Delay-optimal power control for wireless data users with average power constraints

We study the problem of power control for a single mobile user transmitting packets over a fading channel. We find the delay-optimal power control policy which minimizes the average packet delay for a given average power constraint. The transmitter has perfect channel state information but limited queue state information. Our results show that the optimal policy depends on how quickly the channel varies relative to the packet transmission time. In a fast-fading channel the delay-optimal power control is always waterfilling. In a slow-fading channel the optimal policy depends on the amount of incoming traffic. In particular, under moderate traffic conditions the delay-optimal power control is equalization.