Dual selection diversity SNR performance in spatially correlated scattering environments

A new expression is given for the average signal-to-noise ratio (SNR) of a dual selection-combining receiver where the antenna signals are correlated in a Rayleigh fading multipath environment. This formula is based on a recently developed expression for the bivariate Rayleigh cumulative distribution function by associating the correlation parameter of the distribution with the spatial correlation of the multipath field. By examining various multipath and receiver antenna geometries we can determine the critical parameters which affect the average SNR performance. Our results are shown to generalize and subsume well-known expressions based on an independence assumption of the signals at the antennas. We relate the average SNR diversity gain to critical parameters such as the spatial correlation, beamwidth, angle of arrival and antenna separation. These results show the subtle interplay between these parameters and reveal there is a reduction in performance relative to unrealistic models previously studied.