The Joint and Product Meta Distributions of the SIR and Their Applications to Secrecy and Cooperation

The meta distribution (MD) of the signal-to-interference ratio (SIR) provides more fine-grained information about the link performance than the standard success probability. This paper focuses on a fundamental extension of the SIR MD-the joint MD of the SIR at different locations, and studies its applications to physical layer security and cooperative reception. The concept of the joint MD of the SIR is formally introduced for two or more users (locations), as well as the joint conditional success probability and the n -th order product MD, which is a simpler version of the joint MD. The joint MD is first applied to physical layer security. The network reliability of the secrecy transmission based on the MD is studied, taking into account the signal and interference correlations between the legitimate user and the eavesdropper. Next the joint MD is applied to cooperative reception, where we consider the scenario that the base station sends a message to a group of users, and the goal is that at least one user successfully receives the message. The moments of the conditional probability of the event that the transmission succeeds at at least one of the two users are derived. The results demonstrate the practical relevance of the joint MD.