Distribution of the detection time of a primary user in a cognitive network

An analytical formulation of the mean detection time and the distribution of the detection time of a wireless microphone (primary user) in an IEEE 802.22 wireless regional area network (WRAN) is presented. The IEEE 802.22 WRAN has a number of customer-premises equipments (CPEs) in the coverage area of its base station. Out of this number of CPEs, a number of them are within the coverage area of the microphone. All of the CPEs can be inactive or active. This is modeled by a discrete time Markov chain. If the microphone turns on or becomes active, the WRAN must be able to detect the microphone and vacates the channel within a time threshold. It is assumed that as long as one of the active CPEs, within the coverage area of the microphone, detects the microphone as active, the microphone is detected. The mean and the distribution of the detection time of the microphone are derived by modeling the detection time by an absorbing discrete time Markov chain. Numerical results corresponding to typical parameter values are presented. The tradeoffs among the number of CPEs, coverage range of the wireless microphone (primary user) and probability of detection are investigated.