G. Chardon, W. Kreuzer, M. Noisternig, Design of spatial microphone arrays for sound field interpolation, accepted in Journal of Selected Topics in Signal Processing, doi:10.1109/JSTSP.2015.2412097 , [pdf]
This article presents a design method for microphone arrays with arbitrary geometries. Based on a theoretical analysis and on the magic points method, it allows for the interpolation of a sound field in a generic convex domain with a limited number of microphones on a given frequency band. It is shown that only a few microphones are needed in the interior of the considered domain to ensure a low interpolation error in the frequency band of interest, and that most of the microphones have to be located on the boundary of the domain, with a non-uniform density depending on the shape of the domain. Practical design constraints can be included in the optimization process. Comparisons for some particular array geometries with design methods known from the literature are given, showing that the proposed approach results in lower errors.
The code is available here.