Optimizing static degrees of freedom in sound field reproduction

Sound Field Reproduction (SFR) is for creating a desired sound field from a primary source by using multiple loudspeakers. Its research calls for numerical experiments by simulation. SFR performance can be improved by optimizing the static Degrees of Freedom, i.e., the locations and patterns of loudspeakers. The approach is to decrease the sound field reproduction error without increasing the operational complexity, and this requires that the possible locations and frequencies of the primary source are known a priori. To optimize the loudspeaker locations, two placement methods are developed. In the first method, an idealized Acoustic Transfer Function (ATF) matrix that minimizes the reproduction error, but which may not be realizable, is derived for a fixed number of uniformly placed, omnidirectional loudspeakers. The loudspeakers are then re-positioned within their aperture so that their realizable ATF matrix best approximates the idealized ATF matrix. In the second method, a new algorithm is called – Constrained Matching Pursuit (CMP), which optimizes loudspeaker location while constraining the total loudspeaker power to avoid acoustic hotspots. CMP is also used to jointly optimize the radiation patterns and locations of the loudspeakers. These methods optimize for a single frequency, and a method is presented which extends the case to multiple frequencies for the primary source. The multi-frequency method is deployed in the audio layer of an immersive communications system. An existing model for the Head Related Transfer Function (receiving pattern) is adapted for the computation of the loudspeaker excitation functions, called the dynamic Degrees of Freedom. Subjective and objective tests are applied and concur that the quality of speech of the SFR in a reverberant room is significantly improved compared to a system with the same number of loudspeakers that are uniformly spaced and omni-directional, and which have the same total power constraint and computation complexity.