Interference scaling laws in cognitive networks

In cognitive radio networks, two classes of devices exist: primary and secondary. Primary devices are granted privileged access to the spectrum while secondary devices must limit their transmissions so as not to generate harmful interference. In this paper we investigate the minimum size that a low duty cycle secondary network must possess if it is to be deemed useful, i.e., at least one node can transmit without causing significant simultaneous interference to the primary network. We initially consider two cases. First the size of the primary network is fixed to m users, and we ask the question how quickly can the interference to the primary network be reduced as a function of the size k of the secondary network. In this case, there is a tradeoff between the rate at which interference can be reduced and the probability that such interference is achieved, which we denote as secondary outage. The tradeoff in this case is completely characterized for Raleigh fading. In the second case, we allow the size of the primary and secondary network grow simultaneously. Here the tradeoff between the growth rate of the networks, the rate at which the interference is decreased and the rate at which the outage probability vanishes is determined in the regime that the interference decreases sufficiently fast for Raleigh fading. Finally, we consider arbitrary networks for which the outage probability has a non-vanishing limit. We show that the probability that at least l nodes can transmit also has a non- vanishing limit that does not depend on the asymptotic behaviour of the interference threshold, the rate at which the networks grow or even the distribution of the fading. Therefore, there are no tradeoffs for the system designer in this regime.