⚡ electrical engineering

Rethinking Passive RIS: Finite Blocklength Reliability Analysis Under Thermal Noise

This paper presents a unified analytical framework for RIS-assisted short-packet communications in the finite blocklength regime that explicitly accounts for thermal noise, revealing that neglecting this effect significantly overestimates reliability and demonstrating that increasing RIS size can degrade performance in low-power scenarios due to accumulated noise.

Original authors: Farjam Karim, Deepak Kumar, Prathapasinghe Dharmawansa, Nurul Huda Mahmood, Arthur Sousa de Sena, Matti Latva-aho

Published 2026-05-22

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CC BY 4.0

Original authors: Farjam Karim, Deepak Kumar, Prathapasinghe Dharmawansa, Nurul Huda Mahmood, Arthur Sousa de Sena, Matti Latva-aho

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 you are trying to send a very short, urgent text message (like "Stop!" or "Help!") across a city using a giant wall of mirrors. This wall is a Reconfigurable Intelligent Surface (RIS). Instead of building a new tower, you use this smart wall to bounce your signal around obstacles to reach the receiver.

For a long time, engineers assumed these mirrors were perfect. They thought: "If we add more mirrors, the signal gets stronger and stronger, and the message arrives perfectly every time." They treated the mirrors like magic, silent reflectors that added no problems of their own.

The Big Discovery: The Mirrors Aren't Silent
This paper says that assumption is wrong. In the real world, these mirrors aren't just passive glass; they are physical objects that get warm and generate their own tiny bit of static noise (called thermal noise), just like a hot cup of coffee radiates heat.

The authors found that when you use a lot of these mirrors (which is the goal for 6G networks), this "mirror noise" adds up. It's like trying to hear a whisper in a room where everyone is whispering back at you. The more mirrors you add, the louder the background static becomes, eventually drowning out the signal you were trying to boost.

The "Short Message" Problem
Most old math for these systems assumes you are sending long, slow movies (infinite blocklength). But 6G is about sending short, fast packets (like a quick text).

The Old View: "Add 1,000 mirrors, and your connection will be perfect."
The New Reality: "If you add 1,000 mirrors but ignore the static noise they create, you will think your connection is perfect when it's actually failing. The more mirrors you add, the bigger the gap between your prediction and reality."

Key Findings in Plain English

The "Too Many Mirrors" Trap:
The paper shows that simply making the RIS bigger doesn't always help. If you are sending a weak signal (low power), adding more mirrors actually makes things worse because the accumulated noise from all those mirrors becomes louder than the signal itself. It's like trying to amplify a whisper by shouting through a megaphone that has a broken speaker; the noise drowns out the voice.
The "Optimism" Error:
If engineers ignore this mirror noise, they will wildly overestimate how reliable their system is.
- Example: To get a reliable connection, the paper found you might need 10 to 15 times more power than old models predicted if you have a large number of mirrors. Ignoring the noise makes you think you can get away with very little power, which leads to failed connections in the real world.
Uniform vs. Mixed Mirrors:
The team tested two scenarios:
- Uniform: All mirrors are set to the same strength.
- Non-Uniform: Some mirrors are set stronger, some weaker.
- Result: It turns out, having a mix of strengths doesn't change the outcome much. The "average" strength is usually enough to predict what will happen.
The Speed vs. Reliability Trade-off:
When sending short messages, there is a limit to how much you can improve things by waiting longer. The paper shows that if you ignore the mirror noise, you might think you can send data very quickly and reliably. But once you include the noise, you realize you need to send much longer messages to get the same reliability, which defeats the purpose of "low latency" (speed) applications.

The Bottom Line
This paper is a reality check for the future of wireless networks. It tells us that passive mirrors aren't magic; they are physical devices that generate noise.

If we want to build reliable 6G networks using these giant smart walls, we can't just keep adding more mirrors and hoping for the best. We have to design our systems knowing that the mirrors themselves will add static. If we don't, we will build systems that look great on paper but fail in the real world.

