Differential Microphone Arrays Research Articles

Theoretical Analysis of Differential Microphone Array Beamforming and an Improved Solution

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.

Design of robust differential microphone arrays with orthogonal polynomials.

Differential microphone arrays have the potential to be widely deployed in hands-free communication systems thanks to their frequency-invariant beampatterns, high directivity factors, and small apertures. Traditionally, they are designed and implemented in a multistage way with uniform linear geometries. This paper presents an approach to the design of differential microphone arrays with orthogonal polynomials, more specifically with Jacobi polynomials. It first shows how to express the beampatterns as a function of orthogonal polynomials. Then several differential beamformers are derived and their performance depends on the parameters of the Jacobi polynomials. Simulations show the great flexibility of the proposed method in terms of designing any order differential microphone arrays with different beampatterns and controlling white noise gain.

Study of nonuniform linear differential microphone arrays with the minimum-norm filter

The performance of differential microphone arrays (DMAs) depends on many factors such as the number of sensors and the array geometry. This paper develops an approach that exploits nonuniform linear geometries and the minimum-norm filter to improve the robustness of DMAs against white noise. Unlike the conventional way that forms an Nth-order DMA by subtractively combining the outputs of two DMAs of order N-1, this approach works in the short-time Fourier transform (STFT) domain and applies a complex weight to the output of each sensor and then sum the weighted outputs to form the beamforming output in every STFT subband. The minimum-norm filter is obtained by maximizing the white noise gain of the beamformer subject to the so-called fundamental constraints. The nonuniform linear arrays are created by adjusting the interelement spacing according to some rule. We show that the use of nonuniform linear geometries can significantly improve the robustness of DMAs, particularly at low frequencies. We also show that the diagonal loading technique can help improve the robustness of DMA beamformers, though the improvement is not significant.

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.

Noise-Reducing and Effect-Enhancing System for Communication Equipment Mounted on Vehicle

The noise of communication equipment mounted on Vehicle is one of important factors affecting equipment efficiency. Active Noise Control (ANC) technology is applied to noise reduction of the equipment, and a noise reduction mathematics model is built based on accurate noise measurement. An approach to reduce noise based on first-order differential microphone (FDM) array and ANF technology is proposed, which collects and evaluates environmental noise precisely to enhance voice. This approach improves the conversation effects and realizes full fidelity of voice transmission.

Particle velocity gradient based acoustic mode beamforming for short linear vector sensor arrays.

In this paper, a subtractive beamforming algorithm for short linear arrays of two-dimensional particle velocity sensors is described. The proposed method extracts the highly directional acoustic modes from the spatial gradients of the particle velocity field measured at closely spaced sensors along the array. The number of sensors in the array limits the highest order of modes that can be extracted. Theoretical analysis and numerical simulations indicate that the acoustic mode beamformer achieves directivity comparable to the maximum directivity that can be obtained with differential microphone arrays of equivalent aperture. When compared to conventional delay-and-sum beamformers for pressure sensor arrays, the proposed method achieves comparable directivity with 70%-85% shorter apertures. Moreover, the proposed method has additional capabilities such as high front-back (port-starboard) discrimination, frequency and steer direction independent response, and robustness to correlated ambient noise. Small inter-sensor spacing that results in very compact apertures makes the proposed beamformer suitable for space constrained applications such as hearing aids and short towed arrays for autonomous underwater platforms.

A Perspective on Differential Microphone Arrays in the Context of Noise Reduction

In this correspondence, we study the performance of differential microphone arrays (DMAs) in terms of noise reduction, speech distortion, and signal-to-noise ratio (SNR) gain. We also investigate their beampatterns and array gains. We start by establishing the expressions of these performance measures involving general derivatives of the channel transfer functions. Afterwards, we specify our results in the case of anechoic near-field and far-field propagation models.

