🔢 mathematics

Fluid Antenna-Aided Noise Modulation: Spatial Diversity for Variance-Based Wireless Communication

This paper demonstrates that equipping a variance-based NoiseMod receiver with a fluid antenna system restores spatial diversity to combat Rayleigh fading, achieving a bit error probability that improves with the number of ports until saturation, while revealing an intrinsic error floor determined solely by the noise sample count and variance ratio.

Original authors: Hadi Zayyani, Felipe A. P. de Figueiredo, Pedro M. R. Pereira, Fernando D. A. García, Rausley A. A. de Souza

Published 2026-08-18

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Hadi Zayyani, Felipe A. P. de Figueiredo, Pedro M. R. Pereira, Fernando D. A. García, Rausley A. A. de Souza

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

In the world of wireless communication, information usually travels by riding on a steady, predictable wave. Think of a lighthouse beam that flashes in a specific pattern to send a message; the receiver watches the light's brightness, color, or timing to decode the signal. For over a century, engineers have treated random static, or noise, as an enemy to be crushed, a chaotic interference that ruins the clarity of the message. But a different approach, known as noise modulation, flips this idea on its head. Instead of hiding information in a clean signal, it hides the message inside the very statistics of the noise itself. By carefully controlling how much the noise fluctuates—making it slightly more or less chaotic—the transmitter can send a "0" or a "1." This method is incredibly efficient and hard to detect, making it perfect for tiny, battery-powered sensors or secret communications. However, this clever trick has a fatal flaw: when the signal passes through the atmosphere or around obstacles, it fades, and because the message is hidden in the noise's variance, standard fading destroys the ability to read it. The message doesn't just get quieter; it gets unreadable, no matter how much power is used.

To solve this, researchers have been exploring a technology called fluid antennas. Unlike a traditional radio tower with a fixed dish, a fluid antenna is a single, flexible wire that can instantly switch its connection point to any of many small ports along its length. Imagine a long, thin hose with hundreds of tiny nozzles; if the water pressure drops at one nozzle, the system can instantly switch to another nozzle a few inches away where the pressure is better. This allows a single antenna to harvest "spatial diversity," finding the strongest signal path without needing multiple bulky antennas. While this technique has been studied for standard signals, it had never been tested against the unique challenges of noise modulation. A team of researchers set out to combine these two ideas, asking whether a fluid antenna could rescue the fragile noise-based signal from the ravages of fading.

The team built a theoretical model where a receiver uses a fluid antenna to scan through its available ports and instantly lock onto the one with the strongest signal envelope before trying to decode the message. They ran extensive computer simulations to see how well this system would perform under different conditions, specifically looking at how the number of ports and the physical length of the antenna affected the error rate. Their findings revealed a powerful recovery. When the antenna ports were far enough apart to be independent of each other, adding more ports dramatically improved the reliability of the connection. The error rate, which usually stays stubbornly high for noise modulation, began to drop sharply as more ports were added, effectively restoring the signal's resilience. This confirmed that the fluid antenna could indeed provide the diversity needed to make noise modulation viable in real-world environments.

However, the researchers also discovered a hard limit to this improvement. In the real world, the ports on a fluid antenna are often close together, meaning they are correlated; they tend to experience the same fading at the same time. The simulations showed that once the physical size of the antenna was fixed, adding more ports beyond a certain point stopped helping. If the antenna was too short, the extra ports were just listening to the same bad signal as the first few, offering no new information. The performance would hit a floor and stop improving, regardless of how many ports were added. This saturation effect mirrored what was known about fluid antennas in other contexts, but here it was observed specifically for the error rate of noise-based signals.

Perhaps the most surprising discovery was an intrinsic limit that no amount of antenna switching could overcome. Even with a perfect antenna that never fades, the system still has a minimum error rate determined by how many samples of noise are used to make the decision. If the receiver only looks at a small number of noise samples, it cannot perfectly distinguish between the two types of signals, no matter how strong the signal is. This creates a fundamental "floor" for the error rate that is set purely by the design of the noise itself, not by the antenna. While the fluid antenna could push the performance far below what was previously thought possible for noise modulation, it could not eliminate this final barrier. The study concludes that fluid antennas offer a low-complexity, instant way to boost these systems, but they must be paired with careful design of the signal duration to reach their full potential.

Technical Summary: Fluid Antenna-Aided Noise Modulation

Problem Statement
Noise Modulation (NoiseMod) is a communication scheme designed for ultra-low-power and covert links where information is encoded in the variance of a transmitted noise-like waveform rather than in amplitude, phase, or frequency. While attractive for IoT and stealth applications due to its lack of need for stable oscillators or power amplifiers, NoiseMod suffers from a critical weakness: under Rayleigh fading, it exhibits no spatial diversity. Unlike classical modulation schemes, its Bit Error Probability (BEP) decays only linearly with the inverse of the useful-to-thermal noise variance ratio ( $\delta$ ), specifically as $1/(N_s\delta)$ , where $N_s$ is the number of noise samples per bit. Existing remedies, such as Time-Diversity NoiseMod (TD-NoiseMod), require spreading samples over independent fading blocks, which increases latency and reduces information rate.

