Closed-Form Detection Error Rate Analysis in Physical Layer Anonymous Communications

In the fifth generation (5G) communications, the emerging applications involve communication, computing, and storage of confidential data, where privacy protection has attracted much attention in recent years. As a promising technique that resides in the physical layer (PHY), anonymous precoding manipulates the signaling pattern of transmitted signals, for the purpose of user anonymity. It can mask the sender's identity of the PHY, thus scrambling the detection error rate (DER) performance of a legitimate but curious receiver. In the existing literature, the DER performance can only be measured qualitatively, without concrete theoretic analysis. In this paper, we give the first attempt to analyze the DER performance for PHY anonymous communications. To be specific, we demonstrate a closed-form yet tight expression of DER result. It proves to be a function of the precoder employed at the user, propagation channel, block length and noise status. Based on the derived closed-form DER, the fundamentals of anonymous precoding on scrambling the sender detection are revealed, and the anonymity gain of anonymous precoding against conventional precoding is quantified. Also, the impacts of block length, noise, and channel correlation on DER performance are analyzed.