Sound reproduction systems using open arrays of loudspeakers in rooms suffer from degradations due to room reflections. These reflections can be reduced using pre-compensation of the loudspeaker signals, but this requires calibration of the array in the room, and is processor-intensive. This paper examines 3D sound reproduction systems using spherical arrays of fixed-directivity loudspeakers which reduce the sound field radiated outside the array. A generalized form of the simple source formulation and a mode-matching solution are derived for the required loudspeaker weights. The exterior field is derived and expressions for the exterior power and direct to reverberant ratio are derived. The theoretical results and simulations confirm that minimum interference occurs for loudspeakers which have hyper-cardioid polar responses.
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