Ph.D Thesis

Ph.D StudentBuchris Yaakov
SubjectDesign Methods of Sparse and Robust Differential Microphone
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Israel Cohen
Full Thesis textFull thesis text - English Version


This dissertation addresses advanced design approaches of sparse and robust differential microphone arrays (DMAs) which can be integrated into several acoustic

systems like: data service audio devices, video conference rooms, autonomous underwater vehicles (AUVs), drones, and more. Acquiring acoustic data of high quality is a challenging task as the acoustic medium introduces some artifacts like noise and reverberations. In order to mitigate these artifacts, broadband adaptive beamforming techniques are widely used to enhance the signal-to-interference plus noise ratio. One of the promising concepts for broadband adaptive beamforming is the DMAs, which refer to arrays that combine closely spaced sensors to respond to the spatial derivatives of the acoustic field. These small-size arrays yield nearly frequency-invariant (FI) beampatterns and high directivity. In spite of their desired properties, DMAs suffer from noise amplification, especially at low frequencies. Thus, they are highly sensitive to model mismatch errors.

In this thesis, we propose advanced techniques for the design of DMAs, providing better performances in terms of array gain, directivity, computational efforts, and more. We present a time-domain design method of DMAs which is important in some applications where minimal delay is required, such as real-time audio communications. We analytically represent the array input signal vector in a separable form, which enables to apply several array processing algorithms, originally developed in the frequency domain, directly into broadband time-domain DMAs. We also show the convergence of the proposed time-domain model to the traditional model of DMAs.

We also extend the traditional symmetric model of DMAs and establish an analytical asymmetric model for circular DMAs, which allows flexible design of the directivity pattern since additional degrees of freedom are available in placing some directional constraints like directional nulls. Consequently, the proposed model yields better array gain and robustness. We demonstrate these benefits by deriving asymmetric versions for two well-known directivity patterns, namely the hypercardioid and supercardioid, designed to maximize the directivity factor and the front-to-back-ratio, respectively.

In the second part of our work, we focus on sparse designs of DMAs that optimize both the sensors’ gains and their locations, resulting in better performance with a smaller number of sensors. Moreover, sparse designs may help to obtain FI beampatterns with higher accuracies and lower sidelobes levels. We develop an incoherent sparse design which first optimizes the array layout for each frequency bin in the bandwidth of interest. Then, all the decisions are fused together using some data mining tools yielding a joint sparse array layout used in the synthesis step. Simulations comparing our design to other previous sparse and uniform designs, show that the proposed design offers a good compromise between array gain and computational complexity. Finally, we generalize this concept and propose a greedy sparse design for more complicated array geometries like concentric arrays, which supports a flexible steering direction of the desired signal. The essential progress obtained along this research will make the integration of such arrays in acoustic systems more feasible, which is important for the future generations of such devices.