Securing Probabilistic Wireless Transmissions Against a Power-Constrained Eavesdropper

This work proposes a framework for safeguarding probabilistic communications from a transmitter Alice to a receiver Bob in the presence of a power-constrained eavesdropper Eve, where Eve awakens with a prior probability <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lambda$</tex> and employs a detection-and-then-decoding strategy to eavesdrop on Alice's transmissions. We first optimally design Eve's wake-up probability <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lambda$</tex> and her detection threshold to achieve the maximum overall secrecy outage probability <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p_{\text{os }}^{*}$</tex> subject to her average power consumption budget. Our analysis proves that the proposed detection-and-then-decoding strategy requires less power to keep Eve consistently awake for eavesdropping compared to a conventional direct-decoding strategy. Subsequently, from the perspective of Alice, the optimal transmit power and redundancy rate are determined to maximize the effective transmission rate subject to the maximum tolerable secrecy outage probability and Alice's maximum transmit power. We explicitly show that the achievable confidentiality <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1-p_{\text{os }}^{*}$</tex> is a combination of communication covertness, measured by the probability that Eve fails to detect Alice's transmission, and communication secrecy, measured by the probability that Eve fails to decode Alice's communication. Our results unveil the non-trivial tradeoff between the achieved covertness and secrecy with respect to the power-constrained Eve.