⚡ electrical engineering

Movable Signals with Dual-Polarized Fixed Intelligent Surfaces: Beyond Diagonal Reflection Matrices

This paper demonstrates that wireless systems employing movable signals with fixed intelligent surfaces (FIS) significantly outperform traditional reconfigurable intelligent surfaces (RIS), achieving at least a fourfold gain, with further performance enhancements possible through beyond-diagonal reflection matrices when transmitter and receiver polarizations differ.

Original authors: Matteo Nerini, Bruno Clerckx

Published 2026-02-03

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CC BY 4.0

Original authors: Matteo Nerini, Bruno Clerckx

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 shout a message across a large, noisy room to a friend. To make your voice heard clearly, you decide to use a giant wall of mirrors to bounce your sound toward them. This is the basic idea behind Intelligent Surfaces in wireless communication: using a wall of special tiles to reflect signals and boost the connection.

This paper compares two different ways to manage that "wall of mirrors" to get the best possible signal.

The Two Teams: The "Smart Wall" vs. The "Tuning Fork"

Team 1: The Reconfigurable Intelligent Surface (RIS)
Think of this as a wall made of thousands of tiny, high-tech mirrors. Each mirror has a little motor and a brain. To make the signal stronger, the system has to constantly tell every single mirror, "Tilt a little to the left," or "Rotate your angle."

The Catch: This requires a lot of electricity to power the motors and brains, and the system needs to constantly measure the room to know exactly how to tilt the mirrors. It's like trying to direct a choir where every singer needs a personal conductor.

Team 2: Movable Signals with Fixed Intelligent Surfaces (FIS)
Now, imagine a wall made of mirrors that are stuck in place. They cannot tilt or rotate. They are fixed.

The Trick: Instead of moving the mirrors, you change the pitch of your voice (the frequency of the sound). By singing at just the right note, the sound waves bounce off the fixed mirrors in a way that naturally lines up perfectly with your friend's ear.
The Benefit: The wall needs no electricity, no motors, and no complex calculations. You just change the "note" you are singing.

The Experiment: Same Voice vs. Opposite Voices

The researchers tested these two teams in a specific scenario: a room where the person sending the message and the person receiving it have dual-polarized antennas.

Analogy: Imagine the sender is shouting with a "vertical" voice (like a straight line up and down) and the receiver is listening with a "horizontal" ear (like a line side-to-side). Or, they might both be using "vertical" voices.

The paper tested four combinations:

Standard Smart Wall (Diagonal RIS): The mirrors tilt individually but only in one direction.
Super Smart Wall (Beyond-Diagonal RIS): The mirrors tilt and also talk to each other, creating complex patterns.
Fixed Wall + Changing Pitch (Diagonal FIS): The mirrors are stuck, but you change the pitch.
Super Fixed Wall + Changing Pitch (Beyond-Diagonal FIS): The mirrors are stuck but are wired together in a special way to swap vertical and horizontal signals, and you change the pitch.

The Big Findings

1. The "Fixed Wall" Always Wins
No matter what, the team using the Fixed Wall (FIS) and changing the signal pitch performed better than the team using the Smart Wall (RIS).

The Result: The Fixed Wall approach was at least four times more powerful than the Smart Wall approach.
Why? The Smart Wall can only control the reflection part of the signal. The Fixed Wall, by changing the pitch, controls both the reflection and the way the signal bounces off the structure of the wall itself. It's like the Fixed Wall gets to use two tools while the Smart Wall only gets one.

2. The "Super Fixed Wall" is a Magic Trick for Opposite Voices
When the sender and receiver had opposite polarizations (Vertical vs. Horizontal), the results got even more interesting.

The standard Smart Wall struggled a bit because it couldn't easily convert a vertical signal to a horizontal one.
The Super Fixed Wall (BD-FIS) used a special wiring trick (connecting pairs of mirrors) to act like a "polarization converter." It could take a vertical signal and turn it into a horizontal one before bouncing it.
The Result: When the "cross-polar discrimination" (a measure of how well the signals are separated) was low, the Super Fixed Wall's advantage became infinite. It was vastly superior to the Smart Wall.

The Bottom Line

The paper concludes that instead of building expensive, power-hungry walls that need constant reprogramming (RIS), we might get much better results by building simple, fixed walls and just changing the frequency of the signal (FIS).

If you have the same "voice" (polarization): The Fixed Wall is 4x better than the Smart Wall.
If you have opposite "voices": The Super Fixed Wall is even better, potentially offering unlimited gains over the Smart Wall, especially when the signals are very different from each other.

In short: Don't try to move the mirrors; just change the song.

