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Robust Rate-Splitting Design for Mixed Dual-Polarized Integrated Satellite-Terrestrial Networks Under Polarization Mismatch

This paper proposes a robust rate-splitting multiple access (RSMA) framework for mixed dual-polarized integrated satellite-terrestrial networks that jointly mitigates inter- and intra-network interference while accounting for polarization mismatch and imperfect channel state information to maximize the minimum user rate.

Original authors: Jaehyup Seong, Juhwan Lee, Jungwoo Lee, Sean Kwon, Wonjae Shin

Published 2026-04-14

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CC BY 4.0

Original authors: Jaehyup Seong, Juhwan Lee, Jungwoo Lee, Sean Kwon, Wonjae Shin

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

The Big Picture: A Noisy Party in the Sky and on the Ground

Imagine a massive, high-tech party happening in two different rooms at the same time:

The Sky Room: A Low Earth Orbit (LEO) satellite is beaming data down to users. It uses Circular Polarization (think of the signal spinning like a corkscrew). This is great because it doesn't get messed up by the Earth's atmosphere.
The Ground Room: A cell tower is beaming data to people on the ground. It uses Linear Polarization (think of the signal vibrating up-and-down or side-to-side).

The Problem:
Both rooms are trying to use the exact same "frequency" (like speaking the same language) at the same time to save space.

The Mix-up: Because the satellite is spinning fast and the signals are spinning differently (corkscrew vs. straight line), they don't line up perfectly. This is called Polarization Mismatch. It's like trying to fit a square peg into a round hole; some of the signal gets lost, and some of it leaks into the wrong channel.
The Noise: The signals from the satellite crash into the signals from the ground tower, and vice versa. It's like two loud bands playing different songs in the same room. Everyone is shouting, and no one can hear their own music.
The Fog: Sometimes, buildings and trees scatter the signals, making them "depolarized" (the signal gets confused about which way it's vibrating).

The Solution: The "Super-Messenger" Strategy (RSMA)

The authors propose a new way to manage this chaos called Rate-Splitting Multiple Access (RSMA). Instead of trying to make everyone take turns (which is slow) or trying to perfectly separate the signals (which is impossible when things are moving fast), they use a clever "splitting" strategy.

Think of the data stream as a package being delivered to a house.

1. The "Super-Common" Message (The Super-Messenger)

This is the paper's biggest innovation.

The Analogy: Imagine the satellite has a Super-Messenger who carries a note that everyone in both the Sky Room and the Ground Room needs to read first.
How it works: Before anyone listens to their private messages, they all listen to this Super-Messenger. Because this message is designed to be understood by everyone, it helps cancel out the noise caused by the other room.
The Magic: Once everyone reads the Super-Messenger, they can "subtract" it from the noise in their ears. This clears the air so they can hear their own specific messages much better. This is called Inter-Network Rate-Splitting.

2. The "Common" and "Private" Messages (The Inner Circle)

After the Super-Messenger is gone, the satellite and the ground tower still have to talk to their own specific users.

The Analogy: Now, the satellite sends a Group Note (Common Message) that all its users can hear, and then Private Letters (Private Messages) for each individual.
How it works: The users listen to the Group Note first, remove it from the noise, and then read their Private Letter. This handles the interference within the Sky Room and the Ground Room separately.

Why This Paper is Special

Most previous solutions tried to solve this by:

Cooperative Schemes: Asking the satellite and the ground tower to share all their data files. This is like asking two neighbors to swap their entire libraries just to help one person find a book. It's too much work and takes too much time (signaling overhead).
Ignoring the Mess: Pretending the interference doesn't exist or treating it as random static. This works poorly when the satellite is moving fast.

