  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.
