Stochastic power allocation using causal channel information for delay-limited communications

Without delay constraints, ergodic capacity can be achieved through channel coding over time frames spanning the whole fading process of the channel without the need of channel state information (CSI) at the transmitter. If the channel capacity is delay-constrained, then causal CSI at the transmitter becomes important. In this letter, our aim is to resolve the optimal power-and-rate allocation in maximizing the expected capacity subject to total power constraint, given the causal CSI at the transmitter. The proposed solution is adaptive to the current and past CSI, and also the statistics of the future channels. Asymptotically in both the high and low signal-to-noise ratio (SNR) regimes, we show that at a particular constant in time, the optimal power policy has an interpretation of water-filling among the current channel and some estimates of the future channels