White Noise Amplification Research Articles

Design of frequency-invariant uniform concentric circular arrays with first-order directional microphones

Most of the existing frequency-invariant beamformers (FIBs) with circular arrays are implemented with omnidirectional microphones, where uniform circular arrays (UCAs) and uniform concentric circular arrays (UCCAs) have been widely utilized. However, the resulting FIB usually suffers from the deep nulls problem in the white noise gain (WNG) and the white noise amplification problem at low frequencies even if the order of the target beampattern is one. Due to its simple implementation, first-order directional microphones are adopted to improve the robustness of the FIB with UCCAs (FIB-UCCAs) in this paper. We exploit the circular harmonics decomposition rather than the Jacobi–Anger expansion to approximate the beampattern of the FIB-UCCAs with first-order directional microphones, because the directivity pattern of directional microphones is related to the direction of the signal. We show that the FIB-UCCAs can completely avoid the deep nulls problem in the WNG as long as the ring with the largest radius utilizes first-order directional microphones. In addition, the white noise amplification problem at low frequencies can be greatly alleviated if first-order directional microphones are utilized. Specifically, we show that the inherent white noise amplification problem at low frequencies can be completely circumvented when the order of the desired beampattern is one.

Design of a robust MVDR beamforming method with Low-Latency by reconstructing covariance matrix for speech enhancement

Aiming at solving the problems of the conventional minimum variance distortionless response (MVDR) beamformer in practical applications, such as the sensibility of the steering vector mismatch and beampattern distortion, a robust broadband MVDR beamforming method with low-latency by reconstructing covariance matrix is proposed and applied to speech enhancement with a linear microphone array in this paper. In this work, some important steps are optimized, and the main contribution is to consider the problem of correlation terms generated by the low latency. Firstly, the direction of arrival (DOA) is corrected and the steering vector is estimated based on the sparsity of the DOAs corresponding to the sound sources, which improves the ability of anti-mismatches in the steering vector. Secondly, the correlation terms between the sound sources and noise are estimated and eliminated by the Capon power within the eigen-subspace, and the indirect dominant method is used to eliminate the correlation terms between the sound sources, so that the covariance matrix is reconstructed to obtain a more robust MVDR beamformer. Thirdly, the problem of white noise amplification at low frequency bins is analyzed, and a white noise gain (WNG) modification method is proposed to obtain a compromise between the interference suppression and WNG. In the experiments, the TIMIT corpus is used to generate the multi-channel speech data set, and the performance of the proposed method is evaluated with different DOAs and input signal to interference plus noise ratios (SINRs). The experimental results show that the proposed method can effectively suppress the interferences and reduce the noise with strong robustness.

Design of Planar Differential Microphone Array Beampatterns with Controllable Mainlobe Beamwidth and Sidelobe Level.

The differential microphone array, or differential beamformer, has attracted much attention for its frequency-invariant beampattern, high directivity factor and compact size. In this work, the design of differential beamformers with small inter-element spacing planar microphone arrays is concerned. In order to exactly control the main lobe beamwidth and sidelobe level and obtain minimum main lobe beamwidth with a given sidelobe level, we design the desired beampattern by applying the Chebyshev polynomials at first, via exploiting the structure of the frequency-independent beampattern of a theoretical Nth-order differential beamformer. Next, the so-called null constrained and least square beamformers, which can obtain approximately frequency-invariant beampattern at relatively low frequencies and can be steered to any direction without beampattern distortion, are proposed based on planar microphone arrays to approximate the designed desired beampatterns. Then, for dealing with the white noise amplification at low-frequency bands and beampattern divergence problems at high-frequency bands of the null constrained and least square beamformers, the so-called minimum norm and combined solutions are deduced, which can compromise among the white noise gain, directivity factor and beampattern distortion flexibly. Preliminary simulation results illustrate the properties and advantages of the proposed differential beamformers.

