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.

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.

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 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.