Functional analysis guided approach for sound field reproduction with flexible loudspeaker layouts

This paper proposes a design of multiple circular and partial circular loudspeaker arrays for reproducing sound fields originated from a limited spatial region. We apply a functional analysis framework to formulate the sound field reproduction problem in closed form. Analytical solutions are derived for a circular secondary source arrangement, from which circular arc layouts are investigated and the design of placing multiple loudspeaker arrays over the limited region of interest is proposed. Such a design allows for non-spherical and non-uniform loudspeaker placement and thus provides flexibility to suit reproduction in real audio environments. The reproduction using the proposed method are illustrated by numerical simulations in comparison with the Least-squares based schemes.