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

In recent years, physical layer (PHY) anonymous precoding has become imperative in applications that carry personal and sensitive data. While manipulating the signaling pattern of transmitted signals for obtaining high communication utility, the anonymous precoding masks the sender's PHY characteristics for the purpose of sender anonymity. Nevertheless, the anonymity provided by anonymous precoding has only been numerically demonstrated, and the relevant literature still lacks analytic results regarding the detection error rate (DER) performance. In this paper, we give the first attempt to show an analytic DER result of generic precoders. Tight closed-form DER expression is derived, as a function of the precoder employed at the sender, block length, propagation channel, and noise status. Some important properties are revealed, such as the impacts of block length, noise, and channel correlation on the DER result. Finally, simulation results validate that the normalized mean squared error (NMSE) between the closed-form and actual DER results is on the levels of <inline-formula><tex-math notation="LaTeX">$0 \sim 10^{-1}$</tex-math></inline-formula>. The proposed analytic DER results help easily quantify the anonymity performance of existing anonymity-agnostic and anonymous precoders.