Optimal Probabilistic Constellation Shaping for Covert Communications

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