Online Power Allocation For Opportunistic Radio Access In Dynamic Ofdm Networks

User mobility has become a key attribute in the design of optimal resource allocation policies for future wireless networks. This has become increasingly apparent in cognitive radio (CR) systems where the licensed, primary users (PUs) of the network must be protected from harmful interference by the network's opportunistic, secondary users (SUs): here, unpredictability due to mobility requires the implementation of safety net mechanisms that are provably capable of adapting to changes in the users' wireless environment. In this context, we propose a distributed learning algorithm that allows SUs to adjust their power allocation profile (over the available frequency carriers) "on the fly", relying only on strictly causal channel state information. To account for the interference caused to the network's PUs, we incorporate a penalty function in the rate-driven objectives of the SUs, and we show that the proposed scheme matches asymptotically the performance of the best fixed power allocation policy in hindsight. Specifically, in a system with S orthogonal subcarriers and transmission horizon T, this performance gap (known as the algorithm's average regret) is bounded from above as O(T-1 log S). We also validate our theoretical analysis with numerical simulations which confirm that the network's SUs rapidly achieve a "noregret" state under realistic wireless cellular conditions. Moreover, by finetuning the choice of penalty function, the interference induced by the SUs can be kept at a sufficiently low level, thus guaranteeing the PUs' requirements.