Design of distributed beamforming system using semi-definite programming

In this paper, the design of distributed broadband beamforming system is studied. In the configuration, we assume that each microphone is equipped with wireless communications capability. Once their mutual distance information is collected, localization techniques can be used to estimate the microphone locations. A broadband beamformer can then be designed such that the error between the actual response and the desired response is minimized. However, due to variations in the estimated microphone locations, robust design with uncertainties must be considered. This problem is formulated as a minimax optimization problem, which is then transformed into a semi-definite programming problem so that interior point algorithms can be applied. We illustrate the proposed method by several designs and show that the algorithm is robust and efficient.