Frequency-invariant beamformer design via ADPM approach

Frequency-invariant (FI) beamformers play an important role in suppressing speech waveform distortions. Due to the perfect FI beampattern (FIB), differential microphone arrays (DMAs) have been widely used in practical applications like voice communication and human-machine interface systems. Superdirective beamforming generated by DMAs have many useful properties but suffer white noise amplification. To address this drawback, we formulate a least squares broadband FI problem, under the white noise output power constraints, to improve robustness of superdirective beamformers. The problem is challenging to solve since FI beamformers are designed on broadband and initialization parameters corresponding to each frequency are different. We devise broadband beampattern synthesis algorithm based on alternating direction penalty method (ADPM), which utilizes the relationship between residuals and penalty terms to reduce the iteration number under the improved framework of alternating direction method of multipliers (ADMM). The proposed ADPM method can decompose the optimization problem into multi-block convex optimization problems and solve them separately. The fast convergence property of our solution is demonstrated via numerical simulations.

Multistage approach for steerable differential beamforming with rectangular arrays

This paper presents a multistage rectangular approach for steerable differential beamforming. As a first step, we propose employing a two-dimensional (2-D) differentiation scheme that operates independently on the columns and rows of a uniform rectangular array (URA). This yields a differentials matrix controlled by two parameters, Pc and Pr, which indicate the number of differential stages for the URA columns and rows. Then, as a second step, we design a rectangular differential beamformer and apply it to the vector form of the differentials matrix. We show that the proposed differentiation scheme may significantly improve the directivity of the resulted beamformer at the expense of white noise amplification. This improvement is heavily tied to selecting the (Pc,Pr) configuration per the desired signal incident angle. Next, we propose four rectangular differential beamformers and analyze their performances in terms of the white noise gain (WNG) and directivity factor (DF) measures. In addition, we address reverberant scenarios with three distinct incident angles of the desired signal. We examine the performances of each beamformer in terms of four reduction factors calculated from the noisy and enhanced signals and investigate their quality and intelligibility. We demonstrate that the proposed rectangular differential beamformers outperform common linear and differential beamformers in these measures, mainly when the incident angle is far from the endfire direction. Finally, we compare the proposed approach to two existing rectangular differential beamforming approaches from the literature. We show the proposed method to be preferable, considering both the quality and intelligibility of the enhanced signals.

Sensor Imperfection Tolerance Analysis of Robust Linear Differential Microphone Arrays

An $M$ th-order linear differential microphone array (LDMA) is conventionally designed by using a linear array of $M+1$ closely-spaced microphones. It is known that the conventional LDMAs suffer from the white noise amplification problem which may cause significant performance degradation in the presence of sensor imperfections. In order to resolve this, a more advanced solution has been proposed to employ more than $M+1$ microphones in the design of the LDMAs, which is shown to be effective against the white noise amplification and, hence, the resultant LDMAs are known as the robust LDMAs. Previous studies have shown that sensor imperfections can lead to dramatic performance degradation or even failure of the LDMAs due to the presence of the mainlobe orientation reversal (MOR) phenomenon. Therefore, avoiding the occurrence of the detrimental MOR phenomenon can serve as a minimum condition for the design of robust LDMAs in the presence of sensor imperfections. However, it is not yet quite clear how the sensor imperfections, such as microphone gain and phase mismatches, affect the robust LDMAs. Particularly in practical design, it will be of interest to know what the requirement is on the microphone imperfection tolerance for a given number of microphones, or alternatively, how many microphones should be used with a given microphone imperfection tolerance to guarantee no occurrence of the MOR phenomenon, which remains to be addressed. Motivated by the above, in this paper we first give an in-depth analysis of the impact of microphone imperfections on the mainlobe orientation of the robust LDMAs, and reveal how the MOR phenomenon occurs with the robust LDMAs. Then based on our theoretical foundation, the microphone imperfection tolerance analysis is performed, which provides a useful guidance when incorporating the influence of sensor imperfections into the practical design of robust LDMAs. Extensive numerical results are also presented to validate the effectiveness of our analysis.

Binaural Heterophasic Superdirective Beamforming.

The superdirective beamformer, while attractive for processing broadband acoustic signals, often suffers from the problem of white noise amplification. So, its application requires well-designed acoustic arrays with sensors of extremely low self-noise level, which is difficult if not impossible to attain. In this paper, a new binaural superdirective beamformer is proposed, which is divided into two sub-beamformers. Based on studies and facts in psychoacoustics, these two filters are designed in such a way that they are orthogonal to each other to make the white noise components in the binaural beamforming outputs incoherent while maximizing the output interaural coherence of the diffuse noise, which is important for the brain to localize the sound source of interest. As a result, the signal of interest in the binaural superdirective beamformer’s outputs is in phase but the white noise components in the outputs are random phase, so the human auditory system can better separate the acoustic signal of interest from white noise by listening to the outputs of the proposed approach. Experimental results show that the derived binaural superdirective beamformer is superior to its conventional monaural counterpart.

