Exact closed-form expression for average symbol error rate of MIMO-MRC systems

In this paper, we derive closed-form expressions for exact average symbol error rate (SER) of multiple-input multiple-output (MIMO)-maximum ratio combining (MRC) systems with M-ary modulations. We obtain the tractable compact closed-form expressions for the average SER in terms of the Gauss and Appell hypergeometric functions which are provided as library functions in common mathematical softwares such as MAPLE and MATHEMATICA. The analysis is validated by comparing with Monte-Carlo simulations and we further show that our general SER expressions reduce to the previous known results for binary signals (M = 2) as a special case. Applying the series representation of the Gauss and Appell hypergeometric function, we derive a very tight approximation for the average SER.