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 φ_h(τ;Δt) or by its Δt-Fourier transform, the scattering function S_h(τ;λ). 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 φ_h(τ;Δt) 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 φ_h(τ;Δt) and a closed-form expression for S_h(τ; λ). These results generalize the well-known classical approximation for the time-correlation function φ¯_h(Δt)=^def∫φ_h (τ;Δt)dτ≈ J₀(2πλ_mΔt), which corresponds to the zeroth term of our Bessel series