⚡ electrical engineering

Temperature-aware Optimization of Liquid Crystal Reconfigurable Intelligent Surfaces: Physics-based Modeling and Robust Design

This paper proposes a physics-based, temperature-aware optimization framework for Liquid Crystal Reconfigurable Intelligent Surfaces (LC-RIS) that ensures secure mmWave communication by employing robust phase-shift designs which mitigate thermal sensitivity and channel state information overhead without requiring real-time temperature data.

Original authors: Mohamadreza Delbari, Bowu Wang, Arash Asadi, Vahid Jamali

Published 2026-07-27

📖 7 min read🧠 Deep dive

CC BY 4.0

Original authors: Mohamadreza Delbari, Bowu Wang, Arash Asadi, 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 tried to control these waves by building bigger towers or adding more antennas, but there's a smarter way: changing the air itself. Enter the Reconfigurable Intelligent Surface (RIS). Think of it as a giant, high-tech mirror made of thousands of tiny, programmable tiles. Instead of just reflecting light like a bathroom mirror, an RIS can twist and turn radio waves, steering them exactly where we want them to go—like a conductor directing an orchestra of invisible sound.

One of the most promising materials for building these mirrors is Liquid Crystal (LC), the same stuff found in your digital watch or smartphone screen. It's cheap, energy-efficient, and perfect for the super-fast millimeter-wave frequencies that future 6G networks will use. However, there's a catch: liquid crystals are sensitive to heat. Just like how a hot day might make a rubber band stretch out or a chocolate bar melt, changing the temperature changes how these liquid crystal molecules line up. This means the "mirror" might not reflect the signal exactly as planned if the weather gets too hot or too cold, potentially causing the signal to leak to the wrong place.

This paper tackles that exact problem. The authors, Mohamadreza Delbari and his team, realized that if we ignore the temperature, our super-smart mirrors could accidentally help eavesdroppers steal our data. They developed a new way to design these mirrors that either adapts to the current temperature or is built to be "tough" enough to work well even if we don't know the exact temperature. Through detailed computer simulations, they showed that their new designs keep secrets safe and signals strong, even when the weather changes, whereas old designs that ignore heat start to fail.

The Heat Problem with Smart Mirrors

To understand why this matters, let's look at how these liquid crystal mirrors work. Inside the RIS, there are millions of tiny cells. Each cell can be tweaked with a voltage to change the phase of the passing radio wave—basically, deciding exactly when the wave should bounce off. In a perfect world, you could twist the wave anywhere from 0 to a full circle (360 degrees, or $2\pi$ radians). But here's the physics twist: the ability of the liquid crystal to twist depends on how ordered its molecules are.

When it's cold, the molecules are very orderly, like soldiers standing in perfect rows. When it gets hot, they start to jitter and wiggle, like a crowd at a mosh pit. This jitter reduces the maximum amount the mirror can twist the wave. The authors created a physics-based model to show that as the temperature rises, the maximum twist range shrinks. If the temperature gets too high, the mirror might only be able to twist the wave by, say, 270 degrees instead of a full 360. If the system tries to use a twist that is now impossible because of the heat, the signal gets distorted.

This distortion is a nightmare for security. In a secure wireless system, the goal is to boost the signal for the person you're talking to (the "legitimate user") while making it as weak as possible for anyone listening in (the "eavesdropper"). If the mirror gets hot and the phase shifts go wrong, the "weak" signal meant for the eavesdropper might accidentally get stronger, leaking your private information.

The Solution: Adapting and Being Robust

The paper proposes two clever strategies to fix this, depending on what information the system has.

1. The Temperature-Adaptive Approach
Imagine you are driving a car with a smart cruise control that knows the exact temperature outside and adjusts the engine instantly. This is the "temperature-adaptive" design. If the RIS has sensors telling it, "Hey, it's 40°C right now," the system recalculates the perfect settings for the mirror tiles based on that specific heat. The authors developed a complex mathematical method (using something called Semi-Definite Programming, or SDP) to find the best settings. They also created a faster, simpler method that works almost as well but is much quicker to calculate. Their simulations showed that when the temperature changes, this adaptive method keeps the secret communication safe, while a standard design that ignores the heat sees its security drop significantly.

