⚡ electrical engineering

Enabling Full-Duplex LEO Satellite Systems with Non-Reciprocal BD-RIS-Assisted Beamforming

This paper proposes a full-duplex Low Earth Orbit satellite system enhanced by non-reciprocal beyond-diagonal reconfigurable intelligent surfaces (NR-BD-RIS) to break channel reciprocity and enable flexible, simultaneous multi-user beamforming, which numerical results show significantly outperforms conventional RIS architectures in sum-rate while requiring less frequent reconfiguration.

Original authors: Ziang Liu, Wonjae Shin, Bruno Clerckx

Published 2026-04-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ziang Liu, Wonjae Shin, 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 the Earth is a giant party, and we want to send messages to everyone at the same time. For a long time, we've had a problem: we can either shout (send a message down) or listen (receive a message up), but doing both at the exact same time is like trying to talk and listen to a friend while wearing earplugs that let your own voice blast into your ears. This is called Self-Interference, and it usually forces satellites to take turns, which slows everything down.

This paper proposes a brilliant new way to fix this using a "smart mirror" in space. Here is the breakdown in simple terms:

1. The Problem: The "Traffic Jam" in the Sky

Low Earth Orbit (LEO) satellites are like high-speed delivery trucks circling the Earth. They are great because they are close to us (low latency) and cover huge areas. But, as more people want to stream videos and download files, the "roads" (spectrum) are getting crowded.

The Old Way: The satellite sends a message down, then stops, then listens for a message up. It's like a walkie-talkie where you have to say "Over" before you can listen.
The Goal: We want Full-Duplex communication. This means the satellite talks and listens simultaneously, doubling the speed. But the problem is the satellite's own voice drowns out the whispers from the ground.

2. The Hero: The "Smart Mirror" (RIS)

The authors introduce a Reconfigurable Intelligent Surface (RIS). Think of this as a giant, high-tech mirror attached to the satellite.

Normal Mirrors (D-RIS): These are like standard bathroom mirrors. They just bounce light (or radio waves) back. You can change the angle, but they treat everything the same way.
Smart Mirrors (BD-RIS): These are like mirrors made of thousands of tiny, programmable tiles. You can tell each tile to bounce the signal in a specific direction, focus it, or spread it out. This is much more powerful.

3. The Secret Sauce: The "One-Way Street" (Non-Reciprocity)

Here is the real magic of this paper. Most smart mirrors are Reciprocal.

The Analogy: Imagine a hallway. If you walk from the North door to the South door, the path is the same as walking from South to North. A normal smart mirror treats the signal going down and the signal coming up as if they are traveling on the same two-way street. This makes it hard to send two different messages to two different places at the same time without them crashing into each other.

The authors propose a Non-Reciprocal BD-RIS (NR-BD-RIS).

The Analogy: Imagine putting one-way valves (like in a heart or a plumbing system) inside the mirror's wiring. Now, a signal coming from the ground can be bounced in one direction, while a signal going from the satellite can be bounced in a completely different direction.
Why it matters: It breaks the "rules of physics" that usually force signals to behave symmetrically. The satellite can now shout to Person A on the left while whispering to Person B on the right, all at the same time, without the signals getting confused.

4. The Strategy: The "Conductor" (Time-Sharing)

Even with this super-mirror, the satellite can't cover the entire Earth at once with perfect clarity. So, the authors propose a Time-Sharing Schedule.

The Analogy: Think of the satellite as a conductor of an orchestra. Instead of trying to play every instrument for every person in the audience at once, the conductor divides the concert into tiny moments.
- Moment 1: The mirror focuses on a group of people in New York (Downlink) and a group in London (Uplink).
- Moment 2: The mirror instantly re-angles to focus on Tokyo and Sydney.
- Because the mirror is so fast and smart, it switches so quickly that it feels like everyone is being served at the same time.

5. The Results: Why This is a Game Changer

The paper runs computer simulations (like a video game test) to see how this new system works compared to old mirrors.

Speed: The new "One-Way Smart Mirror" (NR-BD-RIS) is significantly faster than the old "Two-Way Smart Mirror" or the "Basic Mirror."
Flexibility: It works great even if the satellite's antennas aren't perfectly lined up.
Efficiency: Because it can handle multiple directions at once, it doesn't need to be reconfigured as often as the old mirrors. This saves battery and computing power on the satellite.

Summary

Imagine you are at a busy airport.

Old System: The gate agent can only speak to one passenger at a time, then turn around to listen to the next.
New System (This Paper): The agent has a special headset and a magic wall. The magic wall (NR-BD-RIS) can take a whisper from a passenger in the back row and bounce it to the agent's ear, while simultaneously taking a shout from the agent and bouncing it to a passenger in the front row, without the two sounds mixing up.

This technology promises to make our future satellite internet faster, more reliable, and capable of handling the massive amount of data we all want to use.

1. Problem Statement

Low Earth Orbit (LEO) satellite systems are critical for providing low-latency, high-data-rate global connectivity. However, future Non-Terrestrial Networks (NTNs) face significant challenges:

Spectral Efficiency: There is a growing demand for higher spectral efficiency, particularly when ground devices utilize low-gain antennas. This motivates the adoption of In-Band Full-Duplex (FD) systems, which allow simultaneous transmission and reception.
Traffic Imbalance: Downlink (DL) and Uplink (UL) traffic often exhibit an imbalance, requiring flexible resource allocation.
Channel Reciprocity Limitation: Conventional Reconfigurable Intelligent Surfaces (RIS), including Diagonal RIS (D-RIS) and Reciprocal Beyond-Diagonal RIS (R-BD-RIS), rely on circuit reciprocity. This means the signal path from Transmit (Tx) to Receive (Rx) is identical to Rx to Tx. In FD systems where DL and UL devices are non-aligned (located at different angles), reciprocal RIS cannot simultaneously optimize beamforming for both directions, leading to performance degradation.
Self-Interference (SI): FD operation introduces severe self-interference. In satellite contexts, the proximity of the RIS to the satellite antennas creates strong loop interference, necessitating effective mitigation strategies.

