Service outage based power and rate control for Poisson fading channels

We consider a service outage based power and rate allocation problem for the Poisson fading channel with perfect channel state information at the transmitter and the receiver. A service outage occurs when the instantaneous transmission rate falls below the basic rate r₀. The objective of the allocation problem is to maximize the expected transmission rate subject to peak and average transmitter power constraints and a constraint on the outage probability epsiv. A general class of probabilistic power allocation schemes are considered, and the optimum power allocation scheme is shown to be deterministic except for channel fades in a boundary set. When the problem is feasible, the optimum scheme is a combination of ergodic capacity-achieving power allocation and outage capacity-achieving power allocation schemes with a randomization between the two deterministic schemes in the boundary set. This randomization is not necessary when the channel fade distribution is continuous.