This paper investigates the design of adaptive differential beamforming using small-spacing linear microphone arrays. We express the differential beamformer as a linear function of the target beampattern coefficients through orthogonal polynomial expansions. Consequently, the design of the beamformer reduces to optimizing these coefficients. To ensure that the maximum array response consistently aligns with the look direction, we derive constraints on the target beampattern coefficients, resulting in two convex sets for the first two orders of beampatterns. This approach uncovers numerous effective beampatterns beyond traditional options such as dipole, cardioid, supercardioid, and hypercardioid. By minimizing the power of the array output while adhering to the beampattern constraints, we develop the MPPCAD beamformer. Simulation results demonstrate that the proposed beamformer significantly enhances speech quality compared to classical differential beamformers.

This paper is devoted to the problem of noise covariance matrix (NCM) estimation. It proposes a time-frequency masking based approach. We first present an optimal mask function based on the mean-squared error criterion. To estimate this mask, we employ the recently developed directional gain method based on the knowledge of the signal incident angle. To demonstrate the effectiveness of the proposed NCM estimator, we integrate it into the minimum variance distortionless response (MVDR) beamformer. The speech enhancement results in noise-plus-interference environments show the advantages of the proposed method over two baseline beamforming algorithms.

Direction-of-arrival (DOA) estimation is challenging in complex acoustic environments with background noise and interference. Utilizing spherical microphone arrays, closed-form estimators can be derived, which are attractive for practical applications due to their computational efficiency, eliminating the need for exhaustive extremum searching. However, current closed-form estimators are susceptible to interference. To address this issue, we propose an estimator that directly computes the DOA of the desired source using the covariance matrix of the observation signals. This approach effectively mitigates the impact of interference when the covariance matrix is accurately estimated. Simulation results demonstrate the superior performance of the proposed method compared to the subspace pseudo-intensity vector (SSPIV) and relative harmonic coefficients (RHC) methods.

Beamforming has been used in a wide range of applications to extract the signal of interest from microphone array observations, which consist of not only the signal of interest, but also noise, interference, and reverberation. The recently proposed interference-controlled maximum noise reduction (ICMR) beamformer provides a flexible way to control the specified amount of the interference attenuation and noise suppression; but it requires accurate estimation of the manifold vector of the interference sources, which is challenging to achieve in real-world applications. To address this issue, we introduce an interference-controlled maximum noise reduction network (ICMRNet) in this study, which is a deep neural network (DNN)-based method for manifold vector estimation. With densely connected modified conformer blocks and the end-to-end training strategy, the interference manifold is learned directly from the observation signals. This approach, akin to ICMR, adeptly adapts to time-varying interference and demonstrates superior convergence rate and extraction efficacy as compared to the linearly constrained minimum variance (LCMV)-based neural beamformers when appropriate attenuation factors are selected. Moreover, via learning-based extraction, ICMRNet effectively suppresses reverberation components within the target signal. Comparative analysis against baseline methods validates the efficacy of the proposed method.

It is well known that an adaptive beamformer can be decomposed as a fixed beamformer followed by a post filter. This decomposition gives a much flexible way to design robust adaptive beamformers with high array gain and consequently it has become a popular approach to speech enhancement. In such a framework, the most critical problem is to estimate the post filter, which is studied in this paper. We present a multistage approach to the design of the post filter, which consists of a primary beamformer, a secondary beamformer and several auxiliary beamformers. Since the designed post filter is a function of source incidence angle by nature, we call it a directional gain. To evaluate the directivity of the beamformers in computing the directional gain, we introduce a modified beampattern, which is a function of both the source incidence angle and the point-source-to-background-noise ratio (PBR). To validate the presented approach, we analyze the principles of the primary, secondary and auxiliary beamformers, and then present a way to design these beamformers under the constraint of minimum white-noise-gain (WNG). Finally, we evaluate the performance of the directional gain and compare it with the traditional beamformers. The results show that the proposed directional gain can help achieve higher directivity factors (DFs), and better point-source-noise attenuation.

This paper studies the problem of microphone array beamforming to enhance a speech signal of interest in adverse acoustic environments, where interference and additive background noise coexist. The problem is formulated as one of convex optimization whose solution under a specified level of interference attenuation leads to an interference controlled maximum noise reduction (ICMR) beamformer, which can be expressed as a linear combination of two MVDR beamformers: one attempts to extract the desired source signal while the other attempts to extract the interference. The combination coefficients are functions of the array manifold vectors, noise coherence matrix, and the specified interference attenuation factor. By tuning the interference attenuation factor, the ICMR beamformer can be implemented to achieve aggressive interference attenuation or even eliminate interference completely; but this may lead to less additive noise suppression or even noise amplification. To control the maximum sacrifice in gain (SG) of the signal-to-noise ratio (SNR) that is acceptable for additive reduction, a variant of ICMR is derived, which is named as the ICMR-SG beamformer. Simulations are performed and the results show that the ICMR beamformer is able to control the amount of interference attenuation. In comparison, ICMR-SG controls the maximum SG of SNR while achieving the optimal possible level of interference attenuation.

