Comparison of microphone array geometries for multi-point sound field reproduction

Multi-point approaches for sound field control generally sample the listening zone(s) with pressure microphones, and use these measurements as an input for an optimisation cost function. A number of techniques are based on this concept, for single-zone (e.g. least-squares pressure matching (PM), brightness control, planarity panning) and multi-zone (e.g. PM, acoustic contrast control, planarity control) reproduction. Accurate performance predictions are obtained when distinct microphone positions are employed for setup versus evaluation. While, in simulation, one can afford a dense sampling of virtual microphones, it is desirable in practice to have a microphone array which can be positioned once in each zone to measure the setup transfer functions between each loudspeaker and that zone. In this contribution, we present simulation results over a fixed dense set of evaluation points comparing the performance of several multi-point optimisation approaches for 2D reproduction with a 60 channel circular loudspeaker arrangement. Various regular setup microphone arrays are used to calculate the sound zone filters: circular grid, circular, dual-circular, and spherical arrays, each with different numbers of microphones. Furthermore, the effect of a rigid spherical baffle is studied for the circular and spherical arrangements. The results of this comparative study show how the directivity and effective frequency range of multi-point optimisation techniques depend on the microphone array used to sample the zones. In general, microphone arrays with dense spacing around the boundary give better angular discrimination, leading to more accurate directional sound reproduction, while those distributed around the whole zone enable more accurate prediction of the reproduced target sound pressure level.