Generalizing the sampling property of the Q-function for Error Rate analysis of cooperative communication in fading channels

This paper extends some approximation methods that are used to identify closed form Bit Error Rate (BER) expressions which are frequently utilized in investigation and comparison of performance for wireless communication systems in the literature. By using this group of approximation methods, some expectation integrals, whose exact analyses are intractable and whose Monte Carlo simulation computations have high complexity, can be computed. For these integrals, by using the sampling property of the integrand functions of one or more arguments, reliable BER expressions revealing the diversity and coding gains are derived. Although the methods we present are valid for a larger class of integration problems, in this work we illustrate the method by showing the step by step derivation of the BER expressions for a canonical cooperative communication scenario as well as a network coded system scenario. The derived expressions agree with the simulation results for a very wide range of signal-to-noise ratio (SNR) values.