Secure Analog Beamforming for Multi-user MISO Systems with Movable Antennas

Movable antennas (MAs) represent a novel approach that enables flexible adjustments to antenna positions, effectively altering the channel environment and thereby enhancing the performance of wireless communication systems. However, conventional MA implementations often adopt fully digital beamforming (FDB), which requires a dedicated RF chain for each antenna. This requirement significantly increase hardware costs, making such systems impractical for multi-antenna deployments. To address this, hardware-efficient analog beamforming (AB) offers a cost-effective alternative. This paper investigates the physical layer security (PLS) in an MA-enabled multiple-input single-output (MISO) communication system with an emphasis on AB. In this scenario, an MA-enabled transmitter with AB broadcasts common confidential information to a group of legitimate receivers, while a number of eavesdroppers overhear the transmission and attempt to intercept the information. Our objective is to maximize the multicast secrecy rate (MSR) by jointly optimizing the phase shifts of the AB and the positions of the MAs, subject to constraints on the movement area of the MAs and the constant modulus (CM) property of the analog phase shifters. This MSR maximization problem is highly challenging, as we have formally proven it to be NP-hard. To solve it efficiently, we propose a penalty constrained product manifold (PCPM) framework. Specifically, we first reformulate the position constraints as a penalty function, enabling unconstrained optimization on a product manifold space (PMS), and then propose a parallel conjugate gradient descent algorithm to efficiently update the variables. Simulation results demonstrate that MA-enabled systems with AB can achieve a well-balanced performance in terms of MSR and hardware costs.