Microphone arrays have been used in wide range of applications for sound acquisition and signal enhancement, the performance of which depends not only on the processing algorithms but also on the array geometry. A large number of efforts have been devoted to the development of beamforming and signal enhancement algorithms for processing microphone array signals in the literature. Relatively, few efforts have been made to investigate the problem of array geometry optimization. This paper studies the problem of geometry optimization for planar arrays and it develops a genetic optimization algorithm that can optimize the positions of the sensors, thereby maximizing the directivity factor (DF) with a constrained level of white noise gain (WNG) given the number of microphones, the region in which they should be placed, and the interested range of steering. Simulation results show that the optimized array geometry outperforms the uniform linear, the uniform circular and the rectangular grid geometries in terms of DF with the same number of sensors and the same constraint on the minimum level of WNG.

This paper is devoted to the problem of adaptive beamforming with small-spaced microphone arrays. In this context, the Wiener filter is an optimal beamformer in the mean-squared error (MSE) sense. However, it requires good estimates of the covariance matrices of the speech signal of interest and noise, which are difficult to achieve in time-varying and reverberant acoustic environments. To deal with this problem, we propose a general method by parametric modeling the covariance matrices of speech and noise, which leads to a simplified Wiener beamformer. This beamformer has only one time-varying parameter to estimate, which is much easier to achieve as compared to the estimation of covariance matrices. As an example, we adopt the parametric model used in the superdirective beamformer, which models the covariance matrices as a combination of the pseudo-coherence matrices of a point source and diffuse noise. Simulation results show that the developed beamformer outperforms the traditional Wiener beamformer in terms of both noise and reverberation suppression.

Estimation of time-varying variances of signals for beamforming in sensor arrays is a challenging problem. Based on the assumption that the array manifold vector and the noise pseudo-coherence matrix are known a priori or are well estimated, we present in this paper two estimators for estimating the time-varying variances of the source signal of interest and the noise. These two estimators are then extended to deal with the following situations: 1) there are multiple candidates of the noise pseudo-coherence matrix or the noise pseudo-coherence matrix is a linear combination of some base pseudo-coherence matrices, and 2) the estimation variance is large and smoothing is needed. Simulations for speech enhancement applications are performed and the results show that the proposed estimators can well track the time-varying variances of both the speech and noise signals. It is also demonstrated that the optimal beamformer using the variance parameters estimated with the presented estimators outperforms the widely used traditional optimal beamformers in terms of improvement in both the signal-to-noise ratio (SNR) and the log-spectral distortion (LSD).

Differential microphone arrays (DMAs) have many interesting properties and have been widely used in acoustic, audio, and speech applications. A critical part of a DMA is the differential beamformer, which is generally designed in two important steps: 1) specifying a target beampattern based on what differential sound pressure field the DMA is expected to respond to and 2) designing the differential beamforming filter so that the resulting beampattern matches the target one. Most efforts in the study of DMAs so far have focused on the second step while choosing one of the limited patterns available in the literature as the target beampattern. Since it governs how the array performs, how to design the target beampattern is an important problem, which this paper addresses. The major contributions of this paper consists of the following four aspects. First, a positive superposition theorem is presented, which shows that the linear combination of effective beampatterns with non-negative coefficients is always an effective beampattern. Second, we propose a general approach to the design of target DMA beampatterns based on the positive superposition theorem. Third, an overview of the classical target beampatterns is provided and discussion is made on how to form effective base patterns. Fourth, we show that the smallest first null of a DMA is π(2N) with N being the DMA order, which provides the rule of setting nulls in practice. Finally, with examples, we show that with the use of the alternating-direction-method-of-multipliers algorithm, the proposed approach is able to generate useful DMA target beampatterns.

