⚡ electrical engineering

Utilizing Improper Gaussian Signaling for Downlink Rate-Splitting Multiple Access with Imperfect Successive Interference Cancellation

This paper demonstrates that incorporating improper Gaussian signaling (IGS) into downlink Rate-Splitting Multiple Access (RSMA) effectively mitigates residual interference from imperfect successive interference cancellation (SIC), offering a standalone solution that outperforms conventional proper Gaussian signaling with increasing SIC imperfections.

Original authors: Wanting Shi, Hao Cheng, Zhe Li, Yili Xia, Wenjiang Pei

Published 2026-04-17

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Wanting Shi, Hao Cheng, Zhe Li, Yili Xia, Wenjiang Pei

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 a busy radio station trying to broadcast two different news stories to two different listeners in the same room. This is the challenge of Rate-Splitting Multiple Access (RSMA), a technology designed for our future wireless networks.

Here is the simple breakdown of what this paper does, using everyday analogies.

The Problem: The "Echo" Effect

In a perfect world, the radio station would send a "Common Story" (heard by everyone) and a "Private Story" (heard only by one person). The listener would first listen to the Common Story, understand it, and then "cancel it out" of their mind so they can focus purely on their Private Story. This process is called Successive Interference Cancellation (SIC).

However, in the real world, our ears (or phone chips) aren't perfect. When a listener tries to cancel out the Common Story, they leave behind a little bit of an echo (residual interference). This echo gets in the way of the Private Story, making it sound garbled.

Usually, engineers try to fix this by turning down the volume of the Common Story or adding more antennas. But this paper suggests a smarter trick: Change the "shape" of the sound itself.

The Solution: "Improper" Signals (IGS)

Most signals we use today are like a perfect circle spinning on a table. They are symmetrical and predictable. This is called Proper Gaussian Signaling (PGS).

This paper introduces Improper Gaussian Signaling (IGS). Imagine taking that perfect spinning circle and squishing it into an oval or an ellipse.

Why squish it? By making the signal oval-shaped, you can "aim" the squished part of the signal away from the person who doesn't need to hear it.
The Magic: This oval shape allows the signal to naturally "hide" from the interference it causes, even when the listener's "ear" (the SIC process) isn't perfect at canceling things out.

The Three Key Discoveries

The authors tested this idea in a simple setup (one transmitter, two listeners) and found three main things:

1. For Private Stories: Go All-In on the "Oval"
When trying to maximize the clarity of the Private Stories, the best strategy is to make the Common Story as "oval" (improper) as possible.

Analogy: Think of the Common Story as a loud drumbeat. If you make the drumbeat "wobble" (improper) in a specific way, the echo it leaves behind becomes less annoying to the person trying to listen to the private whisper. The more you wobble it, the better the whisper sounds.

2. For the Common Story: It Depends on the Situation
When trying to make sure everyone hears the Common Story clearly, the answer isn't always "max the oval." Sometimes, a perfect circle is better; sometimes, a slightly squished oval is best.

Analogy: It's like tuning a guitar. If the room is very noisy (bad interference cancellation), you need to tune the string differently than if the room is quiet. The paper provides a mathematical "recipe" to know exactly how much to squish the signal based on how bad the interference is.

3. When Things Get Too Complicated: Let an AI Coach Help
When trying to balance both the Common and Private stories at the same time to get the best total speed, the math gets incredibly messy (like trying to juggle while riding a unicycle).

The Fix: The authors used a type of Artificial Intelligence called Soft Actor-Critic (SAC). Think of this AI as a coach who watches thousands of practice rounds, makes mistakes, learns from them, and eventually figures out the perfect way to mix the signal shapes and power levels to win the game.

The Big Result

The simulations showed that using these "oval-shaped" signals (IGS) is always better than the standard "circular" signals (PGS), especially when the interference cancellation is messy.

The more imperfect the cancellation is, the bigger the win.
If your phone's interference cancellation is terrible, using this new "oval" trick gives you a massive boost in speed and clarity.

Summary

This paper proves that we don't need expensive new hardware to fix messy wireless connections. Instead, we can just change the shape of the radio waves we send. By making them slightly "improper" (oval instead of round), we can naturally dodge the interference that usually ruins our connection, making our future 6G networks faster and more reliable.

1. Problem Statement

The paper addresses a critical limitation in Rate-Splitting Multiple Access (RSMA) systems: the degradation of performance caused by Imperfect Successive Interference Cancellation (SIC).

