Interference in a Cognitive Network with Beacon

We study a cognitive network consisting of multiple cognitive users communicating in the presence of a single primary user. The primary user is located at the center of the network, and the cognitive users are uniformly distributed within a circle around the primary user. Assuming a constant cognitive user density, the radius of this circle will increase with the number of users. We consider a scheme in which the primary transmitter sends a beacon signaling its own transmission. The cognitive users, upon receiving this beacon, stay silent. Because of channel fading, however, there is a non-zero probability that a cognitive user misses the beacon and hence, with a certain activity factor, transmits concurrently with the primary user. Given the location of the primary receiver, we are interested in the total interference caused by the cognitive users to this receiver. In particular, we provide closed-form bounds on the mean and variance of the interference, and relate them to the outage probability on the primary user. These analytical results can help in the design of a cognitive network with beacon.