Available and Waiting Times for Cognitive Radios

Cognitive radios (CRs) have been recently proposed for the problem of spectrum scarcity. The principle of CRs’ operation is based on the opportunistic access to the frequency spectrum mainly dedicated to primary users (PUs). The statistical time pattern of PUs’ channel usage and arrival can affect the usability of specific frequency bands for CRs. In this note, the effect of the arrival rate and channel holding time of PUs on the available times for CRs is analyzed. To this end, first, based on Poissonian arrivals, the available time for CRs is calculated. Then, assuming a gamma distribution for the inter-arrival times and a uniform distribution of channel holding time of PU in these intervals, the probability density function and moments of the available time for CRs are derived. Next, the effect of PUs statistical parameters on the average number of packets and the average symbol rate that a CR can transmit is analyzed. Also, taking that CR needs at least T seconds, the average waiting time is calculated.