Spatial fading correlation for semicircular scattering: Angular spread and spatial frequency approximations

Spatial frequency approximation (SFA) of spatial fading correlation (SFC) is addressed for the case that the exact infinite summation of Bessel functions is inconvenient or infeasible. The angular spread is derived for semicircular scattering, especially characterized by uniform, Gaussian, Laplacian, and von Mises distributions. The semicircular scattering on the range (-1over2π, 1over2π] happens, e.g., when the antenna is placed on the wall. In the usual SFA of the SFC, a characteristic function is involved with the infinite integration range due to a small angular spread and a near broadside nominal angle. In this paper, we propose a new SFA of the SFC with a finite integration range. Considering the Laplacian angular distribution, numerical examples illustrate that for a moderate angular spread, the new SFA yields higher accuracy in computing the SFC than the conventional SFA. For the von Mises distribution, the new SFA is able to approximate the SFC, while the ordinary SFA provides discrete solutions, which are unreliable to the SFC approximation.