⚡ electrical engineering

Two-Level Distributed Interference Management for Large-Scale HAPS-Empowered vHetNets

This paper proposes a two-level distributed proportional fairness beamforming weight design algorithm, combining the augmented Lagrangian method with a three-block ADMM framework, to effectively manage severe co-channel interference and ensure scalability in large-scale HAPS-empowered vertical heterogeneous networks utilizing harmonized spectrum.

Original authors: Afsoon Alidadi Shamsabadi, Animesh Yadav, Halim Yanikomeroglu

Published 2026-05-21

📖 5 min read🧠 Deep dive

CC0 1.0

Original authors: Afsoon Alidadi Shamsabadi, Animesh Yadav, Halim Yanikomeroglu

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ 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: Building a Better Sky-High Internet

Imagine the future of the internet isn't just on the ground, but also in the sky. The paper talks about a system called vHetNets (Vertical Heterogeneous Networks). Think of this as a two-layer internet:

The Ground Layer: Regular cell towers (like the ones on street corners).
The Sky Layer: High-altitude platforms (HAPS), which are like giant, stationary drones or balloons floating 20 kilometers up in the stratosphere.

The goal is to make these two layers work together perfectly to give everyone fast, reliable internet. However, there's a big problem: Interference.

The Problem: A Noisy Party

Imagine a huge party where everyone is trying to talk at the same time.

The Ground Towers are like people in the room talking to their friends.
The Sky Platform is like a giant speaker system broadcasting to the whole room.

If they all try to use the same frequency (the same "channel" or "room"), it becomes a chaotic mess. The sky speaker is so powerful and covers such a wide area that its voice drowns out the ground conversations, and the ground conversations get in the way of the sky speaker. This is called interference.

In the past, engineers tried to solve this with a Centralized Manager. Imagine one person standing on a stage with a microphone, listening to every single person in the room, calculating exactly who should speak, when, and how loud.

The Flaw: In a massive city with thousands of people (users) and hundreds of towers, this one manager gets overwhelmed. It takes too long to gather all the information, and the "signal" (the instructions) gets clogged with too much data. The system becomes too slow and expensive to run.

The Solution: A Distributed Team of Captains

The authors propose a new way to run this party. Instead of one boss, they use a Two-Level Distributed Team.

1. The "Cell-Free" Concept:
In the old way, you were assigned to one specific tower. In this new "Cell-Free" way, everyone is served by everyone. Imagine that every person at the party has a team of speakers (both ground and sky) working together to amplify their voice. They all beam their signal directly to you, combining their strength.

2. The "Two-Level" Strategy:
To manage the chaos without a single boss, they use a smart, two-step dance:

Level 1 (The Inner Loop): Each tower (ground or sky) acts like a local captain. They look at their immediate neighbors and make quick, local decisions on how to aim their "beams" (like flashlights) to help their users. They don't need to talk to the whole world; they just talk to their local team.
Level 2 (The Outer Loop): These local captains periodically check in with each other to make sure they aren't stepping on each other's toes. They use a mathematical trick (called ADMM and Augmented Lagrangian) to slowly adjust their beams until everyone is happy and the noise is minimized.

Think of it like a group of musicians in a band. Instead of one conductor shouting instructions to 100 people, each musician listens to the person next to them and adjusts their volume and timing. Eventually, the whole band plays in perfect harmony without needing a single dictator.

The "Secret Sauce": Proportional Fairness

The paper focuses on a specific goal called Proportional Fairness.

The Old Way: Sometimes, systems try to maximize the total speed of the whole network. This is like a teacher giving all the extra credit to the smartest student, making the class average look great, but leaving the struggling students behind.
The New Way: This algorithm ensures that everyone gets a fair shot. It makes sure the person with the worst connection gets boosted up, while still keeping the overall network fast. It's like a teacher ensuring no student fails, even if it means the top student gets slightly less extra credit.

Why This Matters (The Results)

The authors ran simulations to test their idea. Here is what they found:

Speed vs. Efficiency: The "Centralized" method (the single boss) was slightly faster (about 13% better), but it required a massive amount of data exchange and computing power.
The Winner: The "Distributed" method (the team of captains) was almost as good as the boss, but it was much lighter and faster to run. It saved a huge amount of "signaling overhead" (the data traffic needed to coordinate).
Scalability: Because the distributed method doesn't rely on one central brain, it can handle huge networks (like a whole city with thousands of users) without crashing.
HAPS Power: They showed that adding the sky platform (HAPS) to the ground network is a game-changer. A network with just 4 ground towers + 1 sky platform performed as well as a network with 12 ground towers alone.

Summary

This paper presents a new "team-based" strategy for managing internet traffic between ground towers and high-altitude sky platforms. Instead of using a slow, overloaded central boss, they use a smart, cooperative system where local towers adjust their signals together. This approach keeps the internet fast and fair for everyone, even in massive, crowded networks, without requiring impossible amounts of data to be exchanged.

Technical Summary: Two-Level Distributed Interference Management for Large-Scale HAPS-Empowered vHetNets

1. Problem Statement
The paper addresses the critical challenge of interference management in HAPS-empowered vertical heterogeneous networks (vHetNets) operating under a harmonized spectrum framework. In this architecture, High Altitude Platform Stations (HAPS) and terrestrial Macro Base Stations (MBSs) share the same frequency band to enhance spectral efficiency (SE) and coverage. However, this integration introduces severe inter-tier and intra-tier interference, particularly because the HAPS, positioned at approximately 20 km altitude, creates a large interference footprint affecting numerous MBSs and User Equipments (UEs) simultaneously.

