How to design a delay-and-sum beamformer for rigid rotationally symmetric arrays?

In this paper we present two novel techniques with low computational complexity and high robustness for beamforming using rigid microphone arrays. For the first one we show which approximations have to be made in terms of applying techniques that are equivalent to delay-and-sum beamforming on rigid microphone arrays. In the second approach we exploit the technique of focused sinks for creating virtual linear microphone arrays with flexible dimensions and spacing. As a result, simple techniques for beamforming using linear arrays can be applied. We derive our approaches analytically, state their theoretical limits and provide simulation results and discuss the results.