Optimizing the Power Allocation for Rayleigh Block-Fading Channels with Outage Capacity Constraints

This letter studies the power distribution over K blocks of coded information to support a certain rate in Rayleigh- fading channels given the causal channel state information at the transmitter (CSIT). For K = 2, we shall show that since the channel in the future is random, the optimal power policy tends to pour all the power for the first block, which disables the time diversity. By introducing outage capacity as a constraint, time-diversity can be unleashed by stochastically distributing the power among the blocks. For K = 2, we derive the stochastic- optimal power allocation in closed-form for the transmit power minimization problem subject to an outage capacity constraint. For K > 2, we propose to minimize the power by constraining the upper bound of the outage probability, and in so doing, the problem is convex which permits to derive the optimal power policy. Numerical results demonstrate that the proposed power policy exploiting CSIT gives significant power reduction when compared to an equal-power policy.