Cooperative Double IRS aided Secure Communication for MIMO-OFDM Systems

Cooperative double intelligent reflecting surface (double-IRS) has emerged as a promising approach for enhancing physical layer security (PLS) in MIMO systems. However, existing studies are limited to narrowband scenarios and fail to address wideband MIMO-OFDM. In this regime, frequency-flat IRS phases and cascaded IRS links cause severe coupling, rendering narrowband designs inapplicable. To overcome this challenge, we introduce cooperative double-IRS-assisted wideband MIMO-OFDM and propose an efficient manifold-based solution. By regarding the power and constant modulus constraints as Riemannian manifolds, we reformulate the non-convex secrecy sum rate maximization as an unconstrained optimization on a product manifold. Building on this formulation, we further develop a product Riemannian gradient descent (PRGD) algorithm with guaranteed stationary convergence. Simulation results demonstrate that the proposed scheme effectively resolves the OFDM coupling issue and achieves significant secrecy rate gains, outperforming single-IRS and distributed multi-IRS benchmarks by 32.0% and 22.3%, respectively.

Enhancing Physical Layer Security in MIMO Systems Assisted by Beyond-Diagonal Reconfigurable Intelligent Surfaces

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.

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.

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.

Role of scrambling and noise in temporal information processing with quantum systems

Scrambling quantum systems have been demonstrated as effective substrates for temporal information processing. While their role in providing rich feature maps has been widely studied, a theoretical understanding of their performance in temporal tasks is still lacking. Here we consider a general quantum reservoir processing framework that captures a broad range of physical computing models with quantum systems. We examine the scalability and memory retention of the model with scrambling reservoirs modelled by high-order unitary designs in both noiseless and noisy settings. In the former regime, we show that measurement readouts become exponentially concentrated with increasing reservoir size, yet strikingly do not worsen with the reservoir iterations. Thus, while repeatedly reusing a small scrambling reservoir with quantum data might be viable, scaling up the problem size deteriorates generalization unless one can afford an exponential shot overhead. In contrast, the memory of early inputs and initial states decays exponentially in both reservoir size and reservoir iterations. In the noisy regime, we also prove exponential memory decays with iterations for local noisy channels. Proving these results required us to introduce new proof techniques for bounding concentration in temporal quantum learning models.

On fundamental aspects of quantum extreme learning machines

Quantum Extreme Learning Machines (QELMs) have emerged as a promising framework for quantum machine learning. Their appeal lies in the rich feature map induced by the dynamics of a quantum substrate - the quantum reservoir - and the efficient post-measurement training via linear regression. Here we study the expressivity of QELMs by decomposing the prediction of QELMs into a Fourier series. We show that the achievable Fourier frequencies are determined by the data encoding scheme, while Fourier coefficients depend on both the reservoir and the measurement. Notably, the expressivity of QELMs is fundamentally limited by the number of Fourier frequencies and the number of observables, while the complexity of the prediction hinges on the reservoir. As a cautionary note on scalability, we identify four sources that can lead to the exponential concentration of the observables as the system size grows (randomness, hardware noise, entanglement, and global measurements) and show how this can turn QELMs into useless input-agnostic oracles. Our analysis elucidates the potential and fundamental limitations of QELMs, and lays the groundwork for systematically exploring quantum reservoir systems for other machine learning tasks.