A geometric model for fading correlation in multipath radio channels

We derive expressions for the correlation of fading between a pair of antenna elements in a wireless communication system. Some prior researchers have assumed uniformly distributed signal angles of arrival with a specified beamwidth. Here, we derive a closed form expression for the angle of arrival density at a cellular base station where local scatterers are uniformly distributed in a circle about the mobile. We show that the density can be parameterized in terms of the ratio of the base-to-mobile distance to the scattering circle radius, D/R. We use this density to derive the correlation of fading between a pair of antenna elements. We then derive a closed form approximation for the correlation of fading and show that the approximation improves with increasing D/R. We show that if the signal arrives broadside to the antenna elements, then the approximation is exact