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 /spl phi//sub h/(/spl tau/;/spl Delta/t) or by its /spl Delta/t-Fourier transform, the scattering function S/sub h/(/spl tau/;/spl lambda/). 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 /spl phi//sub h/(/spl tau/;/spl Delta/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 /spl phi//sub h/(/spl tau/;/spl Delta/t) and a closed-form expression for S/sub h/(/spl tau/; /spl lambda/). These results generalize the well-known classical approximation for the time-correlation function /spl phi/~/sub h/(/spl Delta/t)=/sup def//spl int//spl phi//sub h/(/spl tau/;/spl Delta/t)d/spl tau//spl ap/ J/sub 0/(2/spl pi//spl lambda//sub m//spl Delta/t), which corresponds to the zeroth term of our Bessel series.