This paper investigates the performance limitations of conventional linearly constrained minimum variance (LCMV) beamformers implemented with circular microphone arrays. In particular, we show that imposing null constraints on interference directions can lead to a deviation of the mainlobe from the desired steering angle. A theoretical analysis is presented to characterize this deviation, and a closed-form expression for the deviation is derived to reveal the underlying low-frequency behavior of LCMV beamformers. To address this issue, we propose a mainlobe-controlled LCMV (MC-LCMV) beamformer. Simulation results demonstrate that the proposed method substantially improves spatial directivity and speech enhancement performance compared with conventional LCMV beamformers.

Microphone array beamforming is widely used to extract desired speech signals from noisy environments. While most research in this area focuses on utilizing spatial information, less attention is given to the intrinsic physical mechanisms underlying microphone array observations. This paper aims to address this gap by exploring these underlying factors through dynamic mode decomposition (DMD). Our contributions are twofold. 1) We develop a DMD-based signal model for microphone arrays to capture the relationships between observation signals at adjacent microphones. 2) We introduce a DMD-based preprocessing method and a corresponding beamforming approach based on this model. Simulation results show that our proposed method significantly enhances performance compared to conventional beamforming techniques.

Kronecker product beamforming is an effective technique for designing beamformers with nonuniform linear arrays (NULAs). However, current techniques are restricted to NULAs with specific configurations, where the steering vector of the array is represented as a Kronecker product of steering vectors from smaller virtual arrays. This paper overcomes these constraints by proposing a novel approach to designing Kronecker product beamformers for NULAs from a low-rank perspective. Our approach involves decomposing the NULA into overlapping subarrays and organizing the sensor signals from these subarrays into a matrix. We then apply filters to both sides of this matrix to produce an output, which is then converted into a low-rank beamforming process. This method is highly adaptable and can be utilized for NULAs with any number of microphones.

Superdirective beamformers are highly effective at suppressing directional interference and diffuse noise, but their practical use is often constrained by the problem of white noise amplification. Robust superdirective beamforming methods typically address this by imposing a constraint on the white noise gain (WNG). However, determining the appropriate WNG threshold in varying noise environments remains unclear. This paper introduces a data-driven approach to estimating the optimal WNG threshold. Subsequently, a more versatile and robust superdirective beamformer is developed by solving a quadratic eigenvalue problem (QEP). Experimental results show that this method outperforms traditional superdirective beamformers, which rely on a WNG threshold set through a fixed search range. Importantly, this approach functions as a distortionless beamformer, maintaining high fidelity of the desired acoustic signal and allowing for additional post-filtering if required.

Superdirective beamformers, used with small microphone arrays, are highly attractive due to their high directivity and frequency-invariant beampatterns, making them well-suited for processing broadband acoustic and speech signals. However, these beamformers are very sensitive to array imperfections such as sensor mismatches and self-noise. To improve robustness, robust superdirective (RSD) beamformers have been developed, employing techniques such as diagonal loading or white-noise-gain constraints during their derivation. Although RSD beamformers offer enhanced robustness compared to classical superdirective beamformers, they cannot achieve the maximum directivity factor and lose some frequency-invariant properties, resulting in a beamwidth that is wider at low frequencies and narrower at high frequencies. As a result, RSD beamformers do not fully meet the criteria of true superdirective beamformers, providing less effective noise reduction and introducing some speech distortion. Post-filtering methods have been developed to improve noise reduction after RSD beamforming, but they often fail to address the distortion issues, especially when the speech source deviates from the array’s look direction. To overcome this limitation, this paper proposes a joint optimization approach that combines post-filtering with RSD beamformers. By using the output of RSD beamformers as input data and considering various deviations in look directions and array mismatches, we train a post-filtering network to further enhance the beamformer’s output. Experimental results on speech enhancement demonstrate the effectiveness and robustness of the proposed method.

Direction-of-arrival (DOA) estimation is a key process in microphone array systems. The steered response power-based minimum variance distortionless response (SRP-MVDR) method performs very well in challenging acoustic environments but suffers from exponential complexity as the number of microphones increases. To improve the efficiency of SRP-MVDR for real-time applications, we propose a Kronecker product-based SRP-MVDR (SRP-KPMVDR) method designed for large rectangular microphone arrays. This approach begins with a rank-one approximation that represents the signal covariance matrix of a rectangular microphone array in Kronecker product form, which is essential for SRP-MVDR estimation. By utilizing the Kronecker product properties, the complex matrix inversion in SRP-MVDR is simplified to the inversion of two smaller matrices, significantly reducing computational complexity. Simulation results show that the SRP-KPMVDR method achieves comparable performance to the traditional SRP-MVDR while greatly decreasing the computational demands.

