Optimal Power-Delay Tradeoffs in Fading Channels-Small-Delay Asymptotics

When transmitting stochastically arriving data over fading channels, there is an inherent tradeoff between the required average transmission power and the average queueing delay experienced by the data. This tradeoff can be exploited by appropriately scheduling the transmission of data over time. In this paper, we study the behavior of the optimal power-delay tradeoff for a single user in the regime of asymptotically small delays. In this regime, we first lower bound how much average power is required as a function of the average queueing delay. We show that the rate at which this bound increases as the delay becomes asymptotically small depends on the behavior of the fading distribution near zero, as well as the arrival statistics. We lower bound this rate for two different classes of fading distributions: one class that requires infinite power to minimize the queueing delay and one class that requires only finite power. We then show that for both classes, the bounds can essentially be achieved by a sequence of simple "channel threshold" policies, which only transmit when the channel gain is greater than a given threshold. We also consider several other transmission scheduling policies and characterize their convergence behavior in the small-delay regime.