The second order statistics of a two-branch MRC with power unbalanced Nakagami distributed branches

In this paper, the exact expressions for the second order statistics of the maximum ratio combiner (MRC) output for Nakagami fading channel are derived. The joint characteristic function (CF) for the MRC output and its time derivative is derived, and applied to obtain the level crossing rate (LCR) expression for the case of independent but unbalanced diversity branches, with unequal fading parameters. For the special case of two-branch diversity, the LCR expressions are derived in closed form. The exact closed-form expression for the autocorrelation function (ACF) of the MRC output is derived for an arbitrary number of diversity branches. The analytical results are validated by simulations.