Optimal Probabilistic Constellation Shaping for Covert Communications

TL;DR

This paper introduces an optimal probabilistic constellation shaping method for covert communications, significantly improving covert rates by jointly optimizing constellation distribution and power allocation with efficient algorithms.

Contribution

It proposes the first covert rate expressions for discrete constellations and develops practical optimization algorithms for probabilistic shaping.

Findings

Optimized shaping strategies outperform existing schemes in covert rate.

Joint optimization of constellation distribution and power enhances covert communication.

Efficient algorithms balance performance and computational complexity.

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 nonequiprobable 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.