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.
翻译:在本文中,我们从实用的角度来研究隐蔽通信系统的最佳隐蔽概率星座构造设计设计。不同于具有可装备的星座调制的常规隐蔽通信,我们提出无差别的星座调制计划,以进一步提高隐蔽率。具体地说,我们首次为离散星座的实用投入产生隐蔽率表达方式。然后,我们通过共同优化星座分布和权力分配来研究隐蔽率最大化问题。特别是,为获得最佳的概率星座构造,提出了一种大约的梯度下降方法。为了在计算复杂性和传输性能之间取得平衡,我们进一步制定了一个框架,在可实现率上最大限度地限制一个较低的范围,使最佳概率星座形成问题能够使用弗兰克-沃夫方法有效解决。广泛的数字结果显示,最佳概率星座形成战略在最先进的尖端技术计划可实现的隐蔽率上取得了重大收益。