Differential microphone array for speech recognition

Speech recognition applications embedded on a PDA are already available on the market. The usual hardware for this kind of system is a single microphone mounted on the PDA, giving good results within quiet environments. Though, the recognition rate falls drastically as the signal to noise ratio decreases. Arrays of microphones are then particularly interesting, allowing the discrimination of useful sounds sources within parasitic ones, thanks to an improved directivity pattern. In speech recognition applications on PDA, a trade-off is to be found on an array small enough to guarantee the ergonomics of the whole system, while operating on a bandwidth covering the frequency range of human voice, from 300 Hz up to 6 kHz and low distortion ratio. Differential arrays are well adapted to fulfill these specifications, since they are known to be robust and allow small dimensions for a high directivity index. The performances could be improved by the addition of adaptive post-filtering and noise reduction algorithms. This work describes the design and the implementation of a recording device dedicated to speech recognition applications on PDA, based on overlapping differential arrays. The assessment of its performances in a noisy environment is carried out and show the system efficiencies.

A self-steering close-talking microphone array*

Abstract For communication in extremely noisy environments, close-talking microphone arrays are useful. Differential microphone array systems possessing excellent nearfield directivity and strong farfield-noise reduction capability are very suitable for close-talking situations. In order to improve the focusing effect at the desired bearing in the nearfield we propose a novel self-steering system of close-talking arrays with the first-order differential sub-arrays in this paper. Calculations of directivity patterns and directivity factors show that when a kind of optimized beamforming technique is adopted even small arrays with a focusing configuration will exhibit a satisfactory nearfield directivity which is electronically steerable within a specific range. The superiority of the proposed array system is verified by experiments with real acoustic data. * Supported by National Science Foundation of China (Grant Nos. 60272037 and 60340420325), the Motorola UPR Project, and the Research Fund for the Doctor...

Second-order adaptive differential microphone array

A second-order adaptive differential microphone array (ADMA) has two first-order elements (e.g., 802 and 804 of FIG. 8), each configured to convert a received audio signal into an electrical signal. The ADMA also has (i) two delay nodes (e.g., 806 and 808 ) configured to delay the electrical signals from the first-order elements and (ii) two subtraction nodes (e.g., 810 and 812 ) configured to generate forward-facing and backward-facing cardioid signals based on differences between the electrical signals and the delayed electrical signals. The ADMA also has (i) an amplifier (e.g., 814 ) configured to amplify the backward-facing cardioid signal by a gain parameter; (ii) a third subtraction node (e.g., 816 ) configured to generate a difference signal based on a difference between the forward-facing cardioid signal and the amplified backward-facing cardioid signal; and (iii) a lowpass filter (e.g., 818 ) configured to filter the difference signal from the third subtraction node to generate the output signal for the second-order ADMA. The gain parameter for the amplifier can be adaptively adjusted to move a null in the back half plane of the ADMA to track a moving noise source. In a subband implementation, a different gain parameter can be adaptively adjusted to move a different null in the back half plane to track a different moving noise source for each different frequency subband.

Differential and gradient microphone arrays

Differential microphone arrays have been in existence for more than 7 decades and are the basis of most commercial directional microphones in use today. These microphones obtain directionality by combining the acoustic pressure and the pressure-difference to form what is termed a first-order differential microphone. Differential microphones are inherently superdirectional since they can obtain broadband directional gains of up to 6.0 dB in an array that is physically much smaller than the acoustic wavelength. Differential arrays constructed by subtracting omnidirectional microphones are inherently more flexible in that the directional response can be easily and continuously varied from omnidirectional to hypercardioid. The simultaneous measurement of the acoustic pressure and particle velocity allows one to estimate the complex acoustic intensity along the axis of a microphone pair. A measure of the complex acoustic intensity vector can be obtained using a minimum of four pressure-sensing microphones. Higher-order differential microphones are also possible by using more microphone elements, but the problems of microphone calibration and signal-to-noise combine to practically realize microphones of differential order greater than third order. We will present some of the history of differential microphone array design and discuss some applications related to hands-free communication, hearing aids, and spatial audio recording.

Aspects of first‐order differential microphone arrays in the presence of sensor imperfections

AbstractArray processing for broadband signals like speech is not a trivial task. Most sensor arrangements and the related beamforming algorithms show strong frequency dependent characteristics. Differential microphone arrays promise frequency independent high directional gain with compact arrangements. However, this type of microphone array has also the problem that even small deviations in microphone properties can cause severe degradation of the array's performance. Especially at low frequencies the achievable gain is limited by the influence of sensor mismatch and sensor noise.In this contribution the performance of first‐order differential arrays is examined and important parameters such as array response and directivity index are thoroughly studied. The frequency dependence of these parameters is investigated in order to derive limits for a favorable frequency range. First, the performance of the array is examined for ideal sensors. Then, two different models for sensor mismatch are introduced to describe the degradation of the array's performance. In addition, solutions for sensor calibration and experimental results with real microphones are presented.

