⚡ electrical engineering

Stochastic Analysis of Successive Interference Cancellation in a Narrow-Beam LEO Uplink

This paper investigates the performance of successive interference cancellation (SIC) in narrow-beam low Earth orbit (LEO) uplinks by modeling user equipment distributions and channel conditions to demonstrate that SIC enables a single base station beam to serve multiple users simultaneously, thereby achieving a favorable balance between network throughput and user fairness.

Original authors: Ilari Angervuori, Risto Wichman

Published 2026-07-14

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Ilari Angervuori, Risto Wichman

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 Low Earth Orbit (LEO) satellite zooming high above the Earth, acting like a super-fast, narrow-beam flashlight. Its job is to catch signals from thousands of tiny devices on the ground, like your phone or a smart sensor. But here's the tricky part: the satellite's beam is so narrow that it's like trying to listen to a single person whispering in a crowded room where everyone is shouting at once. This "shouting" is called interference, and usually, it makes it hard for the satellite to hear anyone clearly.

The paper investigates a clever trick called Successive Interference Cancellation (SIC). Think of the satellite as a super-smart detective in a noisy room. Instead of trying to hear everyone at once, the detective listens to the loudest voice first. Once that voice is understood, the detective "mutes" it in their mind, effectively removing that person's shouting from the background noise. Now, the second-loudest voice, which was previously drowned out, becomes much clearer. The detective repeats this process, peeling away the loudest signals one by one to hear the quieter ones underneath.

The researchers wanted to know: Does this "peeling" trick actually work for satellites, and how many people can it help?

To find out, they didn't just guess; they built a complex mathematical model and ran thousands of computer simulations. They imagined the ground users scattered randomly across a city (using a "Poisson point process," which is just a fancy way of saying "randomly but evenly") and tested how the satellite would handle them with narrow beams. They specifically looked at the top three strongest signals in each beam.

Here is what their simulations revealed:

The Big Win for the Underdogs
Without the SIC trick, only the very loudest user gets a good connection. The second and third loudest users are usually stuck in the noise. But with SIC, the story changes dramatically. The paper shows that for the third-strongest user, the chance of getting a successful connection jumps by about 900% compared to not using the trick (specifically, going from a probability of roughly 0.087 to 0.862 when the signal quality threshold is set at -7 dB). It's like the third person in the room suddenly getting a megaphone because the first two stopped shouting.

The "Goldilocks" Zone of Users
The researchers also discovered a sweet spot for how many users should be in one beam. They found that having an average of 3 effective users per beam (denoted as $\kappa_\upsilon = 3$ ) is the magic number.

If there are too few users (like just 1), the signal quality can be wildly unstable, swinging from great to terrible.
With 3 users, the system becomes much more stable. The "variance" (or how much the signal jumps around) stays low, meaning the connection is reliable and fair for everyone.
However, there is a tiny trade-off. While the system becomes fairer and more stable, the total amount of data the satellite can send in one second drops slightly, from about 0.9 bit/s/Hz (with just one user) to 0.7 bit/s/Hz (with three users). The authors suggest this small drop is a fair price to pay for a system where everyone gets a decent connection instead of just one person getting everything.

What They Didn't Say (and What They Ruled Out)
It's important to note what this paper didn't do. They didn't test this on a real satellite in space; all their results come from computer simulations based on a mathematical model of a flat Earth (which they checked against a spherical Earth model and found to be accurate for narrow beams). They also didn't claim this solves every problem. In fact, they point out a downside: even with the trick, the second and third users still get a worse connection quality than the very strongest user. The "loudest" voice still wins, but the others get a fair shot now, whereas before they got nothing.

The Bottom Line
The paper suggests that using Successive Interference Cancellation allows a single satellite beam to serve multiple users at the same time without the whole system crashing. It turns a chaotic shouting match into a structured conversation where the loudest speakers are heard first, then silenced, allowing the quieter ones to be heard. While it requires a slight sacrifice in total speed, it creates a much more stable and fair network for everyone on the ground. The authors conclude that this approach is a promising way to balance speed and fairness, though they admit more work is needed to fully understand the trade-offs for real-world implementation.

Technical Summary: Stochastic Analysis of Successive Interference Cancellation in a Narrow-Beam LEO Uplink

Problem Statement
The paper investigates the performance of Successive Interference Cancellation (SIC) in the uplink of Low Earth Orbit (LEO) satellite networks equipped with narrow Gaussian antenna beams. While stochastic geometry has been extensively applied to terrestrial networks to analyze Signal-to-Interference Ratio (SIR) order statistics, a comprehensive framework for LEO networks has been lacking. A key distinction noted is that LEO networks, characterized by a singular path loss and specific geometric constraints, result in SIR order statistics governed by a Poisson-Dirichlet distribution $PD(0, \cdot)$ (a gamma process), whereas terrestrial networks with singular path loss follow $PD(\cdot, 0)$ . The authors aim to analyze the SIR distributions and order statistics for the three strongest User Equipments (UEs) at a typical LEO base station (BS) under urban shadowing conditions to determine if SIC can enable serving multiple UEs per beam cell while balancing throughput and user fairness.

