Capacity of Cognitive Radio under imperfect secondary and cross link Channel State Information

In this paper, we study the ergodic capacity of secondary user channel in a spectrum sharing scenario in which the secondary transmitter is instantaneously aware of estimated versions of the cross link (between the secondary transmitter and the primary receiver) and the secondary link Channel State Information (CSI). The secondary link optimal power profile along with the ergodic capacity are derived for a class of fading channels, under an average power constraint and an instantaneous interference outage constraint. We also show that our framework is rather general as it encompasses several previously studied spectrum sharing settings as special cases. In order to gain some insights on the capacity behavior, numerical results are shown for independent Rayleigh fading channels where it is found for instance, that at low SNR regime, only the secondary channel estimation matters and that the cross link CSI has no effect on the ergodic capacity; whereas at high SNR regime, the capacity is rather driven by the cross link CSI.