⚡ electrical engineering

Enabling Smart Radio Environments in the Frequency Domain With Movable Signals

This paper proposes "movable signals," a novel frequency-domain approach to Smart Radio Environments that dynamically shifts signal spectra to overcome implementation challenges of existing technologies, demonstrating through analytical results that this method can achieve up to four times the received power of traditional Reconfigurable Intelligent Surface (RIS) systems.

Original authors: Matteo Nerini, Bruno Clerckx

Published 2026-05-04

📖 4 min read☕ Coffee break read

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 to a friend across a large, noisy room. Usually, to make your voice heard clearly, you might try to move your body closer to them (Space Domain) or shout in a specific way that bounces off the walls perfectly (Electromagnetic Domain).

This paper proposes a third, entirely new way to do it: changing the pitch of your voice (Frequency Domain).

Here is the breakdown of the paper's ideas using simple analogies:

1. The Problem: The "Tuning Knob" is Broken

In modern wireless communication, we usually try to fix bad connections by using special surfaces called RIS (Reconfigurable Intelligent Surfaces). Think of these as smart mirrors that can electronically change their shape to bounce signals exactly where you want them.

The Catch: These "smart mirrors" are expensive, complex, and require a lot of power to move their tiny electronic parts. It's like trying to build a mirror that can instantly change its shape every millisecond.

2. The New Idea: "Movable Signals"

Instead of trying to move the mirror or the person, the authors suggest moving the signal itself.

The Analogy: Imagine you are playing a piano. If you want to hit a specific note that resonates perfectly with a room's acoustics, you don't need to rebuild the room or move the piano. You just press a different key.
The Concept: The paper calls this "Movable Signals." Instead of the signal staying at one fixed frequency (like a single note), the system dynamically "slides" the signal up and down the frequency scale to find the "sweet spot" where the signal travels strongest.

3. Scenario A: The Clear Line of Sight (LoS)

Imagine you and your friend are standing in an open field with no obstacles.

Old Way: To get the best signal, you usually need complex equipment to adjust the phase of the signal (like a digital beamformer). This is heavy and loses energy.
New Way: The paper shows that if you simply change the frequency of the signal, you can make the waves from all your antennas line up perfectly, just like soldiers marching in step.
The Result: You get the same strong signal as the complex equipment, but your hardware is much simpler. You don't need expensive phase shifters; you just need a transmitter that can tune its frequency.

4. Scenario B: The Blocked Path (Non-Line-of-Sight)

Now, imagine a wall is between you and your friend. You can't shout directly; you have to bounce the sound off a wall.

The Old Solution (RIS): You use a "smart mirror" (RIS) on the wall that can electronically adjust how it reflects the sound.
The New Solution (FIS + Movable Signals): The authors propose using a "Fixed Intelligent Surface" (FIS).
- What is a FIS? Think of it as a wall made of evenly spaced, simple metal strips. It cannot change its shape or settings. It is "dumb" and static.
- How it works: Even though the wall is "dumb," it has a natural rhythm. If you shout at the exact right pitch (frequency), the wall naturally reflects the sound perfectly toward your friend.
- The Magic: By "moving" the signal's frequency to match the wall's natural rhythm, the system works better than the expensive "smart mirror."
The Big Win: The paper claims that using a "dumb" wall with a movable signal can deliver four times more power than using an expensive "smart mirror" with a fixed signal. It's like getting a Ferrari's performance by tuning a bicycle's gears, rather than buying a new engine.

5. The Trade-Off: The "Radio Dial"

There is one catch. To make this work, you need a very wide range of frequencies to choose from.

The Analogy: If you are playing a piano, you need the whole keyboard to find the perfect note. If you are only allowed to play three keys, you might not find the perfect sound.
The Reality: The system needs a wide "frequency range" to slide the signal around. The paper suggests that if you can slide the signal across a range about 1.8 times wider than its starting point, you get excellent results.

Summary

The paper argues that instead of building complex, expensive, power-hungry "smart mirrors" to fix wireless signals, we can simply tune the radio frequency like a radio dial.

In open spaces: It replaces complex electronics with simple frequency tuning.
In blocked spaces: It turns a "dumb" static wall into a super-efficient reflector by finding the perfect frequency to bounce off it.
The Result: Much cheaper hardware, less power consumption, and surprisingly, up to 4x better signal strength compared to current top-tier technology.

1. Problem Statement

Smart Radio Environments (SREs) aim to enhance wireless communication by treating the channel as a controllable variable. Traditionally, SREs have been realized through two domains:

Electromagnetic (EM) Domain: Using Reconfigurable Intelligent Surfaces (RIS) to dynamically alter the reflection properties of surfaces.
Space Domain: Using movable or fluid antennas to physically change distances and optimize path geometry.

The Challenge: Both RIS and movable antennas rely on electronically tunable components (e.g., PIN diodes, varactors) or mechanical actuators. These introduce significant implementation challenges, including high hardware complexity, power consumption, ohmic losses, and control overhead, which hinder commercialization.

The Gap: The potential of the Frequency Domain as a third enabler for SREs has been largely unexplored. While frequency selection exists, it is typically limited to narrow bands. The paper asks: Can we enable SREs by dynamically "moving" the signal's frequency across a wide range to shape the channel, thereby eliminating the need for tunable hardware?

