Novel Solutions to Integrals of Products of Q-Functions with Wireless Applications

Abstract

Infinite integrals involving the products of two, three and four Gaussian Q-functions of different arguments are solved in closed-form or in single integral form with finite upper and lower limits. 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.