Delay-constrained capacity with causal feedback

A block-fading channel model is considered, and a K-block delay constraint is imposed on data transmission. The key consideration is that the channel state information is fed back to the transmitter in a causal manner. A general cost function μ(x) is considered in solving the delay-constrained transmission problem, under the short-term and the long-term power constraints. A causal power adaptation strategy is needed to maximize the cost function, hence dynamic programming is found to give the optimum solution. The general cost function is then specialized to the cases of expected and outage capacities. In the case of expected capacity, it is observed that optimizing the transmitted power does not give much benefit at high signal-to-noise ratio (SNR), but provides a substantial gain at low SNR. At low SNR, it is proved that the capacity increases by a factor of approximately log K/m, due to power adaptation, when the channel fades according to the χ_2m² statistics. In the case of outage capacity, it is shown that the optimum power adaptation solution to the long-term constraint problem provides a substantial SNR gain at both low and high values of SNR. Random coding bounds are derived for the outage capacity algorithms.