This paper investigates the potential of movable antennas (MAs) to enhance physical layer security within a multiple-input multiple-output multiple-antenna eavesdropper (MIMOME) system. We consider a practical scenario where the transmitter operates with imperfect eavesdropper channel state information (ECSI), knowing only the instantaneous line-of-sight (LoS) component and the statistical properties of non-line-of-sight (NLoS) component. To rigorously quantify secrecy performance under the ECSI uncertainty, we adopt the ergodic secrecy rate (ESR) as the metric. Since deriving an exact analytical expression for the ESR is intractable, we leverage random matrix theory to derive a deterministic equivalent. This avoids heavy Monte Carlo simulations and also provides explicit insights into the effects of channel spatial statistics on secrecy performance. Building upon the deterministic equivalent, we formulate a joint maximization problem for the transmit precoding matrix and the antenna positions at the legitimate transmitter. To tackle the non-convexity of this optimization problem, we develop a comprehensive alternating optimization framework. Specifically, the precoding matrix is optimized via a majorization-minimization (MM) algorithm, where the gradient is computed by solving an implicit fixed-point equation. For the antenna position optimization, the complexity of the objective function prevents the construction of standard MM surrogate. To this end, we further propose a novel AMSGrad-based surrogate function that relies solely on gradient information. We provide a rigorous theoretical proof that guarantees the convergence of this proposed algorithm despite relaxing the strict majorization conditions.

翻译：本文研究了可移动天线（MAs）在增强多输入多输出多天线窃听者（MIMOME）系统中物理层安全性的潜力。我们考虑一个实际场景，其中发射机在非完美窃听者信道状态信息（ECSI）下工作，仅已知窃听信道的瞬时视距（LoS）分量以及非视距（NLoS）分量的统计特性。为了在ECSI不确定性下严格量化保密性能，我们采用遍历保密速率（ESR）作为度量指标。由于推导ESR的精确解析表达式十分困难，我们利用随机矩阵理论推导出一个确定性等价表达式。这避免了繁重的蒙特卡洛模拟，并清晰地揭示了信道空间统计特性对保密性能的影响。基于该确定性等价表达式，我们构建了一个针对合法发射机处的发射预编码矩阵和天线位置的联合最大化问题。为了解决该优化问题的非凸性，我们开发了一个全面的交替优化框架。具体而言，预编码矩阵通过一种最大化-最小化（MM）算法进行优化，其梯度通过求解一个隐式定点方程来计算。对于天线位置优化，目标函数的复杂性阻碍了标准MM代理函数的构建。为此，我们进一步提出了一种仅依赖于梯度信息、基于AMSGrad的新型代理函数。我们提供了严格的理论证明，保证该算法在放宽严格最大化条件的情况下依然收敛。