⚡ electrical engineering

Near-field Liquid Crystal RIS Phase-Shift Design for Secure Wideband Illumination

This paper proposes a near-field phase-shift design for liquid crystal-based reconfigurable intelligent surfaces in wideband OFDM systems that accounts for frequency-dependent responses to securely illuminate legitimate users while minimizing information leakage to eavesdroppers, thereby achieving a significant secrecy rate without requiring full channel state information.

Original authors: Mohamadreza Delbari, Qikai Zhou, Robin Neuder, Alejandro Jiménez-Sáez, Vahid Jamali

Published 2026-07-27

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CC BY 4.0

Original authors: Mohamadreza Delbari, Qikai Zhou, Robin Neuder, Alejandro Jiménez-Sáez, Vahid Jamali

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the air around us is filled with invisible radio waves, carrying our texts, videos, and calls. For decades, we've treated these waves like wild horses: we build tall towers to shout at them, hoping they reach the right house, but often they get lost, bounce off the wrong buildings, or get stolen by eavesdroppers hiding in the shadows. In recent years, scientists have discovered a way to tame these wild horses using "Reconfigurable Intelligent Surfaces" (RIS). Think of an RIS as a giant, magical mirror made of thousands of tiny, programmable tiles. Instead of just reflecting light like a bathroom mirror, this smart mirror can twist and turn the radio waves, steering them exactly where we want them to go, like a conductor directing an orchestra of sound.

However, there's a catch. Most of these smart mirrors are built using a special material called Liquid Crystal (the same stuff found in your digital watch or phone screen). While these mirrors are great at saving energy, they have a quirky personality: they behave differently depending on the "pitch" of the radio wave. If you play a low note, the mirror bends it one way; if you play a high note, it bends it another. This is a huge problem for modern internet, which uses a technique called OFDM to send data across a wide range of frequencies all at once, like a choir singing many notes simultaneously. If the mirror doesn't know how to handle the whole choir, the song gets distorted, and worse, secret messages meant for you might accidentally leak out to a spy listening nearby.

This paper tackles that exact problem. The authors, working at the Technical University of Darmstadt, designed a new way to program these liquid crystal mirrors so they can handle wideband signals securely. They realized that if you try to tune the mirror for just one specific frequency (like tuning a radio to one station), the other frequencies in the signal will get messed up, creating "beam splitting" where the signal leaks into the wrong areas. To fix this, they created a smart algorithm that accounts for how the mirror's behavior changes across the entire frequency range. Instead of just aiming for the center of the signal band, their method ensures the signal stays strong and focused on the intended users while staying weak and hidden from potential eavesdroppers, even when the exact location of the spy isn't known perfectly.

In their simulations, the team tested their idea in a scenario where a base station sends data to a group of users in a specific area while trying to keep a mobile eavesdropper in the dark. They compared their new "frequency-aware" method against three older approaches: one that ignored the mirror's quirks entirely, one that only tuned for the center frequency, and one that assumed they knew the spy's exact location. The results were clear. In a setup with an 8 GHz bandwidth centered at 60 GHz, their proposed method achieved a secrecy rate of about 2 bits per symbol. This means that by acknowledging the mirror's frequency-dependent nature, they successfully kept the signal focused on the good guys and minimized the "leakage" to the bad guys, proving that understanding the hardware's limitations is key to building a secure, high-speed wireless future.

Technical Summary: Near-field Liquid Crystal RIS Phase-Shift Design for Secure Wideband Illumination

Problem Statement
Reconfigurable Intelligent Surfaces (RISs) utilizing Liquid Crystal (LC) technology offer a low-power, scalable solution for future wireless communications, particularly in millimeter-wave (mmWave) bands. However, a critical limitation of LC-based RISs is their inherent frequency-dependent phase-shift response. In wideband systems, such as those employing Orthogonal Frequency Division Multiplexing (OFDM), this frequency dependency can lead to significant performance degradation. This issue is particularly acute in physical layer security scenarios, where unintended variations in the beam pattern may cause information leakage to eavesdroppers. Existing literature often assumes idealized RIS models with frequency-independent phase shifts or relies on precise, instantaneous Channel State Information (CSI) and exact user locations, which are often unavailable in practical, dynamic environments.