Steerable adaptive first- and second-order differential microphones

Directional microphone arrays are spatial filters that can be designed to improve the sound quality of speech in audio telecommunication by removing acoustic signals arriving from undesired directions. Recently, there has been a large interest in adaptive microphone systems (also sometimes referred to as ‘‘smart microphones’’), since these systems automatically self-adjust their spatial response to minimize acoustic interference and thereby increase the desired signal-to-noise ratio. The talk will present adaptive first- and second-order differential microphone arrays that have fixed look directions dependent on the array geometry. A generalized version of the adaptive first-order system will then be presented where the look direction can be arbitrarily oriented (independent of the array spatial orientation). The commensurate problem of acoustic echo cancellation with adaptive microphones will also be discussed and some potential solutions given.

Microphone array systems for hands-free telecommunication

Microphone array systems can be effective in combating the detrimental effects of acoustic noise and reverberation in hands-free telecommunication. This paper discusses classical delay-sum beamformers as well as the more general filter-sum beamformers. Filter-sum beamformers add the ability to control the array beampattern as a function of frequency and a new design method for a constant beamwidth filter-sum beamformer is presented. The delay-sum and filter-sum beamformers require array sizes that are comparable to the acoustic wavelength. These designs can result in arrays that are large in size. For applications that are space constrained, differential microphone array systems are presented. Finally, two types of adaptive beamformers are presented: a broadside array and a two-element differential microphone.

Spatial selectivity of differential microphone arrays in rectangular enclosures

Omni‐directional microphones have been employed in delay‐and‐sum beamformers to mitigate room reverberation and ambient noise. A one‐dimensional beamformer has spatial selectivity in only one dimension. Therefore, higher‐dimensional arrays are used to improve spatial selectivity. In comparison, a single differential microphone provides fixed spatial selectivity. This report discusses the performance of arrays of differential microphones. To compute sound behavior in the enclosure, calculation of the incident angle for every arriving signal is required. An image model using the ray‐tracing method has been developed to calculate the multipath in an enclosure up to a prescribed order of images. Nonuniform wall reflectivities can be included. For the special case of rectangular enclosures, the algorithm efficiently calculates the incident angle for each arriving signal and all of its associated reflection points. Additionally, it is noted that the number of images for a given order more nearly resembles an arithmetic series instead of a geometric series. [Research supported by NSF Grant No. MIP‐9121541 and NSF Subcontract 397‐26740.]

An adaptive subband differential microphone

In a previous talk, ‘‘A new adaptive differential microphone array’’ by Elko and Pong, a differential microphone has been introduced that adapts its directivity pattern to the particular acoustic environment to provide for a good signal-to-noise ratio. There, the selected pattern remains more or less constant with respect to frequency. In this talk an approach is described that contains one more degree of freedom. The spectrum of the signals is partitioned in uniform subbands and different directivity patterns are adaptively chosen in each subband. This allows to cancel multiple noise sources with nonoverlapping spectra. An LMS-based algorithm will be derived with focus on a low computational load and a short delay for the desired signal. Consequences on the speed of adaptation are discussed. Further, experimental results of a first implementation with 33 subbands on a PC-based DSP32C board will be presented. The measurements verify the ability of the algorithm to cancel multiple noise sources with disjoint spectra without distorting the desired signal.

A new adaptive differential microphone array

An adaptive differential microphone has been implemented by combining two omnidirectional elements to form back-to-back cardioid directional microphones. By combining the weighted subtraction of these two outputs, any first-order array can be realized. If certain simple constraints are placed on the combination weighting, the null location can be constrained to defined angular regions. Three algorithms that control the constrained adaptation are presented and discussed for the array: the LMS algorithm, Newton’s algorithm, and a time-varying least-squares Wiener filter. A real-time implementation utilizing an AT&T DSP32C digital signal processor is also described.