce large truncation error in the computation of the final inner-product. Therefore, to have a suitable trade-off between the overall hardware complexity and truncation error, a weight-dependent truncation approach is proposed in this paper. The overall efficiency of the structure is further enhanced by incorporating an input truncation strategy in the proposed method. It is observed that the area, time and energy efficiency of the proposed designs are superior to the existing designs with significantly lower truncation error. Evaluation in the case of noisy image smoothing application is also shown in this paper.

Active sound profiling, or active noise equalization strategies have been proposed to achieve spectral shaping of a primary disturbance signal. The control algorithms proposed to achieve such spectral shaping have either suffered from poor robustness to plant modeling uncertainties or required high levels of control effort. To improve the robustness of active sound profiling to uncertainties in the plant model, while avoiding increased control effort, a modified phase-scheduled-command filtered-x least-mean-square algorithm is proposed in this paper. The new algorithm provides improved stability, while requiring the minimum control effort. This improvement is achieved by replacing the plant model with an intelligent adaptive-hysteresis switching mechanism to allow the necessary estimation of the disturbance signal phase. The improved performance and robustness of the proposed algorithm is demonstrated through a series of simulations using measured acoustic responses.

Acoustic feedback cancellation is one of the challenging tasks in the design of a behind the ear digital hearing aid. This feedback cancellation is usually achieved by using an adaptive filter. The finite correlation between the desired microphone input signal and the input signal to the loudspeaker results in a biased estimation of the adaptive filter, which may produce disturbances in the hearing aid. Prediction error method (PEM) has been used in literature to reduce the bias effects. The convergence of a PEM-based feedback canceller can be improved by implementing the adaptive filter in the subband domain. However, a direct subband implementation results in aliasing issues, band-edge problems, and introduces a delay due to analysis and synthesis filters. In order to reduce the aliasing and delay issues, a delayless subband implementation of a PEM-based feedback canceller is designed in this paper. A delayless multiband-structured subband implementation of the feedback canceller is also attempted to further reduce the aliasing and band-edge effects. This implementation aims at having all the subbands collectively updating the fullband adaptive filter, without the need for a subband to fullband weight conversion and offers improved feedback cancellation at reduced computational load in comparison with a delayless subband implementation of a PEM-based feedback canceller. In addition, an attempt has been made to further improve the convergence behavior by using an improved proportionate learning scheme. The improved convergence offered by the proposed scheme is evident from the simulation study. The improvement has been further quantified using a perceptual evaluation of speech quality and the proposed approach has been shown to provide enhanced speech quality.

In this paper, we focus on the problem of removing noise in the acoustic domain. To this end, we introduce a class of hybrid nonlinear spline filters, which are designed as a cascade of an adaptive spline function and a single layer adaptive nonlinear network. The adaptive nonlinear networks employed in this work are the functional link network and the even mirror Fourier nonlinear network. Suitable update rules, which not only update the adaptive weights of the nonlinear networks, but also introduce adaptability in the developed spline function are derived. The proposed nonlinear filters have been successfully applied to nonlinear system identification as well as nonlinear active noise control. The new filters have been shown to outperform other popular nonlinear filters.