This paper's approach is different:

No Data Sharing: The satellite and ground tower don't need to swap files. They just coordinate their "speaking style" (precoding) to minimize the mess.
Robustness: The system is designed to work even when the satellite is moving at 17,000 mph (causing the polarization mismatch) and when the engineers don't have perfect information about the weather or obstacles (imperfect Channel State Information).
Fairness: The goal isn't just to make the average speed fast; it's to make sure the slowest user (the one with the worst connection) gets the best possible speed. This is like a teacher making sure the student in the back row can hear the lecture just as well as the one in the front.

The "Recipe" (The Algorithm)

To make this work, the authors created a mathematical "recipe" (an algorithm based on Weighted Minimum Mean Square Error).

Imagine a DJ mixing two songs. The DJ constantly adjusts the volume knobs (power allocation) and the equalizer (beamforming) to ensure that even if the speakers are slightly broken or the room is echoey, the music sounds clear to everyone.
The algorithm constantly calculates: "If I send a little more power to the Super-Messenger, will the Ground Room users hear better? If I change the angle of the signal, will the Satellite users hear better?"
It does this over and over again until it finds the perfect balance.

The Results

When they tested this "Super-Messenger" strategy against other methods:

It was faster: Users got higher data speeds.
It was fairer: The users with the worst connections saw the biggest improvement.
It was tougher: Even when the satellite was moving fast or the signal was bouncing off buildings, this method kept working while others failed.

Summary

This paper solves the problem of a satellite and a cell tower shouting at each other by introducing a Universal Translator (Super-Messenger). This translator helps everyone cancel out the background noise first, allowing the satellite and the ground tower to share the same airwaves efficiently, even when they are moving fast and the signal is messy. It's a smarter, more robust way to connect the sky to the ground.

1. Problem Statement

The paper addresses the critical challenge of interference management in Mixed Dual-Polarized Integrated Satellite-Terrestrial Networks (MDP-ISTN). These networks combine:

Satellite Sub-network: Uses Circular Polarization (CP) (Right-Hand and Left-Hand) to mitigate ionospheric Faraday rotation and is typically Low Earth Orbit (LEO).
Terrestrial Sub-network: Uses Linear Polarization (LP) (Vertical and Horizontal), which is standard for cellular networks.

Key Challenges Identified:

Inter-Network Interference: Aggressive reuse of frequency and time resources causes significant interference between the CP satellite and LP terrestrial networks. The orthogonality between CP and LP is not preserved, leading to cross-polar interference.
Intra-Network Interference: Within each sub-network, signal reflections and scattering cause channel depolarization, creating both co-polar and cross-polar interference.
Polarization Mismatch: Due to the high mobility of LEO satellites (approx. 7.56 km/s) and rapid changes in antenna orientation relative to users, there is a dynamic polarization mismatch. This misalignment degrades system performance and increases cross-polar coupling.
Imperfect CSI: Acquiring accurate Channel State Information at the Transmitter (CSIT) is difficult for LEO satellites due to high velocity and propagation delays. Most existing solutions assume perfect alignment or perfect CSIT, making them unsuitable for this dynamic environment.

2. Methodology

The authors propose a novel framework called MDP-RSMA (Mixed Dual-Polarized Rate-Splitting Multiple Access) and develop a robust precoder design algorithm.

A. The MDP-RSMA Framework

The scheme employs a hierarchical rate-splitting strategy to manage interference without requiring data sharing between the satellite and the terrestrial base station (BS):

Inter-Network Rate-Splitting (Super-Common Stream):
- A super-common message is generated at the LEO satellite.
- This stream is designed to be decoded by all users (both Satellite Users - SUs, and Cellular Users - CUs).
- By decoding and removing this stream via Successive Interference Cancellation (SIC) first, the system mitigates the interference from the satellite to the terrestrial network (and vice versa).
Intra-Network Rate-Splitting:
- Satellite Side: Remaining messages are split into a CP-common stream (decoded by all SUs) and private streams (decoded by individual SUs).
- Terrestrial Side: Messages are split into an LP-common stream (decoded by all CUs) and private streams (decoded by individual CUs).
- This structure flexibly manages cross-polar and co-polar interference within each sub-network.

