Difference Pattern Synthesis for Spherical Arrays

Spherical arrays with array processing based on spherical harmonics have been studied for a wide range of applications in the smart antenna community and the acoustic array community. In this paper, a direct difference pattern synthesis method for spherical array based on spherical harmonics is proposed. We first propose to synthesize the spherical array difference pattern with spherical harmonics of degree ±1. Then the mapping relationship between the spherical array difference pattern and the linear array difference pattern is studied with the help of Legendre functions decomposition. With this mapping, uniform linear array specific difference pattern synthesis techniques become readily available in closed form for spherical arrays.