Transmit without Regrets: Online Optimization in MIMO-OFDM Cognitive Radio Systems

In this paper, we examine cognitive radio systems that evolve dynamically over time due to changing user and environmental conditions. To combine the advantages of orthogonal frequency division multiplexing (OFDM) and multiple-input, multiple-output (MIMO) technologies, we consider a MIMO-OFDM cognitive radio network where wireless users with multiple antennas communicate over several non-interfering frequency bands. As the network\´s primary users (PUs) come and go in the system, the communication environment changes constantly (and, in many cases, randomly). Accordingly, the network\´s unlicensed, secondary users (SUs) must adapt their transmit profiles "on the fly" in order to maximize their data rate in a rapidly evolving environment over which they have no control. In this dynamic setting, static solution concepts (such as Nash equilibrium) are no longer relevant, so we focus on dynamic transmit policies that lead to no regret: specifically, we consider policies that perform at least as well as (and typically outperform) even the best fixed transmit profile in hindsight. Drawing on the method of matrix exponential learning and online mirror descent techniques, we derive a no-regret transmit policy for the system\´s SUs which relies only on local channel state information (CSI). Using this method, the system\´s SUs are able to track their individually evolving optimum transmit profiles remarkably well, even under rapidly (and randomly) changing conditions. Importantly, the proposed augmented exponential learning (AXL) policy leads to no regret even if the SUs\´ channel measurements are subject to arbitrarily large observation errors (the imperfect CSI case), thus ensuring the method\´s robustness in the presence of uncertainties.