The core difficulties identified are:

Scalability: The large coverage area of HAPS encompasses many MBSs, and the use of ultra-massive MIMO (umMIMO) results in high-dimensional optimization problems that are computationally intractable for centralized solvers.
Signaling Overhead: Centralized approaches require the collection of global Channel State Information (CSI) from all nodes, which imposes prohibitive latency and signaling overhead, especially given the distance between HAPS and terrestrial nodes.
Nonconvexity: The interference management problem, specifically when formulated for Proportional Fairness (PF), is inherently nonconvex. Standard distributed algorithms, such as the two-block Alternating Direction Method of Multipliers (ADMM), often fail to guarantee convergence for general nonconvex constrained problems without relaxation schemes that may compromise performance.

2. Methodology
To overcome these challenges, the authors propose a Two-Level Distributed Proportional Fairness Beamforming Weight Design (PFBWD) algorithm. The methodology proceeds through the following steps:

System Model: The network is modeled as a cell-free architecture where UEs are jointly served by multiple MBSs and a single HAPS using coherent joint transmission. The channel models account for Rayleigh fading for terrestrial links and 3D Rician fading (with dominant Line-of-Sight) for HAPS links.
Problem Reformulation: The original nonconvex PFBWD problem is reformulated into a distributed structure. The authors introduce slack variables to decouple the interference and desired signal terms. Crucially, they apply Jensen's inequality to upper-bound the interference term, allowing the problem to be decomposed into local constraints per Base Station (BS) and global constraints per UE.
Algorithm Design: The proposed solution utilizes a two-level optimization framework:
- Outer Level: Employs the Augmented Lagrangian Method (ALM) to enforce equality constraints between local and global variables, updating Lagrange multipliers iteratively.
- Inner Level: Embeds a structured three-block ADMM within the ALM framework. This specific structure is chosen because standard two-block ADMM does not guarantee convergence for the nonconvex constraints present in this problem. The three-block ADMM handles the local optimization of beamforming weights, while the ALM ensures the coupling constraints are satisfied.
- Handling Nonconvexity: For the nonconvex subproblems within the ADMM blocks, the authors employ Successive Convex Approximation (SCA) to iteratively solve convex surrogates, ensuring the algorithm finds stationary points.

3. Key Contributions
The paper makes the following specific contributions:

Architecture and Formulation: It studies a harmonized spectrum HAPS-empowered vHetNet under a cell-free architecture where UEs are served by multiple BSs. It formulates a PFBWD optimization problem that explicitly captures strong inter-tier interference coupling.
Distributed Reformulation: It demonstrates that centralized optimization is impractical for this scale and reformulates the problem into a distributed structure. This enables BS-level optimization using only local CSI, eliminating the need for inter-BS channel coefficient exchange.
Algorithm Development: It develops a novel two-level distributed algorithm combining ALM and a structured three-block ADMM. This framework is tailored to handle the nonconvex PFBWD problem while satisfying the convergence conditions required for multi-block ADMM in nonconvex settings.
Theoretical Guarantees: The paper establishes the convergence of the proposed algorithm, proving that it converges to a stationary point of the original nonconvex problem.

4. Numerical Results
Simulation results, conducted in a scenario with 4 MBSs, 1 HAPS, and 16 UEs, demonstrate:

Convergence: The algorithm converges rapidly, with the outer-level objective value saturating after approximately 4 iterations and residuals approaching zero.
Performance Gap: The distributed algorithm achieves an average Spectral Efficiency (SE) of ~18.1 b/s/Hz/UE, compared to ~20.9 b/s/Hz/UE for the centralized benchmark. This represents a performance gap of approximately 13%, with a similar 5% gap in the Proportional Fairness objective function.
Efficiency Gains: Despite the slight performance loss, the distributed approach offers substantial gains in efficiency. The computational complexity is reduced from $O((3328)^{3.5})$ for the centralized case to $O((1280)^{3.5})$ for the distributed case. Signaling overhead is drastically reduced from ~2048 real scalars per HAPS (centralized) to ~48 real scalars per BS (distributed).
Logarithmic Performance-Efficiency Index (LPEI): The proposed distributed algorithm consistently outperforms the centralized solution in terms of the LPEI, indicating superior overall efficiency when balancing performance against computational and signaling costs.
HAPS Integration Benefits: Integrating a single HAPS with 4 MBSs achieves the same average SE as a standalone terrestrial network with 12 MBSs, highlighting the capacity gains of the vHetNet architecture.

5. Significance and Claims
The paper claims that its proposed two-level distributed algorithm provides a scalable and practical solution for interference management in large-scale, harmonized spectrum HAPS-empowered vHetNets. It argues that while centralized algorithms are theoretically optimal, they are practically infeasible due to scalability and signaling constraints. The proposed method successfully bridges this gap by offering near-optimal performance (within ~13% of the centralized bound) while significantly reducing computational complexity and signaling overhead. The work underscores the necessity of advanced distributed optimization frameworks to unlock the potential of future integrated aerial-terrestrial networks, particularly in scenarios involving nonconvex interference management and large-scale antenna arrays.