Technical Summary: Rethinking Passive RIS: Finite Blocklength Reliability Analysis Under Thermal Noise

Problem Statement
Reconfigurable Intelligent Surfaces (RIS) are a pivotal technology for 6G networks, promising enhanced coverage and reliability with low energy consumption. However, existing literature predominantly models passive RIS elements under idealized, noise-free assumptions. This simplification ignores the thermal noise generated by the ohmic losses of passive elements, a phenomenon governed by the Johnson-Nyquist theorem. While previous work by the authors addressed this in the infinite blocklength regime, emerging 6G applications—such as ultra-reliable low-latency communications (URLLC) and Internet-of-Things (IoT)—operate in the finite blocklength (FBL) regime. In this regime, conventional asymptotic performance metrics (e.g., Shannon capacity) are insufficient for accurate reliability characterization. Furthermore, the impact of accumulated RIS thermal noise under short-packet transmission constraints remains unquantified, potentially leading to overly optimistic system evaluations.

Methodology
The authors develop a unified analytical framework to characterize the performance of RIS-assisted systems in the FBL regime while explicitly incorporating thermal noise. The system model consists of a single-antenna transmitter and receiver connected via a passive RIS with $N$ reflecting elements, assuming the direct link is obstructed.

Key methodological components include:

Noise Modeling: The study adopts a physically grounded model where RIS elements generate thermal noise proportional to their reflection coefficients ( $\beta_n$ ), bandwidth ( $B$ ), and temperature ( $T$ ). The total RIS-induced noise power scales linearly with the number of elements and their reflection efficiency.
Signal-to-Interference-plus-Noise Ratio (SINR): The authors derive SINR expressions for both uniform reflection coefficients ( $\beta_n = \beta$ ) and non-uniform configurations, accounting for the interference caused by RIS-generated noise re-radiation.
Finite Blocklength Analysis: Utilizing the normal approximation for the block-error rate (BLER), the paper derives closed-form expressions for BLER and goodput over Nakagami- $m$ fading channels. The analysis employs piecewise linear approximations of the Q-function and moment-matching techniques to handle the statistical distributions of the signal and noise terms.
Asymptotic Characterization: To provide deeper insights, the authors derive asymptotic BLER expressions for high Signal-to-Noise Ratio (SNR) scenarios, identifying the diversity orders for both uniform and non-uniform reflection cases.

Key Contributions

Thermal-Aware FBL Framework: The work establishes the first thermal-noise-aware communication framework for passive RIS specifically within the finite blocklength regime, capturing the joint impact of noise and short-packet constraints.
Analytical Expressions: Closed-form expressions are derived for BLER, asymptotic BLER, and goodput under both uniform and non-uniform RIS reflection configurations.
Generalized Reflection Model: The analysis extends beyond the common uniform assumption to include non-uniform reflection coefficients, offering a more realistic design perspective.
Validation: Monte Carlo simulations are conducted to validate the derived analytical expressions against numerical results.

Results
Numerical results demonstrate that neglecting RIS thermal noise leads to a significant overestimation of system reliability.

Impact of Element Count: As the number of reflecting elements ( $N$ ) increases, the discrepancy between noise-free models and thermal-noise-aware models widens. For instance, achieving a BLER of $10^{-4}$ with $N=20$ requires approximately 15 dB more transmit power when thermal noise is considered compared to when it is ignored.
Diminishing Returns: Increasing the RIS size does not always yield performance improvements. In low transmit power regimes, the accumulated thermal noise from a larger number of elements can become dominant, offsetting the signal gain. In some cases, a configuration with fewer elements ( $N=10$ ) outperforms a larger one ( $N=20$ ) due to lower noise accumulation.
Goodput Saturation: The presence of thermal noise significantly shifts the saturation point of goodput versus blocklength. While a noise-free system might saturate around a blocklength of 2,000, a system with thermal noise may require a blocklength near 10,000 to achieve similar saturation, which contradicts the low-latency requirements of URLLC.
Uniform vs. Non-Uniform: The performance difference between uniform and non-uniform reflection coefficients is found to be marginal, suggesting that average reflection values can effectively approximate non-uniform scenarios.

Significance
The paper argues that the idealized noise-free assumption for passive RIS is fundamentally flawed for accurate system evaluation, particularly in large-scale deployments and short-packet communications. The findings highlight that ignoring RIS thermal noise results in misleading predictions of reliability and energy efficiency gains. The authors conclude that for realistic performance assessment, especially in 6G systems targeting stringent latency and reliability, the thermal noise generated by passive elements must be explicitly incorporated into the system model. This work provides the necessary analytical tools to evaluate these limitations and guides the design of practical RIS-assisted networks.

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