Irregular microphone array design for broadband beamforming

In three-dimensional (3D) medical ultrasound imaging with two-dimensional (2D) arrays, sparse 2D arrays have been studied to reduce the number of active channels. Among them, sparse 2D arrays with regular or uniform arrangements of elements have advantages of low side lobe energy and uniform field responses over the entire field of view. This paper presents two uniform sparse array models: sparse rectangular arrays (SRAs) on a rectangular grid and sparse spiral arrays (SSAs) on a sunflower grid. Both arrays can be easily implemented on the commercially available or the custom-made arrays. To suppress the overall grating lobe levels, the transmit (Tx) and receive (Rx) array pairs of both the array models are designed not to have grating lobes at the same locations in the Tx/Rx beam patterns, for which the theoretical design rules are also proposed. Computer simulation results indicate that the proposed array pairs for both the SRAs and the SSAs achieve peak grating lobe levels below –40 dB using about a quarter of the number of elements in the dense rectangular array while maintaining similar beam widths to that of the dense array pair.

Sparse arrays have grating lobes in the far field pattern due to the large spacing of elements residing in a rectangular or triangular grid. Random element spacing removes the grating lobes but produces large variations in element density across the aperture. In fact, some areas are so dense that the elements overlap. This paper introduces a low discrepancy sequence (LDS) for generating the element locations in sparse planar arrays without grating lobes. This nonrandom alternative finds an element layout that reduces the grating lobes while keeping the elements far enough apart for practical construction. Our studies consider uniform sparse LDS arrays with 86% less elements than a fully populated array, and numerical results are presented that show these sampling techniques are capable of completely removing the grating lobes of sparse arrays. We present the mathematical formulation for implementing an LDS generated element lattice for sparse planar arrays, and present numerical results on their performance. Multiple array configurations are studied, and we show that these LDS techniques are not impacted by the type/shape of the planar array. Moreover, in comparison between the LDS techniques, we show that the Poisson disk sampling technique outperforms all other approaches and is the recommended LDS technique for sparse arrays.

The three-dimensional multiple-input-multiple-output radar (MIMO) system has been applied in various situations such as security inspection and ground exploration. The conventional dense MIMO radar array has excellent imaging performance but large spacing redundancy between antenna elements. In this paper, two-dimensional (2-D) MIMO sparse array design is discussed. The difference basis and the cyclic difference set are combined to construct a one-dimensional (1-D) sparse array with less spacing redundancy, which would be placed reasonably to construct the 2-D MIMO sparse array. Finally, the pattern and target imaging results of the array are given through simulation experiments, demonstrating that the square array proposed has good imaging performance especially in terms of side lobe level and grating lobe. The proposition of 2-D square sparse MIMO array would facilitate the development of sparse MIMO array design and improve the application capabilities of MIMO radar.

Three-dimensional (3-D) imaging sonar systems require large planar arrays, which incur hardware costs. In contrast, a cross array consisting of two perpendicular linear arrays can also support 3-D imaging while dramatically reducing the number of sensors. Moreover, the use of an aperiodic sparse array can further reduce the number of sensors efficiently. In this paper, an optimized method for sparse cross array synthesis is proposed. First, the beamforming of a cross array based on a multi-frequency algorithm is simplified for both near-field and far-field. Next, a perturbed convex optimization algorithm is proposed for sparse cross array synthesis. The method based on convex optimization utilizes a first-order Taylor expansion to create position perturbations that can optimize the beam pattern and minimize the number of active sensors. Finally, a cross array with 100 + 100 sensors is employed from which a sparse cross array with 45 + 45 sensors is obtained via the proposed method. The experimental results show that the proposed method is more effective than existing methods for obtaining optimum results for sparse cross array synthesis in both the near-field and far-field.

Multi-dimensional sparse array operations can be used in the atmosphere and ocean sciences, the image processing, and etc., and have been an extensively investigated problem. Therefore, it becomes an important issue to propose efficient data distribution schemes for multi-dimensional sparse arrays. In our previous work, we have proposed two data distribution schemes Compress Followed Send (CFS) and Encoding-Decoding (ED) for sparse arrays based on the traditional matrix representation (TMR) scheme. We have proposed another scheme, called extended Karnaugh map representation (EKMR), to represent sparse arrays. The EKMR scheme can obtain better performance than the TMR scheme for some sparse array operations. Hence, in this paper, we want to propose efficient data distribution schemes for EKMR-based sparse arrays. We extend the CFS and the ED schemes for TMR-based sparse arrays to EKMR-based sparse arrays first. Then, we compare the performance of these two schemes with that of the Send Followed Compress (SFC), which is an intuitive data distribution scheme for sparse arrays. Finally, we compare these three schemes for EKMR-based sparse arrays with those of TMR-based sparse arrays, respectively. Both the theoretical analysis and the experimental tests were conducted. From the theoretical analysis and the experimental results, we can see that the ED scheme is superior to the CFS scheme that is superior to the SFC scheme for most of testing EKMR-based sparse arrays; the performance of these three schemes for EKMR-based sparse arrays is better than that of TMR-based sparse arrays for all of testing cases, respectively.

