Opportunistic Spectrum Access for Cognitive Radio in the Presence of Reactive Primary Users

Opportunistic spectrum access (OSA) is a key technique for the secondary user (SU) in a Cognitive Radio network to transmit over the "spectrum holes" unoccupied by the primary user (PU). Most existing work on the design of OSA has assumed a non-reactive (NR) PU model, i.e., the PU transmission on-off status is independent of the SU access policy, which may not be practical. In this paper, we propose a new Reactive Primary User (RPU) model for the study of OSA, where the PU's access probability over a particular channel is related to the SU's past access history. We model the channel occupancy of the RPU as a 4-state memoryless Markov chain, as opposed to the conventional 2-state (on/off) counterpart, where the expanded state space and state transition probabilities are used to model the reactions of the PU subject to the SU transmit collision. Under this model, we formulate the optimal OSA design for the SU's throughput maximization as a finite-horizon partially observable Markov decision process (POMDP) problem, subject to a conditional collision probability constraint for protecting the PU. Because of the high complexity of the proposed problem, we further propose a separation principle to obtain the optimal policy for the SU with implementable complexity. Numerical results show the new tradeoff between the SU's and the PU's throughput under the RPU model, as compared to the conventional NRPU model.