Context: RSMA splits user messages into common and private streams to manage interference. Ideally, receivers decode the common stream first, cancel it, and then decode the private stream.
The Issue: In practical scenarios (due to hardware limits, channel estimation errors, etc.), SIC is imperfect. This leaves residual interference that propagates through the decoding pipeline, eroding the spectral efficiency gains RSMA is designed to provide.
Limitations of Existing Solutions: Current countermeasures (e.g., power control, RIS deployment) are external to the signaling domain. They do not address the root cause: the statistical rigidity of Proper Gaussian Signaling (PGS), which ignores half of the available second-order degrees of freedom (specifically the pseudo-variance).
The Gap: While Improper Gaussian Signaling (IGS) has been studied in other contexts (like I/Q imbalance compensation), its potential to directly counteract SIC-induced residual interference in RSMA systems remains unexplored.

2. Methodology

The authors propose integrating Improper Gaussian Signaling (IGS) into a downlink RSMA framework to mitigate residual interference.

System Model:
- A Single-Input Single-Output (SISO) two-user system is established to ensure analytical tractability.
- Signaling Strategy: The common stream ( $W_c$ ) utilizes IGS (characterized by a circularity coefficient $\kappa$ ), while the private streams ( $W_1, W_2$ ) use conventional PGS.
- Imperfect SIC: Modeled by a parameter $\lambda \in [0, 1]$ , where a larger $\lambda$ indicates higher residual interference.
Analytical Approach:
- The authors derive closed-form expressions for the achievable rates of both private and common streams, explicitly incorporating the pseudo-variance introduced by IGS.
- They analyze the monotonicity of these rates with respect to the impropriety degree ( $\kappa$ ).
Optimization Framework:
- Private Rate Maximization: Solved analytically.
- Common Rate Maximization: Solved analytically under minimum private rate constraints, deriving conditions for the optimal $\kappa$ .
- Sum Rate Maximization: Recognized as a non-convex problem due to variable coupling. The authors develop a Soft Actor-Critic (SAC) reinforcement learning algorithm to solve this efficiently.

3. Key Contributions

The paper makes three primary theoretical and practical contributions:

Novel Application of IGS: It demonstrates that IGS alone, without hardware modifications (like I/Q imbalance compensation), can effectively counteract SIC-induced residual interference. It reshapes the interference footprint at undesired receivers.
Closed-Form Optimal Solutions:
- Private Streams: Proves that for private rate maximization, the optimal impropriety degree is maximum ( $\kappa^\star = 1$ ). This is because increasing $\kappa$ strictly reduces the denominator (interference term) in the private rate equation.
- Common Streams: Derives explicit analytical expressions for the optimal $\kappa$ in common rate maximization. The solution depends on monotonicity conditions ( $M_1, M_2$ ) derived from the system parameters, resulting in a piecewise optimal strategy (either $\kappa=0$ , $\kappa=1$ , or an intermediate value).
Reinforcement Learning for Sum Rate: Develops a Soft Actor-Critic (SAC) algorithm to handle the non-convex sum rate maximization problem. The algorithm treats the system as a Markov Decision Process (MDP), balancing reward maximization with entropy to avoid local optima.

4. Results

Numerical simulations (using MATLAB) validate the theoretical findings:

Private Rate Performance: IGS consistently outperforms PGS. The performance gain widens significantly as the SIC imperfection coefficient ( $\lambda$ ) increases.
Common Rate Performance: The theoretical optimal $\kappa$ (derived in closed-form) aligns perfectly with numerical search results. The simulations confirm that the optimal $\kappa$ depends on the trade-off between SIC imperfection ( $\lambda$ ) and minimum rate constraints ( $R_{min}$ ).
Sum Rate Performance: The SAC-based IGS scheme outperforms the PGS baseline, particularly in high SNR regimes and when minimum rate requirements are lower.
Optimal $\kappa$ Trends:
- Higher SIC imperfection ( $\lambda$ ) generally leads to a larger optimal $\kappa$ .
- In high SNR regimes, the optimal $\kappa$ tends to increase with SNR.

5. Significance

Intrinsic Interference Management: The work establishes IGS as a powerful, intrinsic signaling dimension for interference management. Unlike external solutions (e.g., adding antennas or RIS), IGS requires no additional hardware or spectrum resources.
Robustness to Imperfections: It provides a robust solution for practical RSMA deployments where perfect SIC is unattainable, ensuring that the system maintains high spectral efficiency even under hardware limitations.
Analytical Clarity: By using a SISO framework, the authors provide transparent, closed-form insights into how the circularity coefficient shapes rate components. This contrasts with previous MIMO-based studies that relied on opaque numerical optimization.
Future Design Implication: The results suggest that future RSMA transceiver architectures should explicitly incorporate signal impropriety as a design parameter to maximize performance in real-world, imperfect environments.