2. Methodology and System Model

System Architecture

The authors propose an FD LEO satellite system equipped with:

Non-Reciprocal Beyond-Diagonal RIS (NR-BD-RIS): Attached to the satellite, this surface breaks channel reciprocity by incorporating non-reciprocal components (e.g., isolators) into its impedance network.
Non-Aligned Antennas: The satellite uses spatially separated Tx and Rx antennas to reduce propagation-domain self-interference.
Time-Sharing Scheduling: A framework where the NR-BD-RIS serves multiple groups of DL and UL ground devices within specific time slots, covering the entire area over a scheduling period.

Channel Modeling

Near-Field Model: Due to the proximity of the RIS to the satellite antennas, a near-field (Fresnel) spherical wavefront model is used for the satellite-to-RIS link.
Far-Field Model: A Rician fading model is used for the RIS-to-ground device link, accounting for Line-of-Sight (LoS) dominance, path loss, and rain attenuation.
Scattering Matrix: The NR-BD-RIS is modeled with a non-symmetric scattering matrix ( $\Phi \neq \Phi^T$ ), unlike reciprocal RIS where $\Phi = \Phi^T$ . This allows independent control of incident and reflected wave directions.

Optimization Problem

The core objective is to maximize the weighted sum-rate of DL and UL transmissions over the entire scheduling period.

Variables: Precoding matrix ( $P$ ), combining matrix ( $W$ ), and the RIS scattering matrix ( $\Phi$ ).
Constraints: Transmit power limits, unitary constraints on the RIS (lossless impedance network), and symmetry/asymmetry constraints depending on the RIS type.
Algorithm: The problem is non-convex. The authors propose an iterative algorithm based on:
1. Fractional Programming: Transforming the objective function using Lagrangian dual and quadratic transformations.
2. Block Coordinate Descent (BCD): Alternatingly optimizing $P$ , $W$ , and $\Phi$ .
3. Penalty Dual Decomposition (PDD): Specifically used to handle the coupling between the unitary constraint and the symmetry/asymmetry constraint of the scattering matrix.

3. Key Contributions

Novel System Design: Introduction of an NR-BD-RIS-enabled FD LEO satellite system that utilizes non-reciprocal components to break channel reciprocity, enabling simultaneous optimization of non-aligned DL and UL links.
Time-Sharing Framework: Development of a scheduling framework that allows a single NR-BD-RIS configuration to serve multiple user groups over time, reducing the need for frequent reconfiguration.
Advanced Optimization: Formulation of a weighted sum-rate maximization problem and the design of a robust iterative algorithm (BCD + PDD) to solve it, addressing the unique constraints of non-reciprocal and lossless RIS.
Comprehensive Analysis: Detailed evaluation of the system under various conditions, including single-user (SU) vs. multi-user (MU) scenarios, different RIS architectures (D-RIS, R-BD-RIS, NR-BD-RIS), and varying self-interference levels.

4. Numerical Results and Performance

The paper presents extensive simulations comparing NR-BD-RIS against R-BD-RIS and D-RIS:

Sum-Rate Performance: NR-BD-RIS consistently outperforms both R-BD-RIS and D-RIS in both SU and MU scenarios, particularly when DL and UL devices are non-aligned. The performance gap widens as the angular separation between users increases.
Robustness to Update Interval: A critical finding is that NR-BD-RIS maintains high performance even with infrequent reconfiguration (large update intervals). In contrast, D-RIS and R-BD-RIS require frequent updates to adapt to changing user locations. This makes NR-BD-RIS more practical for implementation where real-time control is difficult.
Self-Interference Mitigation: NR-BD-RIS demonstrates superior robustness to self-interference. It outperforms other RIS types when SI power is below 45 dB.
Group Size Impact: Increasing the group size of the BD-RIS (moving from single-connected to fully-connected) improves performance for all types, but NR-BD-RIS retains its advantage across all group sizes due to its non-reciprocal nature.
Convergence: The proposed algorithm converges rapidly (within ~12 iterations) for all RIS types.

5. Significance and Conclusion

This work addresses a fundamental bottleneck in future satellite communications: the inability of conventional reciprocal RIS to efficiently support full-duplex operations with non-aligned users.

Practicality: By demonstrating that NR-BD-RIS requires less frequent reconfiguration than conventional RIS, the paper highlights a path toward more energy-efficient and hardware-feasible satellite systems.
Spectral Efficiency: The ability to simultaneously maximize DL and UL rates without the trade-offs imposed by channel reciprocity significantly boosts spectral efficiency.
Future Directions: The authors suggest future work should focus on the energy efficiency of the non-reciprocal components themselves and the system's robustness under imperfect Channel State Information (CSI).

In summary, the paper establishes Non-Reciprocal BD-RIS as a transformative technology for next-generation Full-Duplex LEO satellite networks, offering superior flexibility, spectral efficiency, and practical implementation potential compared to existing RIS architectures.