Mean-Square-Error-Based Secondary Source Placement in Sound Field Synthesis with Prior Information on Desired Field

A method of optimizing secondary source placement in sound field synthesis is proposed. Such an optimization method will be useful when the allowable placement region and available number of loudspeakers are limited. We formulate a mean-square-error-based cost function, incorporating the statistical properties of possible desired sound fields, for general linear-least-squares-based sound field synthesis methods, including pressure matching and (weighted) mode matching, whereas most of the current methods are applicable only to the pressure-matching method. An efficient greedy algorithm for minimizing the proposed cost function is also derived. Numerical experiments indicated that a high reproduction accuracy can be achieved by the placement optimized by the proposed method compared with the empirically used regular placement.