In recent years, many sound field reproduction techniques that physically reconstruct sound fields using multiple loudspeakers have been studied. However, achieving accurate reproduction typically requires a large number of loudspeakers, making it difficult to reduce their number. To address this challenge, previous studies have proposed methods that actively utilize first-order reflections, such as beamforming-based directional control and the generation of virtual loudspeakers. However, when utilizing wall reflections, the reproduced sound field is significantly influenced by the absorption coefficients of the surfaces and the source directivity. Therefore, accurate reproduction requires accounting for sound propagation paths that include first-order reflections. In this study, we propose a pressure matching method that incorporates first-order reflections based on the equivalent source method, aiming to reduce the number of loudspeakers. By modeling both direct and first-order reflected sounds as a linear combination of point sources from a limited number of measurements, the proposed method enables more accurate sound field reproduction than conventional beamforming approaches that neglect wall absorption. In our experiments, multiple linear loudspeaker arrays are employed, and the effectiveness of utilizing first-order reflections is evaluated through comparison with conventional beamforming methods.
Aoyama et al. (Wed,) studied this question.