2. The Temperature-Robust Approach
But what if the mirror doesn't have a thermometer? What if we can't know the exact temperature in real-time? This is where the "temperature-robust" design comes in. Instead of reacting to the heat, this design is built to be tough. The authors asked a different question: "What is the single best setting for the mirror that will work okay across a whole range of temperatures, from freezing cold to scorching hot?"

They designed an algorithm that looks at all possible temperatures at once and finds a "safe zone" setting. It's like packing a suitcase for a trip where you don't know the weather; you bring layers that work whether it's 10°C or 30°C. The simulations showed that this robust design maintains a high level of security across all temperatures, even without knowing the exact heat level at any given moment. It doesn't perform quite as perfectly as the adaptive version (which knows the exact temp), but it's far better than doing nothing.

What the Numbers Say

The team tested these ideas using a simulated environment. They imagined a base station sending signals to a user while an eavesdropper tried to listen in. They used a 60 GHz carrier frequency (a very fast, high-speed connection) and a RIS with up to 400 elements (tiles).

The results were clear:

Ignoring heat is bad: When they used a standard design that didn't account for temperature, the "secrecy rate" (a measure of how secure the connection is) dropped sharply as the temperature moved away from the design point. At 40°C, the security was much worse than at the reference temperature of 10°C.
Adapting works: The temperature-adaptive design kept the secrecy rate high and steady, no matter the temperature.
Robustness holds up: The temperature-robust design also kept the secrecy rate high across the entire range, proving you don't need a thermometer to stay secure; you just need a smart design.

They also compared their two calculation methods. The "SDP-based" method was like a super-precise calculator that took hours to solve for large mirrors (400 elements). The new "low-complexity" method they invented was like a lightning-fast calculator, solving the same problem in just 7 seconds with almost the same accuracy. This speed is crucial because real-world mirrors might have thousands of elements, and waiting hours for a solution isn't practical.

The Bottom Line

This paper doesn't just say "heat is a problem"; it proves that ignoring the temperature in liquid crystal mirrors can lead to security leaks. By creating models that understand how heat messes with the molecules, and then designing algorithms that either adapt to the heat or are tough enough to ignore it, the authors have made a significant step toward making these smart mirrors practical for the real world. Their work suggests that for the next generation of wireless networks to be truly secure, we can't just look at the signal; we have to look at the weather, too.

Technical Summary: Temperature-aware Optimization of Liquid Crystal Reconfigurable Intelligent Surfaces

Problem Statement
Liquid Crystal (LC) technology offers a cost-effective and energy-efficient solution for implementing Reconfigurable Intelligent Surfaces (RISs), particularly for millimeter-wave (mmWave) communications. However, the phase-shift response of LC-based RISs is inherently temperature-dependent due to the thermal fluctuations of LC molecules. Neglecting this dependency can lead to significant performance degradation, specifically in physical layer security contexts where phase-shift inaccuracies may cause unintended information leakage to eavesdroppers. Furthermore, the massive number of elements required for mmWave RISs to compensate for path loss makes full Channel State Information (CSI) acquisition impractical. Existing literature has not sufficiently addressed the impact of temperature variations on the physical layer security of LC-RIS-assisted systems, nor has it provided scalable optimization methods that operate without precise CSI or real-time temperature data.

Methodology
The paper proposes a framework for secure communication in LC-RIS-aided systems that accounts for thermal dynamics and location uncertainties.

