Robust Time-Invariant Broadband Beamforming as a Convex Optimization Problem

Mabande E (2014)

Publication Language: English

Publication Type: Thesis

Publication year: 2014



Beamformer designs that provide high directional gain with a small array aperture and a small number of sensors are highly desirable for applications such as hands-free communication and telecommunication, and acoustic front-ends for human-machine interfaces. However, their application in practice is greatly limited due to the high sensitivity of these designs to sensor self-noise, mismatch between sensor characteristics, and imprecise sensor positioning, which are typically unavoidable in practice. It is therefore necessary to control the robustness of these beamformer designs. The white noise gain (WNG) is a well-known and widely used robustness measure for beamformers. However, its application in controlling the robustness of broadband beamformer designs has been somewhat limited due to the difficulty of incorporating it directly into the design as a constraint. Beamformer designs that control the robustness by constraining the WNG directly are highly desirable. This thesis provides a generic framework for the design of robust time-invariant broadband beamformers as a constrained optimization problem, where robustness is achieved by constraining the WNG directly. In the constrained problem we seek to minimize a beamformer cost function that is convex subject to constraints on WNG and on the response in the desired look direction. Six special cases of the generic framework were derived. The constrained problems are shown to be convex and therefore well-known methods for convex optimization can be used to solve these problems resulting in globally optimal solutions for the chosen design parameters. Simulations confirmed the ability of these designs to constrain the WNG effectively, thus ensuring robust beamformer designs. Thus the generic framework allows for flexible robustness control via constraining the WNG directly. Furthermore, this thesis provides a method for three-dimensional room geometry inference based on robust and high-resolution beamforming techniques that are special cases of the generic framework. Uncontrolled broadband acoustic sources such as speech are used to infer the room geometry. The high accuracy of the proposed room geometry inference technique is confirmed by experimental evaluations based on both simulated and measured data for moderately reverberant rooms.

How to cite


Mabande, E. (2014). Robust Time-Invariant Broadband Beamforming as a Convex Optimization Problem (Dissertation).


Mabande, Edwin. Robust Time-Invariant Broadband Beamforming as a Convex Optimization Problem. Dissertation, 2014.

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