Upper bound on the capacity of cognitive radio without cooperation

We derive an upper bound on the capacity of cognitive radio using the interference temperature concept. We do not assume any cooperation between the primary and the secondary user. First, assuming all four links associated with the primary/secondary transmitter/receiver experience Rayleigh fading, the capacity is achieved via the water-filling power allocation strategy, subject to an average secondary to primary interference to signal ratio (ISR) constraint and a peak ISR constraint. Second, we extend our result to the case with path loss as well as channel fading to reflect the geometric relations between link pairs and network size. Finally, we numerically show that for K_P primary receivers which are opportunistically scheduled, the capacity of cognitive radio asymptotically grows as logloglogK_P.