A Lower Bound to the Receiver Operating Characteristic of a Cognitive Radio Network

Cooperative cognitive radio networks are investigated by using an information-theoretic approach. This approach consists of interpreting the decision process carried out at the fusion center as a binary (asymmetric) channel, whose input is the presence of a primary signal and output is the fusion center decision itself. The error probabilities of this channel are the false-alarm and missed-detection probabilities. After calculating the mutual information between the binary random variable representing the primary signal presence and the set of sensor (or secondary user) output samples, we apply the dataprocessing inequality to derive a lower bound to the receiver operating characteristic. This basic idea is developed through the paper in order to consider the cases of full channel and signal knowledge and of knowledge in probability distribution. The advantage of this approach is that the ROC lower bound derived is independent of the particular type of spectrum detection algorithm and fusion rule considered. Then, it can be used as a benchmark for existing practical systems.