Solutions to Infinite Integrals of Gaussian Q-Function Products and Some Applications

Infinite integrals involving the products of two and three Gaussian Q-functions of different arguments are solved in closed-form. These solutions provide novel expressions in the error rate analyses of signals such as general rectangular quadrature amplitude modulation, differentially encoded quaternay phase shift keying and new solutions for the error rate of the repetition code. As an example, closed-form expressions for the average symbol error rates of general rectangular quadrature amplitude modulation and the repetition code are obtained for a Nakagami-m fading channel.