Secure Analog Beamforming Design for Wireless Communication Systems With Movable Antennas

Movable antennas (MA) allow flexible positioning within a specified region, enhancing wireless communication performance. This paper explores leveraging MA to improve physical layer security in analog beamforming (AB) systems. Specifically, we aim to maximize the secrecy rate by jointly optimizing the AB and MA positions under constant modulus (CM) and position constraints. To solve the resulting non-convex problem, we propose a penalty product manifold (PPM) method, which converts MA position constraints into a penalty function, reformulating the problem as unconstrained optimization on the product manifold space (PMS). We then derive a parallel conjugate gradient descent (PCGD) algorithm to efficiently update both AB and MA positions, providing analytical solutions at each step and ensuring convergence to a KKT point. Simulation results confirm that the MA system achieves a higher secrecy rate than systems with fixed antenna positions.