Physics-Based Modeling: The authors derive a physics-based model characterizing the temperature-dependent phase-shift response of LC elements. Using the Maier-Saupe mean-field theory and the Haller approximation, they quantify how the maximum achievable phase shift range ( $\Delta\omega_{max}$ ) decreases as temperature rises above a reference baseline. The model establishes a relationship between the applied voltage, temperature, and the resulting phase shift.
System Model: The system consists of a Base Station (BS), a legitimate Mobile User (MU), and a Mobile Eavesdropper (ME). The RIS is assumed to be in the near-field (NF) of the BS and users, modeled using a generalized spherical wave Rician channel. The direct BS-to-user links are assumed blocked, making the RIS the primary communication path.
Optimization Formulation: The authors formulate two non-convex optimization problems to maximize the secrecy rate:
- Temperature-Adaptive Design: Optimizes phase shifts assuming the instantaneous operating temperature is known.
- Temperature-Robust Design: Optimizes a single static phase-shift configuration that guarantees high secrecy rates across a predefined range of temperatures, eliminating the need for real-time thermal tracking.
  Both formulations assume only approximate spatial zones for the MU and ME are known, rather than exact locations or full CSI.
Algorithmic Solutions:
- SDP-based Approach: A high-performance benchmark using Semi-Definite Programming (SDP) with a penalty method to handle rank constraints and non-convex phase limits. This approach has cubic complexity ( $O(N^3)$ ) relative to the number of RIS elements.
- Low-Complexity Scalable Approach: A heuristic method utilizing algebraic reformulations, surrogate lower bounds (Log-Sum-Exp approximation), and alternating optimization. This method reduces complexity to linear scaling ( $O(N)$ ), making it suitable for extremely large RIS deployments.

Key Contributions

Thermal Characterization: The paper rigorously derives a physics-based model linking temperature fluctuations to the phase-shift profile of LC-RIS elements, demonstrating that thermal variations reduce the achievable differential phase-shift range.
Robust Problem Formulation: It introduces optimization problems for both temperature-adaptive and temperature-robust designs that rely solely on approximate user/eavesdropper vicinity data, addressing the impracticality of full CSI acquisition in large-scale mmWave systems.
Scalable Algorithms: The authors propose a low-complexity algorithm that maintains high performance while scaling linearly with the number of RIS elements, a critical advancement for deploying massive surfaces in dynamic environments.
Temperature-Robust Design: A novel design is presented that maintains high security without requiring prior knowledge of the operating temperature, ensuring reliability in unpredictable environmental conditions.

Results
Extensive simulations validate the proposed framework:

Convergence and Complexity: The SDP-based method converges to rank-one solutions but requires hours for large RIS arrays (e.g., $N=400$ ). In contrast, the scalable method converges rapidly (seconds) with linear complexity, making it feasible for real-time applications.
Performance Impact of Temperature: Simulations show that neglecting temperature effects leads to a significant drop in secrecy rate as the operating temperature deviates from the design reference. Specifically, ignoring thermal variations causes signal strength to increase in the eavesdropper's vicinity, compromising security.
Effectiveness of Proposed Designs: The temperature-adaptive design significantly outperforms conventional designs that ignore thermal effects across various temperatures. The temperature-robust design achieves a consistently high secrecy rate across all tested temperature profiles without requiring real-time temperature feedback.
Scenario Analysis: The proposed methods are effective in both "Same Distance, Different Angles" and "Different Distance, Same Angle" eavesdropper scenarios, with the near-field operation providing additional degrees of freedom to secure the link.

Significance
The paper claims that its work is the first to investigate physical layer security in LC-RIS-assisted systems specifically considering the impact of temperature variations. It highlights that while LC technology is promising for scalable RISs, its thermal sensitivity must be addressed to prevent security vulnerabilities. By providing both a high-accuracy benchmark and a scalable, low-complexity solution, the work enables the practical deployment of secure, large-scale LC-RISs in dynamic, real-world environments where temperature and user locations are uncertain. The proposed robust design further removes the hardware and signaling overhead associated with real-time thermal sensing, offering a viable path for secure mmWave communications.

The Heat Problem with Smart Mirrors

The Solution: Adapting and Being Robust

What the Numbers Say

The Bottom Line

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