Inverse incomplete gamma function and its application

Abstract

Communication systems with multiple antennas operating over non-ergodic fading channels are gauged by means of the outage probability against a given communication rate, the solution to which is often expressed in terms of the incomplete gamma function. Practical situations, however, often require the inverse process, i.e. the determination of an optimum rate against a desired outage probability. The contribution of this report is the application of an asymptotic expression that enables the inverse function to be expressed in closed form.