Methodology
This paper proposes combining NoiseMod with Fluid Antenna Systems (FAS) to recover spatial diversity without increasing bit duration or requiring multiple Radio-Frequency (RF) chains. The system model involves a receiver equipped with an FAS consisting of $N_p$ ports distributed over a physical aperture of length $W\lambda$ . The receiver employs ideal selection combining, instantaneously switching to the port with the largest instantaneous envelope ( $g_{FAS} = \max |g_k|$ ) before performing variance-based bit detection.

The analysis derives the average BEP under two distinct channel regimes:

Independent Ports (Idealized Limit): Assuming mutually independent ports (representing a large aperture limit), the paper derives an exact closed-form expression for the average BEP using the order statistics of the port envelopes.
Correlated Ports (Physical Reality): For finite apertures where ports are spatially correlated according to Jake's model, the paper utilizes a semi-analytical approach based on the two-stage channel approximation proposed by Khammassi et al. This involves a low-rank-plus-residual representation of the channel covariance matrix and a specific repetition order parameter ( $R^\star$ ) to approximate the cumulative distribution function (CDF) of the selected envelope.

The theoretical results are validated against full signal-level Monte Carlo simulations, which generate correlated channel realizations via Cholesky factorization and explicitly simulate the noise-modulated waveform transmission and detection process.

Key Contributions

System Formulation: The paper formulates FAS-aided NoiseMod, deriving conditional and average BEP expressions where the receiver selects the optimal port prior to variance estimation.
Exact Closed-Form Solution: For the independent port case, an exact closed-form average BEP is derived, validated to match Monte Carlo simulation accuracy.
Semi-Analytical Analysis for Correlated Ports: A semi-analytical BEP is constructed for the physically accurate Jake's correlation model. The authors identify a specific regime (moderate port count with weak correlation) where the approximation parameter $R^\star$ collapses to unity. In this regime, the tool loses sensitivity to the aperture size $W$ , a limitation previously unexposed because prior FAS studies focused on outage probability (a bulk CDF metric) rather than BEP (which is dominated by the extreme lower tail of the envelope distribution).
Diversity and Saturation Analysis: The study demonstrates that FAS restores a diversity order that grows with $N_p$ when ports are weakly correlated. However, it also identifies that for a fixed aperture $W$ , the BEP gain saturates as $N_p$ increases. This saturation mirrors previously reported outage-probability saturation in FAS literature but is now observed for BEP.
Intrinsic NoiseMod Floor: The paper establishes the existence of an intrinsic, correlation-independent BEP floor determined solely by the number of samples per bit ( $N_s$ ) and the variance ratio ( $\alpha$ ). This floor persists regardless of the antenna diversity order and can only be lowered by increasing $N_s$ or $\alpha$ .

Results

Diversity Gain: In the independent port limit, increasing $N_p$ significantly steepens the BEP decay curve. For example, with $N_p=8$ , the BEP is reduced by approximately 15 orders of magnitude compared to $N_p=1$ at $\delta = 10$ dB.
Correlation Impact: In correlated scenarios, increasing the aperture $W$ lowers the BEP floor and delays saturation. However, for a fixed $W$ , adding more ports beyond a certain point yields diminishing returns. For instance, at $W=1$ , the BEP saturates near $N_p \approx 6$ , whereas the independent bound continues to fall.
Approximation Accuracy: The semi-analytical model tracks Monte Carlo simulations closely for strongly correlated apertures (small $W$ , large $R^\star$ ). However, accuracy degrades as $W$ grows (weak correlation), first gradually and then qualitatively once $R^\star$ rounds down to 1, leading to significant under-estimation of the true BEP in weakly correlated regimes.
Intrinsic Floor: For the operating parameters ( $N_s=120, \alpha=10$ ), the theoretical intrinsic floor is extremely low ( $\approx 10^{-19}$ ), meaning the saturation observed in simulations is driven by the FAS envelope distribution limits rather than the variance-based detection limit.

Significance
The paper concludes that FAS serves as a low-complexity, latency-free complement to temporal diversity for NoiseMod receivers. By replacing temporal repetition with spatial port selection, the system avoids the information rate penalties and latency increases associated with TD-NoiseMod. The findings highlight that while FAS effectively restores diversity to a scheme otherwise devoid of it, the physical aperture size $W$ fundamentally limits the achievable diversity order, not just the number of ports $N_p$ . The work motivates future research into joint FAS port selection strategies with limited channel observation and combined spatio-temporal designs.

Technical Summary: Fluid Antenna-Aided Noise Modulation

More like this