Ph.D Thesis

Ph.D StudentItzhak Gal
SubjectDesign and Analysis of Quadratic and Multistage
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Israel Cohen
Full Thesis textFull thesis text - English Version


This dissertation introduces design approaches of quadratic and multistage beamformers whose properties may come in handy in a variety of practical applications, such as communication systems, speech recognition, human-to-machine interfaces and more.

The problem of reducing undesirable noise and interferences from observation signals is a fundamental problem in acoustic signal processing, for which numerous schemes and algorithms have been suggested over the years. Broadly, these algorithms can be divided into two classes: single-channel noise reduction (SCNR) and multichannel noise reduction (MCNR), whose primary difference is whether a single microphone or multiple microphones are utilized. In this thesis we address them both.

This research thesis focuses on four topics of interest. The first is the quadratic beamforming approach. Traditionally, beamforming in the frequency domain is performed by applying a complex-valued linear filter to a vector of noisy observations to yield an estimate of the desired signal (complex) value. Such approaches are almost exclusively based on the second-order statistics of the observations, even though significant information may underlie in higher-order statistics. In the presented study, we focus on the estimation of the desired signal power and propose a quadratic beamforming approach which makes a direct use of higher-order statistics. We show that the quadratic approach outperforms the traditional linear approach, in particular when the input signal-to-noise ratio (SNR) is low or the number of sensors is small.

The second topic this thesis addresses is a quadratic approach for SCNR, in which we consider the interframe correlation property in the short-time Fourier transform (STFT) domain. We utilize the quadratic formulation and propose a quadratic version for the maximum SNR filter. We demonstrate that the quadratic maximum SNR filter is superior to its linear counterpart, and may in fact achieve a theoretical unbounded approximate SNR gain, assuming the noise statistics is accurately given. The performance gap is particularly significant in low input SNRs.

In the third study, we address the differential microphone array (DMA) beamforming concept. We propose a flexible approach for deriving multistage differential beamformers by employing the Kronecker product (KP) decomposition of the global beamformer into two independent sub-beamformers. We present the notion of multistage differential KP beamformers and analyze the influence of three inherent design parameters which allow a high design flexibility. We demonstrate that the multistage differential KP beamforming approach outperforms previous approaches, depending on the scenario and the selection of the design parameters.

In the fourth study, we focus on DMAs from the beam steering perspective. We present a multistage approach for steerable differential beamforming by exploiting uniform rectangular arrays (URAs). At first, we differentiate along the columns and rows of the observation signals, respectively; then, we design and apply a rectangular differential beamformer. We show that the proposed approach may significantly improve the directivity of the resulted beamformer at the expanse of white noise amplification, depending on the design parameters selection. We demonstrate that the proposed approach outperforms common linear approaches, particularly when the incident angle is far from the endfire direction.