No regrets: Distributed power control under time-varying channels and QoS requirements

The problem of power control in wireless networks consists of adjusting transmit power in order to achieve a target SINR level in the presence of noise and interference from other users. In this paper, we examine the performance of the seminal Foschini-Miljanic (FM) power control scheme in networks where channel conditions and users' quality of service (QoS) requirements vary arbitrarily with time (e.g. due to user mobility, fading, etc.). Contrary to the case of static and/or ergodic channels, the system optimum power configuration may evolve over time in an unpredictable fashion, so users must adapt to changes in the wireless medium (or their own requirements) “on the fly”, without being able to anticipate the system evolution. To account for these considerations, we provide a formulation of power control as an online optimization problem and we show that the FM dynamics lead to no regret in this dynamic context. Specifically, in the absence of maximum transmit power constraints, we show that the FM power control scheme performs at least as well as (and typically outperforms) any fixed transmit profile, irrespective of how the system varies with time; finally, to account for maximum power constraints that occur in practice, we introduce an adjusted version of the FM algorithm which retains the convergence and no-regret properties of the original algorithm in this constrained setting.