Differential beamforming is one of the most popular beamforming approaches, which has the great potential to form frequency-invariant directivity patterns. In this paper, we study the design of beampatterns with multiple nulls in the same direction, which is clearly different from the design of beampatterns with distinct nulls. Our contributions are as follows. First, we show how to constrain multiple nulls to the same direction and design the desired beampattern with both the traditional and robust approaches. Second, we derive an explicit form of the white noise gain (WNG) of the traditional approach as a function of the frequency, interelement spacing, and null direction, which shows that the cardioid is the optimal beampattern as far as the WNG is concerned. Third, we prove that the WNG improvement of the robust approach rarely depends on the null direction at low frequencies. Finally, considering the fact that the robust differential beamforming approach may produce a frequency-dependent beampattern while improving the WNG, we develop a weighted-norm approach that can make a good compromise between the robustness of differential beamforming with respect to white noise and the frequency-invariant beampattern. The performance of the developed approach is verified by simulations.

Sensor arrays for audio and speech signal acquisition are generally required to have frequency-invariant beampatterns to avoid adding spectral distortion to the broadband signals of interest. One way to obtain frequency-invariant beampatterns is via superdirective beamforming. However, traditional superdirective beamformers may cause significant white noise amplification (particularly at low frequencies), making them sensitive to uncorrelated white noise. To circumvent the problem of white noise amplification, a method was developed to find the superdirective beamforming filter with a constraint on the white noise gain (WNG), leading to the so-called WNG-constrained superdirective beamformer. But this method damages the frequency invariance of the beampattern. In this paper, we develop a flatness-constrained robust superdirective beamformer. We divide the overall beamformer into two subbeamformers, which are convolved together: one subbeamformer forms a lower order superdirective beampattern while the other attempts to improve the WNG. We show that this robust approach can improve the WNG while limiting the frequency dependency of the beampattern at the same time.

Differential microphone arrays (DMAs), which are responsive to the differential sound pressure field, have attracted much attention due to their properties of frequency-invariant beampatterns, small apertures, and potential of maximum directivity. Traditionally, DMAs are designed and implemented in a multistage (cascade) way, where a proper time delay is used in each stage to form a beampattern of interest. Recently, it was reported that DMAs can be designed by solving a linear system of equations formed from the information about the nulls of the desired beampattern. This paper deals with the problem of beamforming with linear DMAs. Its major contributions are as follows. 1) By using the spatial${\cal Z}$transform, we present some theoretical analysis of both the traditional cascade and new null-constrained DMA beamforming. It is shown that the cascade and null-constrained DMAs of the same order with the same number of sensors are theoretically identical. 2) We develop a two-stage approach to the study of the robust DMA beamformer, which is based on the principle of maximizing the white noise gain (WNG). The first-stage of this approach is in the structure of the traditional non-robust DMA while the second-stage filter is optimized for improving the WNG. 3) Using the two-stage approach, we show that the robust DMA beamformer may introduce extra nulls in the beampattern at high frequencies; particularly, it introduces$M - N - 1$extra nulls if the interelement spacing is equal to half of the wavelength, where$M$and$N$are the number of sensors and the DMA order, respectively. 4) We develop a method that can solve the extra-null problem while maximizing the WNG in robust DMA beamforming, i.e., a robust solution with a frequency-invariant beampattern.

The minimum variance distortionless response (MVDR) beam-former has been widely studied for extraction of desired speech signals in noisy acoustic environments. The performance of this beam-former, however, depends on many factors such as the array geometry, the source incidence angle, the noise field characteristics, the reverberation conditions, etc. In this paper, we study the performance of the MVDR beamformer in different noise and reverberation conditions with a linear microphone array. Using the gain in signal-to-noise ratio (SNR) as the performance metric, we show that the optimal performance of the MVDR beamformer generally occurs when the source is in the endfire directions in different types of noise, which indicates that, as long as a linear array is used, we should configure it in such a way that the endfire direction is pointed to the desired source. Simulations in reverberant environments also verified this result, though the performance difference between end-fire and broadside directions reduces as the degree of reverberation increases.

Linear microphone arrays combined with the minimum variance distortionless response (MVDR) beamformer have been widely studied in various applications to acquire desired signals and reduce the unwanted noise. Most of the existing array systems assume that the desired sources are in the broadside direction. In this paper, we study and analyze the performance of the MVDR beamformer as a function of the source incidence angle. Using the signal-to-noise ratio (SNR) and beampattern as the criteria, we investigate its performance in four different scenarios: spatially white noise, diffuse noise, diffuse-plus-white noise, and point-source-plus-white noise. The results demonstrate that the optimal performance of the MVDR beamformer occurs when the source is in the endfire directions for diffuse noise and point-source noise while its SNR gain does not depend on the signal incidence angle in spatially white noise. This indicates that most current systems may not fully exploit the potential of the MVDR beamformer. This analysis does not only help us better understand this algorithm, but also helps us design better array systems for practical applications.