On the Correlation and Scattering Functions of the WSSUS Channel for Mobile Communications

The wide-sense stationary-uncorrelated scattering (WSSUS) channel model is a commonly employed model for the multipath channel experienced in mobile communications. The second-order statistics of these channels are described by the delay cross-power density h( ; t) or by its t-Fourier transform, the scattering function Sh( ; ). This paper presents an analysis of the delay cross-power density and scattering functions for mobile communications channels. We assume an arbitrary spatially uncorrelated scattering (US) field with arbitrary propagation-loss factors. Our first result is a general integral expression for h( ; t) that holds with both transmitter and receiver being mobile. We then derive more detailed results for the case of a stationary base station. We derive an infinite Bessel series for h( ; t) and a closed-form expression for Sh( ; ). These results generalize the well-known classical approximation for the time-correlation function h( t) def = h( ; t) d J0(2 m t), which corresponds to the zeroth term of our Bessel series.