Optimal Power and Rate Control for Minimal Average Delay: The Single-User Case

Contemporary wireless systems combine aspects of network theory such as scheduling, throughput, and delay as well as information theory aspects such as capacity, coding, and power control. Design of such systems requires joint optimization of both network and physical layers. In this paper, we analyze a single-user communication system composed of a transmitter preceded by a queue used for retransmissions, Gaussian block-fading channel, and a receiver. The system average delay is optimized by using combined power/rate control under average power constraints. Dynamic programming is used for calculating the optimized policies using numerical analysis as well as analytic analysis for asymptotically large buffer size. Asymptotic results are obtained for all combinations of fixed or variable power and rate controls. The most important result extends the "water-filling" result for systems with average delay constraint