A Contribution to the Design of Sparse Arrays for Data-Independent and Adaptive Broadband Beamformers

Beamforming performs spatial filtering to preserve the signal from given directions of interest while suppressing interfering signals and noise arriving from other directions. For example, a microphone array equipped with beamforming algorithm could preserve the sound coming from a target speaker and suppress sounds coming from other speakers. Beamformer has been widely used in many applications such as radar, sonar, communication, and acoustic systems. A data-independent beamformer is the beamformer whose coefficients are independent on sensor signals, it normally uses less computation since the coefficients are computed once. Moreover, its coefficients are derived from the well-defined statistical models, then it produces less artifacts. The major drawback of this beamforming class is its limitation to the interference suppression. On the other hand, an adaptive beamformer is a beamformer whose coefficients depend on or adapt to sensor signals. It is capable of suppressing the interference better than a data-independent beamforming but it suffers from either too much distortion of the signal of interest or less noise reduction when the updating rate of coefficients does not synchronize with the changing rate of the noise model. Besides, it is computationally intensive since the coefficients need to be updated frequently. In acoustic applications, the bandwidth of signals of interest extends over several octaves, but we always expect that the characteristic of the beamformer is invariant with regard to the bandwidth of interest. This can be achieved by the so-called broadband beamforming. Since the beam pattern of conventional beamformers depends on the frequency of the signal, it is common to use a dense and uniform array for the broadband beamforming to guarantee some essential performances together, such as frequency-independence, less sensitive to white noise, high directivity factor or high front-to-back ratio. In this dissertation, we mainly focus on the sparse array of which the aim is to use fewer sensors in the array, while simultaneously assuring several important performances of the beamformer. In the past few decades, many design methodologies for sparse arrays have been proposed and were applied in a variety of practical applications. Although good results were presented, there are still some restrictions, such as the number of sensors is large, the designed beam pattern must be fixed, the steering ability is limited and the computational complexity is high. In this work, two novel approaches for the sparse array design taking a hypothesized uniform array as a basis are proposed, that is, one for data-independent beamformers and the another for adaptive beamformers. As an underlying component of the proposed methods, the dissertation introduces some new insights into the uniform array with broadband beamforming. In this context, a function formulating the relations between the sensor coefficients and its beam pattern over frequency is proposed. The function mainly contains the coordinate transform and inverse Fourier transform. Furthermore, from the bijection of the function and broadband beamforming perspective, we propose the lower and upper bounds for the inter-distance of sensors. Within these bounds, the function is a bijective function that can be utilized to design the uniform array with broadband beamforming. For data-independent beamforming, many studies have focused on optimization procedures to seek the sparse array deployment. This dissertation presents an alternative approach to determine the location of sensors. Starting with a weight spectrum of a virtual dense and uniform array, some techniques are used, such as analyzing a weight spectrum to determine the critical sensors, applying the clustering technique to group the sensors into different groups and selecting representative sensors for each group. After the sparse array deployment is specified, the optimization technique is applied to find the beamformer coefficients. The proposed method helps to save the computation time in the design phase and its beamformer performance outperforms other state-of-the-art methods in several aspects such as the higher white noise gain, higher directivity factor or more frequency-independence. For adaptive beamforming, the dissertation attempts to design a versatile sparse microphone array that can be used for different beam patterns. Furthermore, we aim to reduce the number of microphones in the sparse array while ensuring that its performance can continue to compete with a highly dense and uniform array in terms of broadband beamforming. An irregular microphone array in a planar surface with the maximum number of distinct distances between the microphones is proposed. It is demonstrated that the irregular microphone array is well-suited to sparse recovery algorithms that are used to solve underdetermined systems with subject to sparse solutions. Here, a sparse solution is the sound source's spatial spectrum that need to be reconstructed from microphone signals. From the reconstructed sound sources, a method for array interpolation is presented to obtain an interpolated dense and uniform microphone array that performs well with broadband beamforming. In addition, two alternative approaches for generalized sidelobe canceler (GSC) beamformer are proposed. One is the data-independent beamforming variant, the other is the adaptive beamforming variant. The GSC decomposes beamforming into two paths: The upper path is to preserve the desired signal, the lower path is to suppress the desired signal. From a beam pattern viewpoint, we propose an improvement for GSC, that is, instead of using the blocking matrix in the lower path to suppress the desired signal, we design a beamformer that contains the nulls at the look direction and at some other directions. Both approaches are simple beamforming design methods and they can be applied to either sparse array or uniform array. Lastly, a new technique for direction-of-arrival (DOA) estimation based on the annihilating filter is also presented in this dissertation. It is based on the idea of finite rate of innovation to reconstruct the stream of Diracs, that is, identifying an annihilating filter/locator filter for a few uniform samples and the position of the Diracs are then related to the roots of the filter. Here, an annihilating filter is the filter that suppresses the signal, since its coefficient vector is always orthogonal to every frame of signal. In the DOA context, we regard an active source as a Dirac associated with the arrival direction, then the directions of active sources can be derived from the roots of the annihilating filter. However, the DOA obtained by this method is sensitive to noise and the number of DOAs is limited. To address these issues, the dissertation proposes a robust method to design the annihilating filter and to increase the degree-of-freedom of the measurement system (more active sources can be detected) via observing multiple data frames. Furthermore, we also analyze the performance of DOA with diffuse noise and propose an extended multiple signal classification algorithm that takes diffuse noise into account. In the simulation, it shows, that in the case of diffuse noise, only the extended multiple signal classification algorithm can estimate the DOAs properly