In this paper, we derive spatial correlation functions of linear and circular antenna arrays for three types of angular energy distributions: a Gaussian angle distribution, the angular energy distribution arising from a Gaussian spatial distribution, and uniform angular distribution. The spatial correlation functions are investigated carefully. The spatial correlation is a function of antenna spacing, array geometry and the angular energy distribution. In order to emphasize the research and their applications in diversity reception, as an example, performance of the antenna arrays with MRC in correlated Nakagami fading channels is investigated, in which analytical formulas of average BER for the spatial correlation are obtained.