Complete solutions for the outage probability of maximal ratio combining diversity on Nakagami- m fading channels with unequal power branches valid for integer m

Maximal ratio combining (MRC) diversity is fundamental in wireless communication theory and widely implemented in practice. There are limited results in the theory for the probability density function (PDF) of MRC diversity on Nakagami channels when the branches have unequal powers. In addition to being restricted, the known solutions are complex and in some cases unwieldy. Novel, complete solutions for the PDF of MRC signal-to-noise ratio (SNR), valid for integer values of the Nakagami fading parameter m and arbitrary branch powers, are derived. In addition to being solutions for the unsolved cases, the new solutions give different and much simpler expressions for the known restricted cases than previous solutions. The effects of branch channel power imbalances on the PDF of MRC and on the outage probability are investigated quantitatively. The new solutions are used to derive asymptotic large SNR performance measures for MRC diversity with unequal branch powers, insights not obtainable from previous solutions. The new solutions are used to derive intuitive simple approximations for the densities and distributions of MRC output signal power and amplitude, as well as for the outage probability. The approximations are shown to have excellent accuracies for power imbalances $\lt $< 30% and good accuracies for power imbalances $\lt $< 60%.