Dynamic Power Allocation Under Arbitrary Varying Channels - The Multi-User Case

We consider the power control problem in a time-slotted wireless channel, shared by a finite number of mobiles that transmit to a common base station. The channel between each mobile and the base station is time varying, and the system objective is to maximize the overall data throughput. It is assumed that each transmitter has a limited power budget, to be sequentially divided during the lifetime of the battery. We deviate from the classic work in this area, by considering a realistic scenario where the channel quality of each mobile changes arbitrarily from one transmission to the other. Assuming first that each mobile is aware of the channel quality of all other mobiles, we propose an online power-allocation algorithm, and prove its optimality under mild assumptions. We then indicate how to implement the algorithm when only local state information is available, requiring minimal communication overhead. Notably, the competitive ratio of our algorithm (nearly) matches the one we previously obtained for the (much simpler) single-transmitter case [BLMNO09], albeit requiring significantly different algorithmic solutions.