LPD Communication: A Sequential Change-Point Detection Perspective

In this paper, we establish a framework for low probability of detection (LPD) communication from a sequential change-point detection (SCPD) perspective, where a transmitter, Alice, wants to hide her transmission to a receiver, Bob, from an adversary, Willie. The new framework facilitates modeling LPD communication and further evaluating its performance under the condition that Willie has no prior knowledge about when the transmission from Alice might start and that Willie wants to determine the existence of the communication as quickly as possible in a real-time manner. We consider three different sequential tests, i.e., the Shewhart, the cumulative sum (CUSUM), and the Shiryaev-Roberts (SR) tests, to model Willie's detection process. Communication is said to be covert if it ceases before being detected by Willie with high probability. Covert probability defined as the probability that Willie is not alerted during Alice's transmission is investigated. We formulate an optimization problem aiming at finding the transmit power and transmission duration so as to maximize the total amount of information that can be transmitted subject to a high covert probability. Under the Shewhart test, closed-form approximations of the optimal solutions are derived, which will approximate the solutions obtained from exhaustive search. As for the CUSUM and SR tests, we provide effective algorithms to search for the optimal solutions. Numeric results are presented to show the performance of LPD communication.