Generalized Equations for Spatial Correlation for Low to Moderate Angle Spread

In this paper we derive generalized formulas for three types of angular energy distributions: a Gaussian angle distribution, the angular energy distribution arising from a Gaussian spatial distribution, and a uniform angular distribution. These generalized equations are parameterized by d sigma where d is the distance between antennas and sigma is the standard deviation of the angular energy distribution and approximate the true correlation with the approximation being very good for angle spreads below approximately 25degrees.