Optimizing secondary source placement by bidirectional stepwise iteration for sound field reproduction

Sound field reproduction uses multiple loudspeakers to create a desired sound field within a target area. The placement of the secondary sources is a particularly critical factor influencing reproduction performance. Iterative optimization is a common class of placement optimization methods, but existing methods tend to either only select or only remove secondary sources unidirectionally. This characteristic often causes the search-algorithm to get stuck in a local optimum. This study proposes a secondary source placement optimization method based on bidirectional stepwise iteration. In each iteration, the proposed method first selects the two loudspeakers from the candidate set with the highest contribution to sound reproduction to become secondary sources. It then removes the secondary source with the lowest contribution from the entire set of selected sources and returns it to the candidate set. The proposed method was validated by simulations and a public experimental dataset. Results show that this method is less likely to get stuck in a local optimum compared to unidirectional iterative optimization methods, thus achieving better performance. This study also explores how factors like the number of secondary sources and room reverberation affect the performance and compares the computational complexity of our method with that of unidirectional optimization methods.