Solutions to Generalized Integrals Involving the Generalized Marcum <inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math> </inline-formula>-Function With Application to Energy Detection

Abstract

We investigate analytic solutions for three generalized integrals involving arbitrary powers, generalized Marcum Q-function, and exponential functions, which are more general than the existing integrals and have been extensively employed in the performance evaluations in various areas of wireless communications, especially in cognitive radios. Closed-form solutions for the general integrals in terms of Meijer's G-function are derived and validated by comparing with the analytic expressions for the existing integrals involving the generalized Marcum Q-function, which are the special cases of the general integrals addressed in this letter. Moreover, one of the analytic solutions for the general integrals is employed to derive the exact closed-form expression for the average detection probability of energy detection over the α-μ fading channels.