B. System Modeling

Channel Model: The authors model the channel considering:
- Polarization Mismatch: Modeled via a rotation matrix $R(\zeta)$ accounting for the angle difference between the satellite and user antennas.
- Channel Depolarization: Characterized by the Cross-Polarization Discrimination (XPD) factor, distinguishing between Line-of-Sight (LOS) and Non-Line-of-Sight (NLOS) components.
- Imperfect CSIT: The design relies on statistical channel information (geometry, Rician K-factor, XPD) rather than instantaneous fading coefficients, which are unavailable due to rapid channel variations.

C. Optimization Algorithm

Objective: Maximize the minimum user spectral efficiency (Max-Min Fairness) across all SUs and CUs.
Approach: The problem is non-convex. The authors reformulate it using the Weighted Minimum Mean Square Error (WMMSE) method.
- They introduce auxiliary variables (equalizers and weights) to transform the non-convex rate constraints into convex forms.
- A Sample Average Approximation (SAA) technique is used to estimate ergodic spectral efficiencies based on statistical channel knowledge.
- An Alternating Optimization (AO) algorithm is developed to iteratively update the precoding vectors (beamforming) and power allocation until convergence.

3. Key Contributions

Novel Framework: Proposed the first MDP-RSMA framework that jointly manages inter-network and intra-network interference in heterogeneously polarized (CP/LP) integrated networks without data sharing.
Super-Common Stream: Introduced a super-common stream specifically to mitigate inter-network interference between the CP satellite and LP terrestrial networks, a feature absent in previous dual-polarized RSMA studies.
Robustness to Practical Constraints: The design explicitly accounts for polarization mismatch, channel depolarization, and imperfect CSIT, making it viable for real-world LEO SATCOM scenarios.
Algorithm Development: Developed a tailored WMMSE-based algorithm that jointly optimizes beamforming vectors and power allocation for super-common, common, and private streams under statistical channel uncertainty.

4. Simulation Results

The proposed MDP-RSMA-ISTN scheme was evaluated against several baselines (SDMA-OMA, RSMA-OMA, SDMA-ISTN, and other RSMA variants) across various scenarios:

Transmit Power: The proposed scheme significantly outperforms benchmarks in minimum spectral efficiency. At 22 dBW satellite power, it achieved >25% improvement over the best existing RSMA scheme (RSMA-PD-ISTN). The advantage of the super-common stream grows with higher transmit power.
User Density: The framework maintains superior performance as the number of satellite users increases, demonstrating scalability in dense deployments.
Channel Conditions (Rician K-Factor & XPD): The scheme remains robust across varying Rician K-factors and Cross-Polarization Discrimination (XPD) levels. Notably, it outperforms schemes with perfect CSIT when the Rician K-factor is high, highlighting its resilience to CSI uncertainty.
Imperfect CSIT: The proposed scheme shows minimal performance degradation under imperfect CSIT compared to baselines, validating its robustness.

5. Significance

This work provides a critical solution for next-generation 6G integrated networks. As LEO satellite constellations expand to provide global coverage, they must share spectrum with terrestrial 5G/6G networks.

Spectral Efficiency: It demonstrates how dual-polarization can be effectively reused even in mixed (CP/LP) environments, potentially doubling capacity.
Practical Viability: By addressing polarization mismatch and imperfect CSI, the paper moves theoretical RSMA concepts closer to practical implementation in high-mobility satellite scenarios.
Interference Management: The hierarchical rate-splitting approach offers a flexible mechanism to handle complex interference landscapes that traditional orthogonal or non-orthogonal multiple access schemes cannot efficiently manage.

In conclusion, the paper establishes that MDP-RSMA is a superior, robust, and fair transmission strategy for future integrated satellite-terrestrial networks operating under realistic physical and channel constraints.