Heterophasic Binaural Differential Beamforming for Speech Intelligibility Improvement

Differential beamformers with small-size microphone arrays are very attractive for audio and speech signal acquisition thanks to their high directivity and frequency-invariant spatial responses. However, such beamformers often suffer from significant white noise amplification at low frequencies, which makes their implementation in real-world systems challenging. One widely used way to circumvent this issue is to increase the number of microphones in the design of a given order differential beamformer, leading to the so-called robust differential beamformer in which the redundancy provided by the additional sensors are used to improve the white noise gain (WNG). But even with this robust solution, white noise amplification at low frequencies still exists. In this article, instead of trying to improve WNG, we adopt a method to render the white noise in such a way that it affects less the perception of the speech signal of interest. Specifically, we propose a binaural differential beamforming method in which a differential beamformer is designed with two sub-beamforming filters that simultaneously generates two outputs, one for the left ear and the other for the right ear. Motivated by psychoacoustic experiments, we design these two filters in such a way that they are orthogonal so that the coherence between the white noise at the binaural outputs is minimized while the coherence between diffuse noise is maximized. With the proposed binaural differential beamformers, the desired signal components and (amplified) white noise at the binaural differential beamformer's outputs are rendered into different directions or zones. Consequently, the human perception system can better distinguish the desired signal from white noise for improved speech intelligibility. The superiority of the proposed binaural beamforming technique is justified by simulations, experiments, as well as listening tests.

Design of Planar Differential Microphone Arrays With Fractional Orders

Differential microphone arrays (DMAs) often encounter white noise amplification, especially at low frequencies. If the array geometry and the number of microphones are fixed, one can improve the white noise amplification problem by reducing the DMA order. With the existing differential beamforming methods, the DMA order can only be a positive integer number. Consequently, with a specified beampattern (or a kind of beampattern), reducing this order may easily lead to over compensation of the white noise gain (WNG) and too much reduction of the directivity factor (DF), which is not optimal. To deal with this problem, we present in this article a general approach to the design of DMAs with fractional orders. The major contributions of this article include but are not limited to: 1) we first define a directivity pattern that can achieve a continuous compromise between the pattern corresponding to the maximum DMA order and the omnidirectional pattern; 2) by approximating the beamformer's beampattern with the Jacobi-Anger expansion, we present a method to find the proper differential beamforming filter so that its beampattern matches closely the target directivity pattern of fractional orders; and 3) we show how to determine analytically the proper fractional order of the DMA with a given target beampattern when either the value of the DF or WNG is specified, which is useful in practice to achieve the desired beampattern and spatial gain while maintaining the robustness of the DMA system.

Microphone array beamforming based on maximization of the front-to-back ratio.

Microphone arrays are typically used in room acoustic environments to acquire high fidelity audio and speech signals while suppressing noise, interference, and reverberation. In many application scenarios, interference and reverberation may mainly come from a certain region, and it is therefore necessary to develop beamformers that can preserve signals of interest while minimizing the power of signals coming from the region where interference and reverberation dominate. For this purpose, this paper first reexamines the so-called front-to-back ratio and the classical supercardioid beamformer. To deal with the white noise amplification problem and the limited directivity factor associated with the supercardioid beamformer, a set of reduced-rank beamformers are deduced by using the well-known joint diagonalization technique, which can make compromises between the front-to-back ratio and the amount of white noise amplification or the directivity factor. Then, the definition of the front-to-back ratio is extended to a generalized version, from which another set of reduced-rank beamformers and their regularized versions are developed. Simulations are conducted to illustrate the properties and advantages of the proposed beamformers.

