Sound Field Reproduction Using Ambisonics and Irregular Loudspeaker Arrays

Sound field reproduction systems seek to realistically convey 3D spatial audio by re-creating the sound pressure inside a region enclosing the listener. High-order Ambisonics (HOA), a sound field reproduction technology, is notable for defining a scalable encoding format that characterizes the sound field in a system-independent way. Sound fields sampled with a particular microphone array and encoded into the HOA format can be reproduced using any sound presentation device, typically a loudspeaker array, by using a HOA decoder. The HOA encoding format is based on the spherical harmonic decomposition; this makes it easier to design a decoder for large arrays of loudspeakers uniformly distributed over all directions. In practice, it is seldom possible to cover all directions with loudspeakers placed at regular angular intervals. An irregular array, one where the angular separation between adjacent loudspeakers is not constant, does not perform as well as a regular one when reproducing HOA due to the uneven sampling of the spherical harmonics. This paper briefly introduces the techniques used in HOA and advances a new approach to design HOA decoders for irregular loudspeaker arrays. The main difference between conventional methods and our proposal is the use of a new error metric: the radial derivative of the reconstruction error. Minimizing this metric leads to a smooth reproduction, accurate over a larger region than that achieved by conventional HOA decoders. We evaluate our proposal using the computer simulation of two 115-channel loudspeaker arrays: a regular and an irregular one. We find that our proposal results in a larger listening region when used to decode HOA for reproduction using the irregular array. On the other hand, applying our method matches the high-quality reproduction that can be attained with the regular array and conventional HOA decoders.