No more tears: A no-regret approach to power control in dynamically varying MIMO networks

In this paper, we address the trade-off between radiated power and achieved throughput in wireless multiple-input and multiple-output (MIMO) systems that evolve over time in an unpredictable fashion (e.g. due to changes in the wireless medium or the users´ QoS requirements). Contrary to the static/stationary channel regime, there is no optimal power allocation profile to converge to (either static or in the mean), so the system´s users must adapt to changes in the environment “on the fly”, without being able to predict the system´s evolution ahead of time. In this dynamic context, we formulate the users´ power/throughput trade-off as an online optimization problem and we provide a matrix exponential learning algorithm that leads to no regret - i.e. the proposed transmit policy is asymptotically optimal in hindsight, irrespective of how the system varies with time. As a result, users are able to track the evolution of their individually optimum transmit profiles remarkably well, even in arbitrarily changing wireless environments.