Optimal Probabilistic Constellation Shaping for Covert Communications

Abstract

In this paper, we investigate the optimal probabilistic constellation shaping design for covert communication systems from a practical view. Different from conventional covert communications with equiprobable constellations modulation, we propose non-equiprobable constellations modulation schemes to further enhance the covert rate. Specifically, we derive covert rate expressions for practical discrete constellation inputs for the first time. Then, we study the covert rate maximization problem by jointly optimizing the constellation distribution and power allocation. In particular, an approximate gradient descent method is proposed for obtaining the optimal probabilistic constellation shaping. To strike a balance between the computational complexity and the transmission performance, we further develop a framework that maximizes a lower bound on the achievable rate where the optimal probabilistic constellation shaping problem can be solved efficiently using the Frank-Wolfe method. Extensive numerical results show that the optimized probabilistic constellation shaping strategies provide significant gains in the achievable covert rate over the state-of-the-art schemes.

Covert Surveillance Video Transmission with QAM Constellations Modulation

“…In previous works [40,43], the performance metrics of covert transmission, i.e., KL divergence and mutual information, have been approximated using intricate integration calculations or less stringent constraints. As depicted in Figure 3, in this section, we introduce a precise approximation method based on the Taylor series expansion theory.…”

“…Additionally, we conduct comparisons of transmission rates and covertness metric values based on various channel coefficients and receiver noise levels. To assess the effectiveness and superiority of the proposed optimal probability theory, we compare optimization results obtained using the backtracking line method from [40].…”