Ergodic Capacity of Cognitive Radio under Imperfect Channel State   Information
  A spectrum-sharing communication system where the secondary user is aware of the instantaneous channel state information (CSI) of the secondary link, but knows only the statistics and an estimated version of the secondary transmitter-primary receiver (ST-PR) link, is investigated. The optimum power profile and the ergodic capacity of the secondary link are derived for general fading channels (with continuous probability density function) under average and peak transmit-power constraints and with respect to two different interference constraints: an interference outage constraint and a signal-to-interference outage constraint. When applied to Rayleigh fading channels, our results show, for instance, that the interference constraint is harmful at high-power regime in the sense that the capacity does not increase with the power, whereas at low-power regime, it has a marginal impact and no-interference performance corresponding to the ergodic capacity under average or peak transmit power constraint in absence of the primary user, may be achieved. 
Zouheir Rezk and Mohamed-Slim Alouini
cs.IT math.IT