The problem of multiple incident signals’ direction of arrival (DOA) estimation for spatially separated polarisation sensitive array (SS‐PSA) is studied. The proposed SS‐PSA is a sparse uniform array with orthogonally oriented and spatially separated dipole‐triads. The proposed array can reduce the array mutual coupling by using the spatially separated polarised antenna instead of conventional spatially collocated polarised antenna. Moreover, the DOA estimation accuracy can be improved greatly due to the extended aperture offered by sparse array. Computer simulation results verify the effectiveness of the proposed algorithm.

A novel high degree of freedom sparse array with displaced multistage cascade subarrays

Sparse arrays are special geometrical arrangements of sensors which overcome some of the drawbacks associated with dense uniform arrays and require fewer sensors. For direction finding applications, sparse arrays with the same number of sensors can resolve more sources while providing higher resolution than a dense uniform array. This has been verified numerically and with real data for one-dimensional microphone arrays. In this study the use of nested and co-prime arrays is examined with sparse Bayesian learning (SBL), which is a compressive sensing algorithm, for estimating sparse vectors and support. SBL is an iterative parameter estimation method and can process multiple snapshots as well as multiple frequency data within its Bayesian framework. A multi-frequency variant of SBL is proposed, which accounts for non-flat frequency spectra of the sources. Experimental validation of azimuth and elevation [two-dimensional (2D)] direction-of-arrival (DOA)estimation are provided using sparse arrays and real data acquired in an anechoic chamber with a rectangular array. Both co-prime and nested arrays are obtained by sampling this rectangular array. The SBL method is compared with conventional beamforming and multiple signal classification for 2D DOA estimation of experimental data.

This paper shows how to compile sparse array programming languages. A sparse array programming language is an array programming language that supports element-wise application, reduction, and broadcasting of arbitrary functions over dense and sparse arrays with any fill value. Such a language has great expressive power and can express sparse and dense linear and tensor algebra, functions over images, exclusion and inclusion filters, and even graph algorithms. Our compiler strategy generalizes prior work in the literature on sparse tensor algebra compilation to support any function applied to sparse arrays, instead of only addition and multiplication. To achieve this, we generalize the notion of sparse iteration spaces beyond intersections and unions. These iteration spaces are automatically derived by considering how algebraic properties annotated onto functions interact with the fill values of the arrays. We then show how to compile these iteration spaces to efficient code. When compared with two widely-used Python sparse array packages, our evaluation shows that we generate built-in sparse array library features with a performance of 1.4× to 53.7× when measured against PyData/Sparse for user-defined functions and between 0.98× and 5.53× when measured against SciPy/Sparse for sparse array slicing. Our technique outperforms PyData/Sparse by 6.58× to 70.3×, and (where applicable) performs between 0.96× and 28.9× that of a dense NumPy implementation, on end-to-end sparse array applications. We also implement graph linear algebra kernels in our system with a performance of between 0.56× and 3.50× compared to that of the hand-optimized SuiteSparse:GraphBLAS library.

Multiple sound source localization is one of the important topic in speech processing. GCC function is used as a traditional algorithm for sound source localization. This function estimates DOA for multiple speakers by calculation the cross-correlation between microphone signals but its accuracy decreases in adverse conditions. The aim of proposed method in this paper is localization of multiple simultaneous speakers in undesirable condition. The proposed method is based on novel 3D nested microphone array in combination with obtained information of Discrete Wavelet Transform (DWT) and subband processing. The proposed 3D nested microphone array prepares the condition for 3D localization and eliminates the spatial aliasing between microphone signals. Also, we propose the DWT for extraction the information of speech signal. Since, the spectral information of speech signal concentrates on low frequencies, we propose a structure of filter bank based on DWT to increase the frequency resolution on low frequencies. The performed evaluation on real and simulated data shows the superiority of our proposed method in comparison with Fullband and subband processing with uniform filters and uniform microphone array.