Constrained minimum power combination for broadband beamformer design in the STFT domain

Beamforming using sensor array is widely used in spatial signal processing since it offers better spatial focusing capability than single sensor. However, in practical applications for broadband signal, there always exists a trade-off issue between the directivity capability of an array and its robustness on system errors. In this paper, in order to combine merits of different beamformers instead of trade-off their performances, we propose a constrained minimum-power combination method. We firstly analyze two optimal beamformers that maximize Directivity Factor (DF) and White Noise Gain (WNG) respectively. Then we propose a non-linear combination method, which automatically selects the best beamformer that has the minimum output power, so as to control the unwanted white noise amplification and keep the maximum DF if possible. Two solutions to the proposed combination strategy are given. They do not need to determine the correct trade-off factor used in linear combination method, and avoid challenge estimations on noise and target statistics required in adaptive beamforming. The performance of the proposed beamformer is evaluated in ideal noise fields and complicated noise fields respectively. It is shown that the proposed beamformer integrates merits of different beamformers. It always achieves the best speech quality and biggest noise reduction compared to other popular beamformers.

Design of robust concentric circular differential microphone arrays.

Circular differential microphone arrays (CDMAs) have been extensively studied in speech and audio applications for their steering flexibility, potential to achieve frequency-invariant directivity patterns, and high directivity factors (DFs). However, CDMAs suffer from both white noise amplification and deep nulls in the DF and in the white noise gain (WNG) due to spatial aliasing, which considerably restricts their use in practical systems. The minimum-norm filter can improve the WNG by using more microphones than required for a given differential array order; but this filter increases the array aperture (radius), which exacerbates the spatial aliasing problem and worsens the nulls problem in the DF. Through theoretical analysis, this research finds that the nulls of the CDMAs are caused by the zeros in the denominators of the filters' coefficients, i.e., the zeros of the Bessel function. To deal with both the white noise amplification and deep nulls problems, this paper develops an approach that combines different rings of microphones together with appropriate radii. The resulting robust concentric circular differential microphone arrays (CCDMAs) can mitigate both problems. Simulation results justify the superiority of the robust CCDMA approach over the traditional CDMAs and robust CDMAs.

On the Design of Frequency-Invariant Beampatterns With Uniform Circular Microphone Arrays

This paper deals with two critical issues about uniform circular arrays (UCAs): frequency-invariant response and steering flexibility. It focuses on some optimal design of frequency-invariant beampatterns in any desired direction along the sensor plane. The major contributions are as follows. 1) We explain how to include the steering information in the desired directivity pattern. 2) We show that the optimal approximation of the beamformer's beampattern with a UCA from a least-squares error perspective is the Jacobi–Anger expansion. 3) We develop an approach to the design of any desired symmetric directivity pattern, where the deduced beampattern is almost frequency invariant and its main beam can be pointed to any wanted direction in the sensor plane. 4) With the proposed approach, we derive an explicit form of the white noise gain (WNG) and the directivity factor (DF), and explain clearly the white noise amplification problem at low frequencies and the DF degradation at high frequencies. The analysis also indicates that increasing the number of microphones can always improve the WNG. We show that the proposed method is a generalization of circular differential microphone arrays. The relationship between the proposed method and the so-called circular harmonics beamformers is also discussed.

Superdirective Beamforming Based on the Krylov Matrix

Superdirective beamforming has attracted a significant amount of research interest in speech and audio applications, since it can maximize the directivity factor (DF) given an array geometry and, therefore, is efficient in dealing with signal acquisition in diffuse-like noise environments. However, this beamformer is very sensitive to sensor self-noise and mismatch among sensors, which considerably restricts its use in practical systems. This paper develops an approach to superdirective beamforming based on the Krylov matrix. We show that the columns of a proposed Krylov matrix, which span a chosen dimension of the whole space, are interesting beamformers; consequently, all different linear combinations of those columns lead to beamformers that have good properties. In particular, we develop the Krylov maximum white noise gain and Krylov maximum DF beamformers, which are obtained by maximizing the WNG and the DF, respectively. By properly choosing the dimension of the Krylov subspace, the developed beamformers that can make a compromise between reasonable values of the DF and white noise amplification. We also extend the basic idea to the design of the Krylov maximum front-to-back ratio, parametric superdirective, and parametric supercardioid beamformers.