2. Methodology and Proposed Solution

The authors propose a new concept called Movable Signals, where the center frequency of the transmitted signal is dynamically optimized based on the channel realization. To support this, they introduce Fixed Intelligent Surfaces (FIS) for Non-Line-of-Sight (NLoS) scenarios.

Key Concepts:

Movable Signals: Instead of adjusting phase shifters (RIS) or moving antennas, the system adjusts the signal frequency $f$ . This exploits the natural frequency selectivity of the wireless channel (path length differences relative to wavelength).
Fixed Intelligent Surfaces (FIS): In NLoS scenarios, the authors propose using surfaces with fixed reflection properties (specifically, elements short-circuited to ground, resulting in a fixed reflection coefficient of $\Gamma = -1$ ). Unlike RIS, FIS does not require online reconfiguration.
System Models:
- LoS (Line-of-Sight): A Multi-Input Single-Output (MISO) system with a Uniform Linear Array (ULA).
- NLoS: A Single-Input Single-Output (SISO) system aided by an FIS.

Optimization Approach:

The core problem is formulated as maximizing received power $P_R$ by optimizing the wavelength $\lambda$ (or frequency $f$ ) while keeping the precoder or surface reflection matrix fixed.

LoS: The precoder is fixed to Equal Gain Transmission (EGT) with equal weights ( $w = 1/\sqrt{N}$ ). The frequency is tuned so that the phase shifts across the antenna array align constructively at the receiver.
NLoS: The FIS reflection matrix is fixed to $\Theta = -I$ (all elements reflect with a $180^\circ$ phase shift). The frequency is tuned so that the reflected path ( $h_R \Theta h_T$ ) and the specular scattering path ( $-h_R h_T$ ) interfere constructively.

3. Key Contributions

Proposal of Frequency-Domain SREs: The paper defines a new paradigm where the signal frequency is the primary control variable for channel shaping, removing the need for reconfigurable RF components.
Closed-Form Solutions for Optimal Frequency:
- LoS: Derived the optimal frequency $f^*$ as a function of the receiver angle $\theta$ : $f^*(\theta) = f_A / |\sin(\theta)|$ , where $f_A$ is the frequency corresponding to the antenna spacing. This achieves the theoretical maximum received power ( $P_R = P_T N$ ).
- NLoS: Derived the optimal frequency for FIS-aided systems: $f^*(\theta_R, \theta_T) = f_A / |\sin(\theta_R) + \sin(\theta_T)|$ .
Coverage Analysis: Analyzed the trade-off between the available frequency range width ( $W = f_{max}/f_{min}$ ) and the spatial coverage. The paper provides analytical expressions for the coverage region where the optimal frequency can be achieved within the available spectrum.
Performance Comparison with RIS:
- Proved that a FIS-aided system with movable signals can achieve a received power of $4 P_T N^2$ .
- Compared this to a RIS-aided system with fixed frequency, which achieves approximately $P_T N^2$ (specifically $P_T(N + |h_R h_T|)^2$ ).
- Result: Movable signals with FIS can achieve up to 4 times the received power of a RIS-aided system.
Practical Transmission Protocol: Proposed a three-stage protocol (pilot transmission, power measurement, feedback) to select the optimal frequency from a discrete set of subchannels without requiring explicit Channel State Information (CSI).

4. Key Results

LoS Performance:
- Movable signals achieve the same maximum received power as ideal Equal Gain Transmission (EGT) but with significantly reduced hardware complexity (no phase shifters).
- When the frequency range width $W$ is sufficient (e.g., $W=1.8$ ), movable signals outperform quantized EGT (1-bit phase shifters) on average.
- Joint optimization of frequency and precoding yields the highest performance.
NLoS Performance:
- Power Gain: In the asymptotic regime ( $N \to \infty$ ), FIS-aided movable signals provide a 4x power gain over RIS-aided systems with fixed frequencies.
- Reasoning: RIS can only control the phase of the reflected path ( $h_R \Theta h_T$ ), leaving the specular scattering term ( $-h_R h_T$ ) uncontrolled. Movable signals, by tuning frequency, align both terms constructively.
- Hardware Simplicity: FIS requires no tunable loads (diodes/varactors), drastically reducing cost, loss, and control overhead compared to RIS.
Coverage vs. Bandwidth:
- Coverage increases with the frequency range width $W$ .
- Full half-space coverage ( $C=\pi$ ) requires an infinite frequency range, but significant coverage is achievable with practical ranges (e.g., $W \le 1.8$ ).

5. Significance and Implications

Hardware Efficiency: The most significant contribution is the elimination of electronically tunable components. This addresses the primary bottleneck for RIS commercialization (cost, power, complexity).
New Design Paradigm: Shifts the focus from "reconfiguring the environment" to "adapting the signal to the environment's natural frequency response."
Spectrum Utilization: The approach suggests a new spectrum allocation strategy where operators utilize fragmented, wide-range spectrum blocks (via carrier aggregation) rather than contiguous blocks, allowing for flexible frequency hopping to optimize channel conditions.
Future Applications: The paper outlines future directions including multi-user interference suppression (orthogonalizing channels via frequency), offline optimization of FIS geometry, and hybrid multi-domain SREs (combining EM, space, and frequency).

In conclusion, this paper demonstrates that movable signals combined with fixed intelligent surfaces offer a highly efficient, low-complexity alternative to traditional RIS and movable antennas, capable of achieving superior received power gains by exploiting the frequency domain.