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 signal transmission to a receiver, Bob, under the surveillance of an adversary, Willie. The new framework facilitates to model LPD communication and further evaluate its performance under the condition that Willie has no prior knowledge on when the transmission from Alice starts and that Willie wants to detect the existence of the communication as quickly as possible in real-time manner. We consider three different sequential tests for Willie, i.e., the Shewhart test, the cumulative sum (CUSUM) test, and the Shiryaev-Roberts (SR) test, to model the detection procedure. Communication is said to be covert if it stops before detection by Willie with high probability. Covert probability defined as the probability that Willie is not alerted during the communication procedure is investigated. We formulate an optimization problem aimed at finding the transmit power and transmission duration such that the total amount of information that can be transmitted is maximized subject to a high covert probability. Under Shewhart test, closed-form approximations of the optimal transmit power and transmission duration are derived, which well approximate the solutions obtained from exhaustive search. As for CUSUM and SR tests, we provide an effective algorithm to search the optimal solution. Numeric results are presented to show the performance of LPD communication.