On multiuser secrecy rate in flat fading channel

We consider a physical layer security based on the wiretap channel for wireless communication systems in which there are one transmitter and multiple receivers/users who report their channel state information (CSI) to the transmitter. This scenario is practically useful since it models the forward link of cellular systems where the systems can take advantage of the multiuser diversity. We are curious about the role of the multiuser diversity in the secure communication under the wiretap channel framework. Although it is well known that fixed transmit power is not optimal when CSI is available to the transmitter, to get useful insights, we consider a fixed transmit power case. In return, we can have some of important performance measures such as outage probability, average secrecy rate, failure rate, and average wait time in closed forms. The analysis interestingly shows that the multiuser diversity becomes always disadvantageous for the secure communications. We substantiate our claims with the analytic results and numerical evaluations.