Methodology
The authors propose a novel optimization framework for designing RIS phase shifts in a wideband downlink scenario involving a Base Station (BS), an LC-RIS, multiple legitimate Mobile Users (MUs), and a mobile eavesdropper. The system operates under the following constraints and assumptions:

Channel Model: The direct links between the BS and users/eavesdropper are blocked; communication relies on RIS-reflected Line-of-Sight (LOS) paths modeled with Rician fading.
Uncertainty: The exact locations and instantaneous CSI of both legitimate users and the eavesdropper are unknown. Instead, the system only knows their approximate locations within specific spatial regions ( $P_u$ for users and $P_e$ for eavesdroppers).
Frequency Dependency: The phase shift of each LC element is modeled as a function of frequency. Specifically, the phase shift at any subcarrier $f_k$ is linearly scaled relative to the phase shift at the center frequency $f_c$ , governed by a frequency-dependent factor $\beta_k$ .

The core objective is to maximize the worst-case secrecy rate across all subcarriers and all possible user/eavesdropper locations within their respective regions. The authors formulate this as a non-convex optimization problem (P1) involving the RIS phase shifts and the BS beamformer. To solve this, they employ an Alternating Optimization (AO) approach:

Beamformer Design: For a fixed RIS configuration, the optimal beamformer is derived based on the LOS component at the center frequency, justified by the observation that beam squinting is negligible for the considered BS antenna counts.
RIS Phase-Shift Design: For a fixed beamformer, the problem is reformulated using Semidefinite Programming (SDP). The non-convex rank-one constraint and the Hadamard power constraint (arising from the frequency scaling) are addressed using a penalty method and first-order Taylor approximations. This results in an iterative algorithm (Algorithm 1) that converges to a sub-optimal solution.

Key Contributions
The paper makes the following specific contributions:

Frequency-Dependent Modeling: The authors develop a model characterizing how the phase-shift response of LC-RIS elements varies with frequency, deriving a scaling relationship that links phase shifts across subcarriers to a reference phase shift at the center frequency.
Robust Secrecy Setup: A novel security scenario is introduced where the RIS must ensure secure illumination for users in a designated area while suppressing signals in an eavesdropper's potential region, without requiring exact location or CSI knowledge.
Optimization Framework: A non-convex optimization problem is formulated and solved via a sub-optimal algorithm based on rank relaxation and semidefinite programming, explicitly accounting for the hardware-limited frequency response of LC elements.
Performance Validation: The proposed method is evaluated against three benchmark schemes that neglect frequency dependency, use only center-frequency optimization, or rely on exact location knowledge.

Results
Simulation results, conducted with a center frequency of 60 GHz and a bandwidth of 8 GHz, demonstrate the efficacy of the proposed approach:

Secrecy Rate: The proposed algorithm achieves a secrecy rate of approximately 2 bits/symbol across the 8 GHz bandwidth. This significantly outperforms benchmark methods that ignore frequency-dependent effects or rely on center-frequency-only designs.
Spatial Distribution: Heat maps of the Signal-to-Noise Ratio (SNR) at 57 GHz show that the proposed method maintains a uniform SNR within the desired user coverage area while effectively minimizing SNR in the eavesdropper region. In contrast, benchmark methods exhibit beam splitting or non-uniform coverage, leading to increased leakage or reduced user performance.
Robustness: The method successfully handles the uncertainty in user and eavesdropper locations, ensuring security even in worst-case scenarios within the defined regions.

Significance
The paper claims that its primary significance lies in bridging the gap between theoretical wideband beamforming and the practical hardware limitations of LC-RIS technology. By explicitly modeling and optimizing for the frequency-dependent behavior of LC elements, the proposed method prevents the performance degradation and information leakage associated with wideband operation. The authors note that, to their knowledge, this is the first investigation into the frequency-dependency of LC-RISs in a wideband secure communication scenario. The work highlights that neglecting these hardware-specific frequency characteristics can lead to considerable security risks, and that accounting for them is essential for realizing secure, wideband RIS-assisted systems.

Technical Summary: Near-field Liquid Crystal RIS Phase-Shift Design for Secure Wideband Illumination

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