Outage in a cellular network overlaid with an ad hoc network: The uplink case

We analyze the uplink outage probability at the randomly, but not necessarily independently nor homogeneously, distributed cellular network receivers caused by an overlaid secondary ad hoc network. Unlike the previous works that assumed exact circular exclusion regions (or guard zones), we incorporate a sensing mechanism to decrease the significant effect of the nearby interferers. We consider Rayleigh-faded links, large-scale power control, and the knowledge of the initial outages in the absence of the secondary network. We derive an upper bound on the outage probability and show it to be tight when the co-channel primary receivers are separated by relatively significant distances, which is inherently the case for the cellular network. Furthermore, we derive a closed-form expression that shows the significant impact of the sensing mechanism on the spectrum sharing gains.. Additionally, we optimize the decision threshold, which is used by secondary network users to decide whether to transmit or not, in order to maximize the spectrum sharing gains under the given outage constraints.