Technical Summary: Movable Signals with Dual-Polarized Fixed Intelligent Surfaces

Problem Statement
Reconfigurable Intelligent Surfaces (RISs) are widely investigated for shaping wireless channels by adjusting the electromagnetic (EM) properties of reflecting elements. However, practical deployment faces challenges, including the power consumption of dedicated control circuitry, the overhead of accurate channel estimation, and concerns regarding unpredictable interference. An alternative approach, Fixed Intelligent Surfaces (FIS) paired with movable signals, has been proposed to circumvent these issues by keeping the surface properties fixed and instead reconfiguring the carrier frequency of the transmitted signal. While previous work established the benefits of movable signals with FIS in single-polarized systems, the performance of dual-polarized intelligent surfaces—specifically those utilizing reflection matrices beyond the diagonal (BD-RIS/BD-FIS)—remains unexplored. This paper investigates the performance limits of dual-polarized RIS and FIS systems, comparing diagonal and beyond-diagonal configurations under both same-polarization and opposite-polarization transmitter-receiver scenarios.

Methodology
The authors analyze a Single-Input Single-Output (SISO) system aided by a surface composed of $N$ dual-polarized elements (half vertical, half horizontal). The channel model incorporates both the signal reflected by the surface (controlled by a reflection matrix $\Theta$ ) and the specular reflection due to structural scattering (independent of $\Theta$ ), which is often neglected in prior literature.

The study compares four distinct designs:

Diagonal RIS (D-RIS): $\Theta$ is a diagonal phase-shift matrix, reconfigured dynamically.
Beyond-Diagonal RIS (BD-RIS): $\Theta$ is a unitary matrix, allowing coupling between elements, reconfigured dynamically.
Diagonal FIS (D-FIS): $\Theta$ is a fixed diagonal matrix; the signal frequency $f$ is dynamically reconfigured.
Beyond-Diagonal FIS (BD-FIS): $\Theta$ is a fixed unitary matrix; the signal frequency $f$ is dynamically reconfigured.

The performance metric is the received power ( $P_R$ ). The authors derive closed-form expressions for the average received power for all four designs, considering two cases: when the transmitter and receiver share the same polarization, and when they have opposite polarizations. The analysis accounts for the cross-polar discrimination (XPD), represented by the parameter $\chi$ (where $0 \le \chi \le 1$ ).

Key Contributions and Results

Same Polarization Scenario:
- When the transmitter and receiver have the same polarization, the paper demonstrates that BD-RIS and BD-FIS offer no performance gain over their diagonal counterparts (D-RIS and D-FIS).
- Crucially, movable signals with FIS (both D-FIS and BD-FIS) consistently outperform RIS. The received power with FIS is approximately four times higher than with RIS ( $P_R^{FIS} \approx 4 \times P_R^{RIS}$ ). This gain is achieved because movable signals can align both the reflected term ( $h_R \Theta h_T$ ) and the specular reflection term ( $-h_R h_T$ ) constructively, whereas RIS can only control the former.
Opposite Polarization Scenario:
- In this case, BD-RIS provides a significant gain over D-RIS, particularly when the cross-polar discrimination is low (small $\chi$ ).
- Movable signals with FIS again outperform RIS. D-FIS achieves a fourfold gain over D-RIS.
- BD-FIS yields the most substantial improvement. By employing a specific fixed reflection matrix that acts as a polarization converter (coupling vertically and horizontally polarized elements via phase shifters), BD-FIS achieves a received power scaling of $(1 + \chi + 2\sqrt{\chi})^2 N^2 / 4$ .
- As the inverse of XPD ( $\chi$ ) approaches zero, the performance gain of BD-FIS over D-RIS approaches infinity. Even at $\chi=1$ (identical polarization), BD-FIS maintains a fourfold gain over D-RIS.

Significance and Claims
The paper claims that movable signals with FIS represent a superior strategy to conventional RIS, offering at least a fourfold increase in received power without requiring reconfigurable hardware or high channel estimation overhead. The introduction of dual-polarization and beyond-diagonal architectures significantly enhances this advantage in scenarios where transmitter and receiver polarizations differ.

Specifically, the authors highlight that BD-FIS is particularly appealing because its reconfigurability relies solely on the signal frequency, while the surface reflection matrix remains fixed and simple to implement (e.g., using phase shifters to connect co-located elements). This architecture avoids the complexity and power consumption of dynamic control circuitry associated with RIS, while still leveraging the benefits of element coupling and polarization conversion to maximize channel strength. The results suggest that for dual-polarized systems, especially those with mismatched polarizations, BD-FIS offers a path to substantially higher performance than current RIS technologies.

The Two Teams: The "Smart Wall" vs. The "Tuning Fork"

The Experiment: Same Voice vs. Opposite Voices

The Big Findings

The Bottom Line

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