This paper considers a movable antenna (MA)-aided secure multiple-input multiple-output (MIMO) communication system consisting of a base station (BS), a legitimate information receiver (IR) and an eavesdropper (Eve), where the BS is equipped with MAs to enhance the system's physical layer security (PLS). Specifically, we aim to maximize the secrecy rate (SR) by jointly optimizing the transmit precoding (TPC) matrix, the artificial noise (AN) covariance matrix and the MAs' positions under the constraints of the maximum transmit power and the minimum distance between MAs. To solve this non-convex problem with highly coupled optimization variables, the block coordinate descent (BCD) method is applied to alternately update the variables. Specifically, we first reformulate the SR into a tractable form by utilizing the minimum mean square error (MMSE) method, and derive the optimal TPC matrix and the AN covariance matrix with fixed MAs' positions by applying the Lagrangian multiplier method in semi-closed forms. Then, the majorization-minimization (MM) algorithm is employed to iteratively optimize each MA's position while keeping others fixed. Finally, simulation results are provided to demonstrate the effectiveness of the proposed algorithms and the significant advantages of the MA-aided system over conventional fixed position antenna (FPA)-based system in enhancing system's security.

翻译：本文研究了一种基于可移动天线（MA）辅助的安全多输入多输出（MIMO）通信系统，该系统包含基站（BS）、合法信息接收者（IR）和窃听者（Eve），其中基站配备MA以增强系统的物理层安全（PLS）。具体而言，我们旨在通过联合优化发射预编码（TPC）矩阵、人工噪声（AN）协方差矩阵以及MA的位置，在最大发射功率和MA间最小距离的约束下，最大化保密速率（SR）。为解决这个具有高度耦合优化变量的非凸问题，采用块坐标下降（BCD）方法交替更新变量。首先，利用最小均方误差（MMSE）方法将SR重新表述为易于处理的形式，并在固定MA位置的情况下，通过应用拉格朗日乘子法以半闭式形式推导出最优TPC矩阵和AN协方差矩阵。然后，采用主最小化（MM）算法在保持其他MA位置不变的情况下迭代优化每个MA的位置。最后，提供仿真结果以展示所提算法的有效性，以及MA辅助系统相较于传统固定位置天线（FPA）系统在提升系统安全性方面的显著优势。