An Optimal Probabilistic Multiple-Access Scheme for Cognitive Radios

We study a time-slotted multiple-access system with a primary user (PU) and a secondary user (SU) sharing the same channel resource. The SU senses the channel at the beginning of the slot. If found free, it transmits with probability 1. If busy, it transmits with a certain access probability that is a function of its queue length and whether it has a new packet arrival. Both users, i.e., the PU and the SU, transmit with a fixed transmission rate by employing a truncated channel inversion power control scheme. We consider the case of erroneous sensing. The goal of the SU is to optimize its transmission scheduling policy to minimize its queueing delay under constraints on its average transmit power and the maximum tolerable primary outage probability caused by the miss detection of the PU. We consider two schemes regarding the secondary´s reaction to transmission errors. Under the so-called delay-sensitive (DS) scheme, the packet received in error is removed from the queue to minimize delay, whereas under the delay-tolerant (DT) scheme, the said packet is kept in the buffer and is retransmitted until correct reception. Using the latter scheme, there is a probability of buffer loss that is also constrained to be lower than a certain specified value. We also consider the case when the PU maintains an infinite buffer to store its packets. In the latter case, we modify the SU access scheme to guarantee the stability of the PU queue. We show that the performance significantly changes if the realistic situation of a primary queue is considered. In all cases, although the delay minimization problem is nonconvex, we show that the access policies can be efficiently obtained using linear programming and grid search over one or two parameters.