Joint Analog Beamforming and Antenna Position Design for Secure Communication systems With Movable Antennas

Movable antennas (MA) are a novel technology that allows for the flexible adjustment of antenna positions within a specified region, thereby enhancing the performance of wireless communication systems. In this paper, we explore the use of MA to improve physical layer security in an analog beamforming (AB) communication system. Our goal is to maximize the secrecy rate by jointly optimizing the transmit AB and MA position, subject to constant modulus (CM) constraints on the AB and position constraints for the MA. The resulting problem is non-convex, and we propose a penalty product manifold (PPM) method to solve it efficiently. Specifically, we convert the inequality constraints related to MA position into a penalty function using smoothing techniques, thereby reformulating the problem as an unconstrained optimization on the product manifold space (PMS). We then derive a parallel conjugate gradient descent (PCGD) algorithm to update both the AB and MA position on the PMS. This method is efficient, providing an analytical solution at each step and ensuring convergence to a KKT point. Simulation results show that the MA system achieves a higher secrecy rate than systems with fixed-position antennas.

Constant-Modulus Secure Analog Beamforming for an IRS-Assisted Communication System with Large-Scale Antenna Array

Physical layer security (PLS) is an important technology in wireless communication systems to safeguard communication privacy and security between transmitters and legitimate users. The integration of large-scale antenna arrays (LSAA) and intelligent reflecting surfaces (IRS) has emerged as a promising approach to enhance PLS. However, LSAA requires a dedicated radio frequency (RF) chain for each antenna element, and IRS comprises hundreds of reflecting micro-antennas, leading to increased hardware costs and power consumption. To address this, cost-effective solutions like constant modulus analog beamforming (CMAB) have gained attention. This paper investigates PLS in IRS-assisted communication systems with a focus on jointly designing the CMAB at the transmitter and phase shifts at the IRS to maximize the secrecy rate. The resulting secrecy rate maximization (SRM) problem is non-convex. To solve the problem efficiently, we propose two algorithms: (1) the time-efficient Dinkelbach-BSUM algorithm, which reformulates the fractional problem into a series of quadratic programs using the Dinkelbach method and solves them via block successive upper-bound minimization (BSUM), and (2) the product manifold conjugate gradient descent (PMCGD) algorithm, which provides a better solution at the cost of slightly higher computational time by transforming the problem into an unconstrained optimization on a Riemannian product manifold and solving it using the conjugate gradient descent (CGD) algorithm. Simulation results validate the effectiveness of the proposed algorithms and highlight their distinct advantages.