Reduced-Order Robust Superdirective Beamforming With Uniform Linear Microphone Arrays

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 beamforming with circular microphone arrays

Differential beamforming cannot only achieve high directional gain but also can form frequency-invariant beampatterns. Therefore, it has the great potential to be widely used in voice communications to process broadband speech signals. The performance of a differential beamformer in terms of directivity factor (DF), white noise gain (WNG), and frequency invariance of the beampattern depends on many factors including the array geometry, the number of sensors, the inter-sensor spacing, etc. In the literature, most studies on differential beamforming have been focused on linear microphone arrays and not much efforts have been devoted to other array geometries. This paper is devoted to the study of circular microphone arrays. In comparison with linear arrays whose spatial response is a function of the steering angle, circular microphone arrays can have the same spatial response along many different directions. The focal point of this paper is on differential beamforming with uniform circular microphone arrays. The main topics addressed include: (1) major properties of circular microphone arrays, (2) how to design differential beamformers with different beampatterns, (3) how to design differential beamformers with different orders, and (4) how to achieve a good control of the white noise amplification problem, high directional gains, and frequency-independent responses.

Design of robust differential microphone arrays with the Jacobi–Anger expansion

Abstract Due to their small size, differential microphone arrays (DMAs) are very attractive. Moreover, they have been effective in combating noise and reverberation. Recently, a new class of DMAs of different orders have been developed with the MacLaurin’s series and the frequency-independent patterns. However, the MacLaurin’s series does not approximate well the exponential function, which appears in the general definition of the beampattern, when the intersensor spacing is not small enough. To circumvent this problem, we propose in this paper to approximate the exponential function with the Jacobi–Anger expansion. Based on this approximation and the frequency-independent Chebyshev patterns, we derive first-, second-, and third-order DMAs. Furthermore, in order to improve the robustness of DMAs against white noise amplification, we propose to use more microphones combined with minimum-norm filters. It is also shown that the Jacobi–Anger expansion is optimal from a mean-squared error perspective. Simulations are carried out to evaluate the performance of the proposed DMAs.

On the design and implementation of linear differential microphone arrays.

Differential microphone array (DMA), a particular kind of sensor array that is responsive to the differential sound pressure field, has a broad range of applications in sound recording, noise reduction, signal separation, dereverberation, etc. Traditionally, an Nth-order DMA is formed by combining, in a linear manner, the outputs of a number of DMAs up to (including) the order of N - 1. This method, though simple and easy to implement, suffers from a number of drawbacks and practical limitations. This paper presents an approach to the design of linear DMAs. The proposed technique first transforms the microphone array signals into the short-time Fourier transform (STFT) domain and then converts the DMA beamforming design to simple linear systems to solve. It is shown that this approach is much more flexible as compared to the traditional methods in the design of different directivity patterns. Methods are also presented to deal with the white noise amplification problem that is considered to be the biggest hurdle for DMAs, particularly higher-order implementations.

Design of Robust Differential Microphone Arrays

Differential microphone arrays (DMAs), due to their small size and enhanced directivity, are quite promising in speech enhancement applications. However, it is well known that differential beamformers have the drawback of white noise amplification, which is a major issue in the processing of wideband signals such as speech. In this paper, we focus on the design of robust DMAs. Based on the Maclaurin’s series approximation and frequency-independent beampatterns, the robust first-, second-, and third-order DMAs are proposed by using more microphones than the order plus one, and the corresponding minimum-norm filters are derived. Compared to the traditional DMAs, the proposed designs are more robust with respect to white noise amplification while they are capable of achieving similar directional gains.

A combined QFT/H ∞ design technique for TDOF uncertain feedback systems

A new way of incorporating QFT principles into H X -control design techniques for solving the two-degrees of freedom feedback problem with highly uncertain plants is developed. The proposed practical design approach consists of two stages. In the first stage, the robustness problem, due to plant uncertainties, is solved by H X -norm optimization. In this stage, the controller inside the loop (the first degree of freedom) is designed, with the ultimate goal of minimizing the cost of feedback. Minimization of the sensor white noise amplification at the input to the plant is also performed using QFT principles. In the second stage of the design, the prefilter outside the loop (the second degree of freedom), is used to achieve the tracking specifications by conventional classical control theory, as practiced by the QFT design procedure. The combined QFT/H X design procedure for single input-single output (SISO) feedback systems is directly applicable to multi input-multi output (MIMO) feedback uncertain systems. The efficiency of the proposed technique is demonstrated with SISO and MIMO design examples for higly uncertain plants.