  In Cognitive Radio (CR) networks, multiple secondary network users (SUs)
attempt to communicate over wide potential spectrum without causing significant
interference to the Primary Users (PUs). A spectrum sensing algorithm is a
critical component of any sensing strategy. Performance of conventional
spectrum detection methods is severely limited when the average SNR of the
fading channel between the PU transmitter and the SU sensor is low. Cooperative
sensing and advanced detection techniques only partially remedy this problem. A
key limitation of conventional approaches is that the sensing threshold is
determined from the miss detection rate averaged over the fading distribution.
In this paper, the threshold is adapted to the instantaneous PU-to-SU Channel
State Information (CSI) under the prescribed collision probability constraint,
and a novel sensing strategy design is proposed for overlay CR network where
the instantaneous false alarm probability is incorporated into the belief
update and the reward computation. It is demonstrated that the proposed sensing
approach improves SU confidence, randomizes sensing decisions, and
significantly improves SU network throughput while satisfying the collision
probability constraint to the PUs in the low average PU-to-SU SNR region.
Moreover, the proposed adaptive sensing strategy is robust to mismatched and
correlated fading CSI and improves significantly on conventional cooperative
sensing techniques. Finally, joint adaptation to PU channel gain and SU link
CSI is explored to further improve CR throughput and reduce SU collisions.
