Integrating massive multiple-input multiple-output (mMIMO) systems with intelligent reflecting surfaces (IRS) presents a promising paradigm for enhancing physical-layer security (PLS) in wireless communications. However, deploying high-resolution quantizers in large-scale mMIMO arrays, along with numerous IRS elements, leads to substantial hardware complexity. To address these challenges, this paper proposes a cost-effective PLS design for IRS-assisted mMIMO systems by employing one-bit digital-to-analog converters (DACs). The focus is on jointly optimizing one-bit quantized precoding at the transmitter and constant-modulus phase shifts at the IRS to maximize the secrecy rate. This leads to a highly non-convex fractional secrecy rate maximization (SRM) problem. To efficiently solve this problem, two algorithms are proposed: (1) the WMMSE-PDD algorithm, which reformulates the SRM problem into a sequence of non-fractional programs with auxiliary variables using the weighted minimum mean-square error (WMMSE) method and solves them via the penalty dual decomposition (PDD) approach, achieving superior secrecy performance; and (2) the exact penalty product Riemannian gradient descent (EP-PRGD) algorithm, which transforms the SRM problem into an unconstrained optimization over a product Riemannian manifold, eliminating auxiliary variables and enabling faster convergence with a slight trade-off in secrecy performance. Both algorithms provide analytical solutions at each iteration and are proven to converge to Karush–Kuhn–Tucker (KKT) points. Simulation results confirm the effectiveness of the proposed methods and highlight their respective advantages.

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.

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.

In this paper, we focus on the secure beamforming design in a beyond-diagonal reconfigurable intelligent surface (BD-RIS) assisted multiple-input multiple-output (MIMO) downlink network. We consider a scenario where a transmitter sends an information signal to a multi-antenna legitimate user while a multi-antenna eavesdropper attempts to intercept it. In this setting, a BD-RIS reconfigures the wireless environment to enhance secrecy. Aiming at the secrecy rate (SR) maximization, the joint optimization of transmit beamforming and BD-RIS reflection coefficients is formulated as a non-convex problem with power constraints on beamforming and symmetric and unitary constraints on BD-RIS reflection coefficients. To efficiently solve this challenging problem, a low-complexity framework that combines the augmented Lagrangian (AL) method and product manifold gradient descent (PMGD) algorithm is proposed to obtain a high-quality suboptimal solution. Numerical results show that BD-RIS-assisted systems achieve higher secrecy rates compared to conventional RIS-assisted systems.

Reconfigurable intelligent surfaces (RISs) hold significant promise for enhancing physical layer security (PLS). However, conventional RISs are typically modeled using diagonal scattering matrices, capturing only independent reflections from each reflecting element, which limits their flexibility in channel manipulation. In contrast, beyond-diagonal RISs (BD-RISs) employ non-diagonal scattering matrices enabled by active and tunable inter-element connections through a shared impedance network. This architecture significantly enhances channel shaping capabilities, creating new opportunities for advanced PLS techniques. This paper investigates PLS in a multiple-input multiple-output (MIMO) system assisted by BD-RISs, where a multi-antenna transmitter sends confidential information to a multi-antenna legitimate user while a multi-antenna eavesdropper attempts interception. To maximize the secrecy rate (SR), we formulate it as a non-convex optimization problem by jointly optimizing the transmit beamforming and BD-RIS REs under power and structural constraints. To solve this problem, we first introduce an auxiliary variable to decouple BD-RIS constraints. We then propose a low-complexity penalty product Riemannian conjugate gradient descent (P-PRCGD) method, which combines the augmented Lagrangian (AL) approach with the product manifold gradient descent (PMGD) method to obtain a Karush-Kuhn-Tucker (KKT) solution. Simulation results confirm that BD-RIS-assisted systems significantly outperform conventional RIS-assisted systems in PLS performance.

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.

In this paper, we study the joint admission control and beamforming problem within a network where one multi-antenna base station tries to serve multiple single-antenna users. Unlike most existing studies which merely identify the users that should be denied, our work further suggest better positions in the neighbouring area for them where the previously-rejected users are allowed to access the network. To address this, we assume the knowledge of channel vectors within the network coverage area, and then jointly optimize the transmit beamformer and the channel vector associated with each user to minimize the network power cost, with a penalty measuring the mismatch between the optimized channel and the reference channel with current user position. Specifically, a non-zero mismatch means that the corresponding user is inadmissible at present, but may access network if moving to the position with the channel closest to the optimized result. Basically, this is a challenging non-convex problem, and we design a penalty dual decomposition (PDD)-based algorithm to iteratively achieve a stationary solution. The algorithm is highly efficient since a simple analytical solution is derived in each step.

The Multiple-Input Multiple-Output (MIMO) radar transmit beampattern matching under the Constant Modulus Constraint (CMC) is a key technology. Most existing approaches address this problem by relaxation, which result in performance degradation. Different from these methods, we notice that the CMC is the product of complex circles. Based on this characterisic, a Riemannian Complex Circle Manifold (RCCM) method without relaxation is developed. More precisely, the aforementioned problem is firstly reformulated as an unconstraint quartic function over the RCCM. After that, an efficient Riemannian conjugate gradient algorithm is developed to solve it. Compared with the existing methods, the proposed method obtains better performance with lower computational cost.