Adaptive Spectrum Management in MIMO-OFDM Cognitive Radio: An Exponential Learning Approach

In this paper, we examine cognitive radio systems that evolve dynamically over time as a function of changing user and environmental conditions. To take into account the advantages of orthogonal frequency division multiplexing (OFDM) and recent advances in multiple antenna (MIMO) technologies, we consider a full MIMO-OFDM Gaussian cognitive radio system where users with several antennas communicate over multiple non-interfering frequency bands. In this dynamic context, the objective of the network's secondary users (SUs) is to stay as close as possible to their optimum power allocation and signal covariance prole as it evolves over time, with only local channel state information at their disposal. To that end, we derive an adaptive spectrum management policy based on the method of matrix exponential learning, and we show that it leads to no regret (i.e. it performs asymptotically as well as any xed signal distribution, no matter how the system evolves over time). As it turns out, this online learning policy is closely aligned to the direction of change of the users' data rate function, so the system's SUs are able to track their individual optimum signal prole even under rapidly changing conditions.