Optimal rate and delay performance in non-cooperative opportunistic spectrum access

We study transmission rate control and performance delay in cognitive radio (CR) links from a cross-layer perspective. We assume a hierarchical CR network where the secondary users (SU) access the spectrum band in an opportunistic and noncooperative way. The SU goal is to transmit a fixed-size file (fixed amount of data packets) during the sojourn time of the primary users (PU´s) idle state. We assume that the SU´s support frames retransmission through an automatic repeat request (ARQ) mechanism. By formulating the problem as a Markov decision process, we demonstrate that there is always an optimal stationary rate adaptation policy, and we propose a simple algorithm to obtain it. We derive an exact closed-form expression for the probability of successful transmission as a function of the PU´s access probability and the signal-to-noise ratio at the link receiver. We also study the performance delay, understood as the time required to transmit the entire data file, taking into account frames retransmission. To do that, we analyze the Markov process associated with the optimal rate policy in the transform domain. Then, using probabilistic flow-graph techniques, we derive exact closed-form expressions for the statistical distribution of transmission delay.