Multi-zone sound field reproduction via sparse spherical harmonic expansion

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Multi-zone sound field reproduction is a method that can create personal audio zones to individual listeners within an enclosed environment. The accuracy requirements at the listening positions of this method results in increased number of loudspeakers and the array effort used in the computation. Additionally, in-order to increase the effective listening area (sweet spot), it is required to place loudspeakers in every possible direction. Spherical array processing has been used in the design of such multi zone spatial audio systems. However, the requirement of number of loudspeakers increases rapidly with small increase in the reproduction area in the spherical harmonic domain. Therefore, addressing the multi-zone sound field reproduction problem in spherical harmonics domain is a challenging task due to practical limitation in implementing the loudspeaker array configurations. Hence, computing the optimal number of loudspeakers and their corresponding locations using spherical array processing is of interest in multi zone sound field reproduction.In this context, a sparsity based framework that reproduces accurate 3-D multi-zone sound fields is developed herein. A sparse spherical harmonics expansion framework is proposed for this purpose. The sparse framework computes an optimal set loudspeaker positions from a set of all possible loudspeaker positions sufficient enough to span all the directions of interest. This optimal set of loudspeakers reduces both the reproduction error and the array effort when compared to a set of loudspeakers having the same array size and chosen randomly. The target pressures are defined by the local spherical harmonic coefficients corresponding to the desired spatial sound fields in each sound zone separately. Subsequently, the multi-zone sound field reproduction is formulated as a non-convex optimization problem where the loudspeaker weights required to accurately reproduce desired sound field over the bright zones and minimize the energy flow in the dark zones need to be found. This multi objective problem is solved using a sparse iterative method based on Bregman Iteration. Hence, the solution to the multi-zone reproduction problem proposed in this work obtains the global sound field coefficient corresponding to the target pressures for each zone of interest.The performance of the proposed method is evaluated using simulations. Under free-field conditions, using the obtained optimal set of loudspeaker positions, the target sound fields in two bright zones arriving from two different directions are reproduced simultaneously in the presence of two dark zones. The reproduced sound fields in both the bright zones are evaluated on the basis of reconstruction error, average error distribution and the acoustic contrast obtained at various sparsity levels. The proposed multi-zone sparse iterative (MZ-SI) method is also compared with constraint least-squares (CLS) method to show its effectiveness in terms of reproduction error and number of active loudspeakers required. The proposed framework is also evaluated for its performance in reproducing broadband audio signals. The performance of proposed framework is also analysed using both subjective and objective evaluations. For subjective evaluation, average mean opinion scores (MOS) for various spatial attributes are obtained by performing the listening test on human subjects. Objective evaluations are carried out by measuring the scores obtained for parameters such as perceptual evaluation of audio quality (PEAQ), perceptual similarity measure (PSM) and distortion index(DI). The experimental results and reproduced sound fields in the zones of interest support the effectiveness of the proposed method.