Spatial fading correlation for local scattering: A condition of angular distribution

Local scattering in the vicinity of the receiver or the transmitter leads to the formation of a large number of multipath components along different spatial angles. A condition of angular distribution, which is valid for only a uniform linear array, is proposed in this paper to justify whether the spatial fading correlation (SFC) remains simple as a Bessel function. If an angular distribution satisfies the condition, a class of angular distributions is revealed and results in simplifying the analysis of the SFC. To demonstrate its practical use, we apply the condition to several angular distributions that are considered in previous works. It is found that cosine and von Mises distributions follow the condition, whereas uniform, Gaussian, and Laplacian distributions do not satisfy the condition, and then, one needs to calculate the sinusoidal coefficients in the SFC computation.