This paper studies energy-efficient precoding designs for multi-user visible light communication (VLC) systems from the perspective of physical layer security where users' messages must be kept mutually confidential. For such systems, we first derive a lower bound on the achievable secrecy rate of each user. Next, the total power consumption for illumination and data transmission is thoroughly analyzed. We then tackle the problem of maximizing energy efficiency, given that each user's secrecy rate satisfies a certain threshold. The design problem is shown to be non-convex fractional programming, which renders finding the optimal solution computationally prohibitive. Our aim in this paper is, therefore, to find sub-optimal yet low complexity solutions. For this purpose, the traditional Dinkelbach algorithm is first employed to reformulate the original problem to a non-fractional parameterized one. Two different approaches based on the convex-concave procedure (CCCP) and Semidefinite Relaxation (SDR) are utilized to solve the non-convex parameterized problem. In addition, to further reduce the complexity, we investigate a design using the zero-forcing (ZF) technique. Numerical results are conducted to show the feasibility, convergence, and performance of the proposed algorithms depending on different parameters of the system.

翻译：本文从物理层安全视角研究多用户可见光通信（VLC）系统中能效优化的预编码设计，要求各用户消息保持相互保密。针对此类系统，我们首先推导各用户可达保密速率的下界。随后系统分析照明与数据传输的总功耗。在此基础上，我们在各用户保密速率满足特定阈值的约束下，求解能效最大化问题。该设计问题被证明为非凸分式规划问题，导致最优解的计算复杂度极高。因此，本文目标是寻求次优但低复杂度的解决方案。为此，首先采用传统Dinkelbach算法将原问题转化为非分式参数化形式，随后分别利用凸凹过程（CCCP）与半定松弛（SDR）两种方法求解该非凸参数化问题。此外，为进一步降低复杂度，我们研究了基于迫零（ZF）技术的设计方案。数值结果验证了所提算法在不同系统参数下的可行性、收敛性与性能表现。