Passive RIS Is Not Silent: Revisiting Performance Limits Under Thermal Noise

1. Problem Statement

Reconfigurable Intelligent Surfaces (RIS) are a cornerstone technology for 6G networks, promising energy-efficient and flexible spectrum usage. A prevailing assumption in existing literature is that passive RIS elements are noiseless because they lack active circuitry (amplifiers). Consequently, most performance evaluations ignore the thermal noise generated by these passive components.

The authors argue that this assumption is physically incorrect. According to the Johnson–Nyquist theorem, every passive resistive component inherently generates thermal noise ($kTB$). Neglecting this noise leads to:

• Overly optimistic performance predictions.
• Misleading design choices regarding RIS deployment (e.g., element count and placement).
• An inaccurate understanding of the trade-offs between signal gain and noise introduction, particularly when the RIS is in close proximity to the receiver.

2. Methodology

The paper proposes a rigorous physical model and analytical framework to quantify the impact of RIS-induced thermal noise.

• System Model:

  • A Base Station (BS) communicates with a single-antenna receiver via a passive RIS with $N$ elements.
  • The direct link is blocked; communication relies entirely on the RIS.
  • Channels follow a Nakagami-$m$ fading model.
  • Noise Modeling:
    • Receiver Noise: Modeled as $J = kTB \cdot NF$ (where $NF$ is the noise figure).
    • RIS Noise: Each of the $N$ elements generates thermal noise power $kTB$. The aggregate noise power is scaled by the reflection efficiency $\alpha$ (where $0 \le \alpha \le 1$). The total RIS noise power is $J_R = N \alpha kTB$.
    • The received signal model explicitly includes a term for the RIS-generated noise vector $\omega_r$, which is reflected along with the signal.

• Analytical Framework:

  • The authors derive the Signal-to-Interference-plus-Noise Ratio (SINR), noting that the noise term is multiplied by the random channel gains, making the analysis complex.
  • To make the analysis tractable, they derive Lower Bound (LB) and Upper Bound (UB) approximations for the SINR.
  • Using these bounds, they derive closed-form expressions for the Outage Probability ($P_{Od}$) and Throughput.
  • The derivation utilizes Meijer-G functions and asymptotic analysis to handle the statistical properties of the cascaded fading channels.

3. Key Contributions

1. First Physically Grounded Noise Model for Passive RIS: Unlike previous studies that either ignored noise or treated it ad-hoc, this paper links RIS noise power directly to fundamental physical constants ($k$, $T$, $B$) and the number of elements ($N$).
2. Closed-Form Performance Metrics: The paper provides tractable analytical expressions for outage probability and throughput that incorporate RIS thermal noise, validated by Monte Carlo simulations.
3. Identification of Critical Trade-offs: The study reveals a counter-intuitive phenomenon where increasing the number of RIS elements ($N$) can degrade performance if the thermal noise contribution becomes dominant over the signal gain, particularly in low transmit power regimes or short distances.
4. Asymptotic Analysis: The authors derive the diversity order of the system, showing how RIS noise affects the slope of the outage probability curve at high SNR.

4. Key Results

The simulation results, validated against the derived analytical bounds, highlight several critical findings:

• Significant Performance Overestimation: Ignoring RIS thermal noise leads to a substantial overestimation of system performance.
  • For $N=5$, the error is approximately 5 dB.
  • For $N=10$, the error widens to approximately 12 dB.
  • This discrepancy grows as the number of RIS elements increases.
• Distance Dependency: The impact of RIS thermal noise is highly dependent on the distance between the RIS and the receiver ($d_{RIS-Rec}$) and the receiver's own noise floor ($\sigma_d^2$).
  • Low Receiver Noise: If the receiver is very quiet (e.g., $\sigma_d^2 = -128$ dB), RIS thermal noise significantly impacts throughput up to 30 meters.
  • High Receiver Noise: If the receiver noise is higher (e.g., $\sigma_d^2 = -110$ dB), the RIS noise becomes negligible even at short distances (15 meters) because it is "drowned out" by the receiver's own noise.
• Diminishing Returns on $N$: Increasing $N$ does not always improve energy efficiency. In scenarios where RIS noise is significant, increasing $N$ from 5 to 10 yielded only a 3 dB improvement (when noise is considered) compared to an 8.4 dB improvement (when noise is ignored).
• Approximation Limits: The derived analytical bounds are tight for moderate distances (up to 5 meters) but show deviation at larger distances (8 meters) due to the behavior of the parameter $\lambda$ (the ratio of RIS noise to receiver noise).

5. Significance and Implications

This paper fundamentally challenges the "noise-free black box" paradigm of passive RIS in 6G research. Its significance lies in:

• Realistic Deployment Strategies: It suggests that RIS deployment must be context-aware. In ultra-low-noise environments or when the RIS is very close to the user, the thermal noise penalty may outweigh the beamforming gains.
• Design Optimization: It prompts a re-evaluation of RIS element design. Future designs may need to optimize the reflection efficiency ($\alpha$) to balance signal reflection against thermal noise generation, or develop new materials/circuits to minimize resistive losses.
• Theoretical Correction: It highlights the need for new mathematical frameworks that move beyond simple bounding techniques to accurately model the correlation between signal and noise in passive RIS systems, especially for large-scale deployments.

In conclusion, the authors assert that passive RIS is not silent. Ignoring thermal noise leads to flawed performance evaluations, and future 6G systems must account for this physical reality to achieve robust and efficient network designs.