The impact of angular energy distribution on spatial correlation

We derive a simple generalized formula for spatial correlation and show that it provides a good approximation for spatial correlation for three very different angular energy distributions: a Gaussian angle distribution, a Laplacian angle distribution, and a uniform angular distribution. We also derive an equation for spatial correlation when the angular energy distribution is bimodal. These generalized equations are parameterized by dσ/λ where d is the distance between antennas, λ is the carrier wavelength and σ is the standard deviation of the angular energy distribution. This allows for a single curve to be used for any value of d/λ and σ. It is found that the standard deviation of the angular energy distribution or angle spread is the dominant factor for determining correlation as opposed to the specific angular energy distribution.