Useful integrals for performance evaluation of communication systems in generalised η - μand κ - μ fading channels

The author obtains closed-form expressions for the averages of the Gaussian Q-function and product of two Gaussian Q-functions over the generalised eta-mu and kappa-mu distributions. These results can be useful in many practical applications when evaluating error rate performances of communication systems operating in radio channels modelled by the eta-mu and kappa-mu distributions. The formulas are obtained in terms of Appell´s (F₁(middot) and Phi₁(middot)) and Lauricella´s (F_D ³(middot) and Phi₁ ⁽³⁾(middot)) hypergeometric functions. As examples of application, the average symbol error rates of general order rectangular quadrature amplitude modulation (QAM) in middotmiddotmiddot and middotmiddotmiddot radio channels are evaluated.