When the Warden Does Not Know Transmit Power: Detection Performance Analysis and Covertness Strategy Design

In this paper, we consider a novel covert communication scenario where the warden does not have prior knowledge of the transmitter's power. In this scenario, the current widely adopted likelihood ratio test (LRT)-based detector is not optimal anymore. To address this, we formulate a detection framework based on the generalized likelihood ratio test (GLRT), which replaces the unknown parameter with maximum likelihood estimation (MLE) and is proven optimal in the scenario. Based on the GLRT-based framework, two different detection models are proposed, where one only utilizes observations of the current time and the other can exploit observations of past time slots. We analyze the estimation and fisher information of the transmit power, and even the detection and covert performance under two different detection models, respectively. Based on the analytical results, we further derive the maximum number of tolerable slots under which the transmitter can remain the same transmit power while the detection error probability of the warden is still larger than the regulated threshold. Moreover, the transmit power and the number of tolerable slots are jointly optimized to maximize the transmission throughput subjecting to covertness constraint. The numerical results demonstrate the correctness of the theoretical analysis. We show how the covert rate is influenced by the number of transmitting slots and the transmit power, which can guide the design of the covert transmission strategy.