Methodology
The study employs a stochastic geometry framework with the following modeling choices:

System Model: A planar system model is proposed where UEs are distributed on Earth according to a homogeneous Poisson Point Process (PPP) with density $\lambda$ . The LEO BSs form a homogeneous point process at altitude $h$ . The analysis focuses on a "typical" beam, assuming translation invariance.
Shadowing: The authors utilize a Gaussian Mixture shadowing model (combining Line-of-Sight and Non-Line-of-Sight components) to represent urban environments. For analytical tractability, this is approximated by a mixture exponential distribution with an atomic probability measure at zero. This approximation matches the first two moments of the original log-normal mixture.
Effective UEs: The concept of "effective" UEs is introduced to account for transmitters not entirely attenuated by shadowing. The number of effective UEs ( $\kappa_\upsilon$ ) is kept constant (specifically $n=3$ ) by adjusting the beam half-width $\phi_{RX}$ relative to the elevation angle $\epsilon$ .
Analytical Derivation:
- The received signal power process is defined as a Gain Process (GP), which is shown to be a non-homogeneous PPP.
- The total interference is characterized as a gamma process, leading to a Poisson-Dirichlet distribution for the Signal-to-Total-Interference Ratio (STIR) process.
- Closed-form expressions are derived for the density of the $k$ -th factorial moment measure of the STIR and SIR processes.
- The coverage probability for the $k$ -th strongest UE under perfect SIC is derived, requiring that the preceding $k-1$ signals be successfully decoded and removed.
Validation: Analytical results are verified against Monte Carlo simulations using a realistic spherical Earth model with the original Gaussian mixture shadowing.

Key Contributions

Stochastic Framework for LEO SIC: The paper provides a novel stochastic geometry framework specifically for analyzing SIR order statistics in LEO uplinks, distinguishing the underlying gamma process from terrestrial models.
Shadowing Approximation: It introduces a mixture exponential distribution to approximate complex Gaussian mixture shadowing, enabling tractable analytical solutions while maintaining statistical consistency (matching mean and variance).
SIC Performance Analysis: The authors derive the coverage probabilities and throughput for the top three strongest UEs under SIC, explicitly modeling the dependency of the $k$ -th user's success on the successful decoding of all stronger users.
Trade-off Quantification: The study quantifies the trade-off between total network throughput and user fairness (link quality stability) when increasing the number of served UEs per beam.

Results

SIR Improvement: The analysis demonstrates that SIC significantly enhances the performance of the 2nd and 3rd strongest UEs compared to non-SIC scenarios. For the 3rd UE with a threshold of $\theta = -7$ dB, the coverage probability improves by approximately 900% compared to the non-SIC case.
Variance and Fairness: The study highlights that maintaining an average of three effective UEs per beam ( $\kappa_\upsilon = 3$ ) places the system in a finite-variance region for the SIR distribution. In contrast, scenarios with fewer UEs (e.g., $\kappa_\upsilon = 1$ ) result in infinite SIR variance, leading to unstable link quality. Thus, serving more UEs with SIC improves user fairness and link stability.
Throughput Trade-off: While SIC improves fairness, there is a throughput trade-off. The total bandwidth-normalized throughput for serving three UEs ( $T_3 \approx 0.7$ bit/s/Hz) is slightly lower than serving a single UE in an infinite-variance region ( $T_1 \approx 0.9$ bit/s/Hz). The authors note this is a "considerable but not overwhelming" trade-off.
Link Quality: Despite the aggregate throughput benefits, the individual link quality for the 2nd and 3rd strongest UEs remains poorer than that of the strongest UE, and the overall signal quality for individual connections is described as "rather poor" when multiple users share a beam.

Significance and Claims
The paper claims that SIC enables LEO BSs to serve multiple UEs per beam cell, achieving a balance between good average network throughput and user fairness. The authors emphasize that by increasing the number of UEs served (specifically to a point where the SIR variance is finite), the link quality becomes more stable, mitigating the instability associated with sparse user densities. However, the paper remains modest regarding implementation, noting that while SIC improves fairness, individual connection quality for weaker users is still limited. The authors conclude that further studies are required to clarify the specific trade-offs and implementation considerations for deploying such schemes in real-world LEO networks.

Technical Summary: Stochastic Analysis of Successive Interference Cancellation in a Narrow-Beam LEO Uplink

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