Towards optimal loudspeaker placement for sound field reproduction

With a view to the suppression of unwanted sound, a planar array of loudspeakers is used to recreate a sound field in a nearby cubic listening area. Using free-space propagation, the formulation for selecting optimal locations of loudspeakers is developed so that numerical experiments can give a feel for the best possible suppression. First, to provide a benchmark, a target Acoustic Transfer Function (ATF) matrix is found that minimizes the reproduction error for a number of uniformly placed loudspeakers. Then the same number of loudspeakers is positioned by selecting from densely placed candidates so that their ATF matrix best approximates the target sound field. For recreating the field of a point source located in the direction of the array, the loudspeaker array with selected locations is shown to improve the reproduction accuracy over a reasonable bandwidth.