  This paper is concerned with spectrum sharing cognitive radio networks, where
a secondary user (SU) or cognitive radio link communicates simultaneously over
the same frequency band with an existing primary user (PU) link. It is assumed
that the SU transmitter has the perfect channel state information (CSI) on the
fading channels from SU transmitter to both PU and SU receivers (as usually
assumed in the literature), as well as the fading channel from PU transmitter
to PU receiver (a new assumption). With the additional PU CSI, we study the
optimal power control for the SU over different fading states to maximize the
SU ergodic capacity subject to a new proposed constraint to protect the PU
transmission, which limits the maximum ergodic capacity loss of the PU resulted
from the SU transmission. It is shown that the proposed SU power-control policy
is superior over the conventional policy under the constraint on the maximum
tolerable interference power/interperferecne temperature at the PU receiver, in
terms of the achievable ergodic capacities of both PU and SU.