Fixed broadband beamformers for speech applications using small-sized microphone arrays are known to be highly sensitive to errors in the microphone array characteristics. This paper describes two procedures for designing broadband beamformers with an arbitrary spatial directivity pattern, which are robust against gain and phase errors. The first design procedure optimises the mean performance of the broadband beamformer and requires knowledge of the gain and phase probability density functions, whereas the second design procedure optimises the worst-case performance by using a minimax criterion. Simulations with a small-sized microphone array show the performance improvement that can be obtained by using a robust broadband beamformer design procedure.

In order to improve the robustness of microphone array beamformer in existing mismatch errors, robust beamforming algorithm based on linear constrained minimum variance and diagonal loading method is proposed. The proposed algorithm incorporates the spatial response variation function into the linear constrainted minimum variance criterion to design the frequency invariant beamformer and improve the robustness against microphone array mismatch errors in the actual environment by diagonal loading method. Simulation results and analyses illustrate that the array response within passband is robust, the stopband amplitude is controlled in the appropriate range, and the proposed algorithm based closed solution is better than the proposed algorithm based on convex optimization algorithm. Introduction As one of the key technologies for microphone arrays, broadband beamforming has been used in a wide range of audio and speech processing applications[1]. In many popular methods, the traditional linear constrained minimum variance(LCMV) beamforming method is mainly used to design narrow-band antenna beamformer[2]. If it is used to design a broadband beamformer of microphone array, it isn’t fit. It is necessary for microphone array to design broadband beamformer without specific arrays[3][4]. In order to achieve broadband frequency invariant beamformer[3], it is necessary to consider frequency invariant beamformer with mismatch errors caused by the gain, phase and position of the microphone[5][6]. For this purpose, in this paper, frequency invariant beamforming algorithm based on the linear constrainted minimum variance (LCMV), the spatial response variation function(SRV) of the microphone array, and diagonal loading method are used to design frequency invariant beamformer and improve the robustness on the given frequency range and the region. Array Model Consider a M-element linear microphone array in the far-field (not general, this method can be applied to arbitrary array structure), FIR subfilter with tap length L is added to microphone. The array output signal can be expressed as ( ) ( ) H k k = y w x , where H denotes conjugate transpose.The weight vector of microphone array response is written as 11 1 1 ( ) [ ( ), , ( ), , ( ), , ( )] T M L ML k w k w k w k w k = w L L L , T denotes transpose. 11 1 1 ( ) [ ( ), , ( ), , ( ), , ( )] T M L ML k x k x k x k x k = x L L L and it denotes the received signal of microphone array, the definition of the angle between the direction of the sound source and the line array is θ , the beam-pattern at frequency f and angle θ of arrival can be expressed as ( , ) | ( , )| T H f f θ θ = w d ,where frequency f is belongs to [ , ] l h f f ,the angle θ of the received signal is in[ , ] l h θ θ , and ( , ) f θ d denotes the array response vector. 4th International Conference on Computer, Mechatronics, Control and Electronic Engineering (ICCMCEE 2015) © 2015. The authors Published by Atlantis Press 102 Frequency Invariant Beamforming Algorithm and Diagonal Loading Method The spatial response variation function(SRV) is given by

Acoustic imaging is a technology for visualizing sound fields, which can be used in fault diagnosis of power equipment and gas leak detection. A spiral microphone array with a large number of microphones is generally used in ultrasonic acoustic imaging, but its application is limited due to the high cost. This paper addresses the issue of the high cost for acoustic imaging microphone arrays. On one hand, an adaptability function suitable for acoustic imaging applications is designed, and the genetic algorithm is used for sparse array arrangement to reduce the cost. On the other hand, the beam forming algorithm is also improved by using a time-varying smoothing coefficient to update the cross-power spectral matrix, further enhancing the performance. Experimental results show that by using the algorithms proposed in this paper, a sparse array can achieve acoustic imaging performance close to that of a large array, the cost of usage is significantly reduced.

We have developed a method for designing sparse periodic arrays. Grating lobes in the two-way radiation pattern are avoided by using different element spacings on transmission and reception. The transmit and receive aperture functions are selected such that the convolution of the aperture functions produces a desired effective aperture. A desired effective aperture is simply an aperture with an appropriate width, element spacing, and shape such that the Fourier transform of this function gives the desired two-way radiation pattern. If a synthetic aperture approach is used, an exact solution to the problem is possible. However, for conventional imaging, often only an approximation of the desired effective aperture can be found. Different strategies for obtaining these approximate solutions are described. The radiation pattern of a sparse array designed using the effective aperture concept is compared experimentally with the radiation patterns of a dense array, and sparse arrays with periodic and random element spacing. We show that the number of elements in a 128-element linear array can be reduced by at least four times with little degradation of the beam forming properties of the array.

Analysis of the fourth-order co-array for a mixture of circular and noncircular signals