Solutions to Integrals Involving the Marcum Q-Function and Applications

Novel analytic solutions are derived for integrals that involve the generalized Marcum Q−function, exponential functions and arbitrary powers. Simple closed-form expressions are also derived for specific cases of the generic integrals. The offered expressions are both convenient and versatile, which is particularly useful in applications relating to natural sciences and engineering, including wireless communications and signal processing. To this end, they are employed in the derivation of the average probability of detection in energy detection of unknown signals over multipath fading channels as well as of the channel capacity with fixed rate and channel inversion in the case of correlated multipath fading and switched diversity. Index Terms Marcum Q−function, energy detection, switch-and-stay combining, correlation, special functions. P. C. Sofotasios is with the Department of Electronics and Communications Engineering, Tampere University of Technology, 33101 Tampere, Finland and with the Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece (e-mail: [email protected]) S. Muhaidat is with the Department of Electrical and Computer Engineering, Khalifa University, PO Box 127788, Abu Dhabi, UAE and with the Centre for Communication Systems Research, Department of Electronic Engineering, University of Surrey, GU2 7XH, Guildford, U.K. (e-mail: [email protected]) G. K. Karagiannidis is with the Department of Electrical and Computer Engineering, Khalifa University, PO Box 127788 Abu Dhabi, UAE and with the Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece (e-mail: [email protected]) B. S. Sharif, is with the Department of Electrical and Computer Engineering, Khalifa University, P.O. Box 127788, Abu Dhabi, UAE. (e-mail: [email protected])