A General Framework for Symbol Error Probability Analysis of Wireless Systems and Its Application in Amplify-and-Forward Multihop Relaying

New exact single-integral expressions for the evaluation of the average error probability of a wireless communication system are derived for a variety of modulation schemes in terms of the moment-generating function (MGF) of the reciprocal of the instantaneous received signal-to-noise ratio (SNR). The expressions obtained form a framework for performance evaluation of wireless communication systems for which the well-known MGF-based performance analysis method cannot be used, that is, systems for which the MGF of the instantaneous received SNR is not known or cannot be derived in closed-form. Using the framework obtained, the error probability performance in general fading of an amplify-and-forward (AF) multihop relaying system with both variable-gain and fixed-gain relays is then evaluated. In particular, a new expression for the MGF of the reciprocal of the instantaneous received SNR of an AF multihop system with fixed-gain relays is derived. Numerical examples show precise agreement between simulation results and theoretical results.