Differential microphone arrays (DMAs) have garnered significant attention in recent research and development due to their high directivity and frequency-invariant beampatterns. However, DMAs frequently encounter substantial white noise amplification, which limits their practical applications. This paper addresses this issue by introducing a general method for designing robust DMAs with microphone arrays of arbitrary planar topology. The proposed approach approximates the beampattern using the Jacobi-Anger series expansion and constrains the white noise gain (WNG) to a specified value. This minimizes the error between the beampattern and the ideal directivity pattern while ensuring a reasonable level of robustness. A closed-form solution for the robust differential beamformer filter is derived using the quadratic eigenvalue problem (QEP) method. Simulation results demonstrate the feasibility and effectiveness of the proposed approach.

Differential microphone arrays are widely used for far-field sound acquisition due to their high directivity and compact geometry. However, they lack the flexibility to adapt in dynamic acoustic environments with multiple or moving interferers. This paper proposes a novel method for fusing multiple differential beamformers to improve robustness under such conditions. A set of beamformers is designed with distortionless constraints in the target direction and nulls in various potential interference directions. An online fusion strategy is then applied, where a subset of beamformer outputs is selected and adaptively combined at each time frame based on the criterion of minimizing the instantaneous output variance. Simulation results demonstrate that the proposed method achieves superior interference suppression and speech quality, while maintaining low computational complexity suitable for real-time processing.

Thanks to their high directivity, compact size, and reliable performance, differential microphone arrays (DMAs) have attracted great interest from both industry and academia as they have demonstrated great potential to be used in a wide range of applications for high-fidelity speech acquisition. Nevertheless, in many real-world applications, DMAs powered with fixed differential beamformers are often inadequate in suppressing interference, particularly in environments with multiple or moving sources. To address this issue, this work develops an adaptive convex combination (ACC)-based method, which combines multiple differential beamformers in an online manner for enhanced performance. While the major contribution is a new real-time processing algorithm that facilitates optimal linear combinations of different differential beamformers, making them adapted to dynamic environments, the presented method also provides valuable insights as how to combine different beamformers for online robust implementation.

This paper investigates the problem of designing differential beam-formers with planar microphone arrays to achieve not only the desired target directivity pattern but also control the beamwidth (BW) or sidelobe level (SLL). We first discuss the target directivity patterns and express the Dolph-Chebyshev polynomial based form of target directivity patterns into linear combination of cylindrical harmonics. We then address the problem of designing differential beamformers through beampattern approximation based on the Jacobi-Anger series expansion. Two methods are subsequently developed: the first one involves designing beamformers to achieve the target directivity pattern while minimizing SLL under a pre-specified value of BW and the second one aims to attain the target directivity pattern while minimizing the null-to-null BW under a pre-specified level of SLL. Simulations are carried out to validate the method and the results demonstrate the properties of the proposed method.

Linear differential microphone arrays (LDMAs) are commonly integrated into thin and portable devices to achieve high-fidelity speech acquisition. Traditional LDMAs typically consist of only omnidirectional microphones, which impose limitations on their ability to produce steerable spatial responses due to constraints in array element directivity and linear array geometry. A recent solution to this limitation involves integrating both omnidirectional and bidirectional microphones in LDMA design, enabling the creation of steerable spatial responses. This paper extends the core idea of integrating omnidirectional and bidirectional microphones, and develops a more general and comprehensive theory and method for designing steerable LDMAs. It makes two main contributions. Firstly, it introduces a general approach to designing steerable LDMAs, in which any type of directional microphones can be used. Secondly, it gives the minimum number of omnidirectional and directional microphones required to achieve a specific order of steerable LDMA. Simulations validate the proposed method and illustrate how omnidirectional and directional sensors can be combined to form the desired LDMAs.

Differential microphone arrays (DMAs) have demonstrated a great potential for solving the high-fidelity sound acquisition problem in a wide range of applications as they possess many good properties such as frequency-independent beampatterns with high directivity. A significant number of efforts have been devoted to the design of DMAs and the associated beamformers. As a result, many different types of DMAs and differential beamforming methods have been developed over the last few decades, some of which have been successfully deployed in real systems and commercial products. However, given an application, how to design a DMA to achieve optimal performances is still an open issue. This work studies the problem of designing linear DMAs (LDMAs) from a geometric perspective. Based on the fundamental observation that most practical and interesting DMA beampatterns have nulls in some directions, we define a criterion based on the orthogonality between the beamforming filter and the steering vector in the nulls' directions. We then derive a family of differential beamformers by optimizing the defined criterion, some of which are well known but derived from a different perspective, while others are new. Simulations and experiments are carried out, and the results validate the proposed method and developed differential beamformers.

