A correlated Gaussian spatial distribution

We consider an angular distribution for modeling the local scattering in the vicinity of the receiver or the transmitter. The Gaussian spatial distribution is extended to capture the correlation between the x-coordinate and the y-coordinate, which gives rise to a generalization to the uncorrelated Gaussian spatial distribution. The probability density function of the correlated Gaussian spatial distribution for the azimuth angle is derived as a closed form. Numerical examples are conducted to illustrate the effects of the correlation coefficient on the distribution.