Abstract: The cognitive radio is proposed as a key technology for improving the utilization of the radio electromagnetic spectrum. In this paper, a multi-user cognitive system in Rayleigh fading channels is analyzed. Several cognitive links coexist in the same spectrum, and their transmission power is restricted by the interference temperature constraint in the primary receiver, as well as constraints on outage probabilities of each link. We study optimal transmission power allocation in order to improve the utilization of the spectrum and satisfy the fairness of each cognitive link. The Rayleigh fading, the channel noise and the interference signal from other cognitive links are all modeled, and the outage probability of the cognitive link is also given. The problem of maximizing the product of the transmitting rates subject to constraints on outage probability and interference temperature is posed as a geometric program. Simulation results show that the approximated solution matches the optimal one very well.

Key words: cognitive radio, interference temperature, outage probability, geometric program