Analytical envelope correlation and spectrum of maximal-ratio combined fading signals

Using results from the theory of multidimensional Gaussian distributions, we provide closed-form or infinite series expressions for the envelope autocorrelation function of the output of a maximal-ratio combiner, for Rayleigh, Nakagami, and Rician fading. These expressions generalize known analytical results obtained for the case of no diversity. The power spectrum of the combined envelope is also obtained for Rayleigh and Nakagami fading. The validity of the analytical approach is verified using computer simulation results obtained with a land-mobile fading emulator. It is observed that, for the land-mobile radio channel, the use of diversity slightly increases the time correlation between the receiver inputs, but in a nonuniform manner across the range of time lags.