Moments of the quadrivariate Rayleigh distribution with applications for diversity receivers

Wireless channels exhibit time, frequency, and spatial correlation. Models in literature that study four-branch diversity receivers make assumptions such as independence, constant correlation, exponential correlation, or some other kind between received signals at each antenna. However, these models are not accurate in many scenarios. Addressing this issue, we provide novel results for the moments, moment-generating function, probability density function, and cumulative distribution function of the quadrivariate Rayleigh distribution with an arbitrary correlation model. To the best of our knowledge, our model is the most comprehensive and the only one that can incorporate the 3GPP suggested spatial correlation structure. We use our new results to derive an analytical expression for the moments of the output signal-to-noise ratio of the four-branch equal gain combining receiver and the four-branch maximal ratio combining receiver. We provide original insight about their output signal-to-noise ratio distributions through their higher order moments in different scenarios. Our expressions are valid for all moments.