Probabilistic Constrained Secure Transmissions: Variable-Rate Design and Performance Analysis

In a wiretap channel, due to the passive nature of eavesdropper and the inevitable errors during channel estimation or feedback, the channel state information is usually imperfectly known at the transmitter. While probabilistic constrained secure transmission provides an elegant formulation to tackle these uncertainties, current works mostly focus on the fixed-rate secure transmission design. To exploit the dynamic channel state information for performance enhancement, this paper investigates a variable-rate transmission scheme with adjustable rate and power, under the outage probabilistic constraints and upper bounding rate constraint. By leveraging the first-order and log-concavity properties of the Marcum Q-function, closed-form optimal secure transmission design is obtained. Furthermore, the optimality of the proposed method empowers us to concisely quantify the performance gain brought by rate variation. Numerical results show that the proposed scheme achieves significantly lower average outage probability and higher throughput than the fixed-rate scheme no matter with or without upper bound rate limitation.