Closed-form expression of the ergodic capacity in a cognitive radio link under power constraints

In this paper, we consider a cognitive radio (CR) link operating in a spectrum sharing (SS) mode with a primary network. In this mode, the primary and secondary users can share the same frequency band as long as the interference caused by the secondary network on the primary network is properly regulated. The optimal ergodic capacity of the secondary link that can be achieved is hence being investigated under the presence of the two practical limiting constraints: i) the average interference power affecting the capacity of the primary user and ii) the peak transmit power in the secondary transmitter. Analytical results for the CR link capacity are derived in the general case of full cross interference channel with Rayleigh fading. The results obtained allow evaluating the effects of the different constraints on the performance of the CR link and are validated with numerical simulations.