This paper studies the design of maximum directivity factor (MDF) beamformers based on uniform linear arrays (ULAs) consisting of acoustic vector sensors (AVSs). We first derive the main lobe constraints, which ensure that the beamformer's beampattern achieves a maximum in the look direction, and prove that any beamformer that satisfies the proposed constraints can be written as the sum of two orthogonal beamformers: the maximum white noise gain (MWNG) beamformer and a reduced-rank beamformer. Then, we derive the MDF beamformer by maximizing the directivity factor (DF) under the deduced constraints. We also derive a robust version of the MDF beamformer, which can keep the WNG above a pre-specified level. Compared to the conventional MDF beamformer based on ULAs with omnidirectional microphones, the designed MDF beamformer with uniform linear AVS arrays (ULAVSAs) can steer the beampattern to any look direction in the 3-dimensional space and achieves a higher directivity. The proposed MDF beamformer also outperforms the two-step MDF beamformer with ULAVSAs since it maximizes the DF. The proposed methods are validated through simulations as well as real experiments.

While differential beamforming with uniform linear arrays (ULAs) has been widely studied, there is little work so far regarding the design of differential beamformers with nonuniform linear arrays (NULAs). This paper attempts to shed some light on the principles of differential beamforming with NULAs. We define spatial difference operators with NULAs, where any order of the spatial difference of the observation signals can be represented as the product of a nonuniform spatial difference operator matrix and the observation vector. Consequently, the design of differential beamformers is performed in two stages. In the first one, a nonuniform spatial difference operator matrix is applied to the array observations, thereby yielding differential signals. In the second stage, beamformers are designed and applied to the obtained differential signals to optimize the array performance. Based on the defined spatial difference operators, we derive from some performance metrics a family of differential beamformers with NULAs, which include the maximum directivity factor (DF), the maximum white noise gain (WNG), and the maximum front-to-back ratio (FBR) differential beamformers. To compromise between the DF and array robustness, we also derive the parameterized maximum DF and parameterized maximum FBR differential beamformers. The null-constraint maximum DF and WNG differential beamformers are also developed so that some nulls can be placed in specified directions for interference suppression. Simulation results validate the theoretical analysis and justify the properties of the proposed methods.

Differential microphone arrays (DMAs) can achieve high directivity and frequency-invariant spatial response with small apertures; they also have a great potential to be used in a wide spectrum of applications for high-fidelity sound acquisition. Although many efforts have been made to address the design of linear DMAs (LDMAs), most developed methods so far only work for the situation where the source of interest is incident from the endfire direction. This paper studies the steering problem of differential beamformers with linear microphone arrays. We present new insights into beam steering of LDMAs and propose a series of steerable differential beamformers. The major contributions of this paper are as follows. 1) A series of ideal functions are defined to describe the ideal, target beampatterns of LDMAs. 2) We prove that first-order differential beamformers with linear microphone arrays are not steerable and their mainlobes can only be at the endfire directions. 3) We deduce the fundamental conditions for designing steerable differential beamformers with LDMAs. 4) We develop a method to design steerable beamformers with LDMAs using null constraints. Simulations and experiments validate the properties of the developed method.

This paper presents a method to design optimal linear differential microphone arrays (DMAs) by optimizing the array geometry. By constraining the DMA beamformer to achieve a given target value of the directivity factor (DF) with a specified target frequency-invariant beampattern while achieving also the highest possible white noise gain (WNG), an optimization algorithm is developed, which consists of the following two steps. 1) The full frequency band of interest is divided into a few subbands. At every subband, the entire linear array is divided into subarrays and the number of subarrays depends on the total number of the sensors and the order of the DMA. A cost function is then defined, which is minimized to determine what subarray produces the optimal performance. 2) The subband optimal subarrays are then combined across the entire frequency band to form a fullband cost function, from which the geometry of the entire array is optimized. These two steps are repeated with the particle swarm optimization (PSO) algorithm until the desired array performance is reached. Simulation results demonstrate that the proposed method can obtain the target DF with a frequency-invariant beampattern over a wide band of frequencies while maintaining a reasonable level of WNG.

This paper is dedicated to the design of fully steerable linear differential microphone arrays (LDMAs). We analyze the steerable ideal spatial responses and explain why conventional LDMAs consisting of only omnidirectional microphones have limited steering ability. In order to circumvent this limitation, we suggest to use both omnidirectional and bidirectional (with a dipole shaped directivity pattern) microphones. We discuss the minimum numbers of omnidirectional and bidirectional sensors required for achieving steerable spatial responses and present a method to design fully steerable differential beamformers with LDMAs through the Jacobi-Anger series expansion. Simulations validate the presented technique and the steering flexibility of the designed LDMAs.