On Primary User Coverage Probabilities and Faulty Cognitive Radios

In a cognitive radio (CR) network, the CR devices opportunistically communicate in the frequency bands occupied by the primary users in order to improve the spectral efficiency in these bands. By sensing the primary users, e.g., the television transmitter-receiver pairs and the wireless microphone systems, each CR device determines whether or not to operate in the band. The CR devices, due to erroneous sensing, either fail to detect the primary user, causing excessive interference at the primary users, or have a false-alarm, causing it to remain silent in a white-space band leading to poor spectrum utility. The impact of these imperfections on the primary user operations in terms of the coverage probability is characterized where the primary users and the CR devices are distributed according to independent homogeneous Poisson point processes on the plane.