Error Performance of Rectangular Signaling with MRC in Nakagami Fading

The average of the product of two Gaussian Q-functions having arguments as different scaled versions of the same Nakagami distributed fading gain magnitude is derived in closed-form. Both the cases when (1) the fading parameter is an integer, and (2) the fading parameter is an odd multiple of one-half, are considered. The results are applied to evaluating in closed-form the symbol error probability (SEP) of rectangular quadrature amplitude modulation with maximal-ratio combining (MRC) in independent Nakagami fading. It is found that with increase in the degree of fading, the robustness to decision distance imbalance between in-phase and quadrature signals increases. In addition, there exists an optimum decision distance ratio at which the SEP has a minimum.