Technical Summary: Tackling Interference in HAPS Networks via Angular-Aware Clustering and RSMA

Problem Statement

High Altitude Platform Stations (HAPS) offer a promising solution for next-generation wireless networks by providing ubiquitous connectivity from the stratosphere. However, HAPS networks face unique interference challenges distinct from terrestrial networks. Due to the high altitude of HAPS, links to ground users are dominated by strong Line-of-Sight (LoS) conditions with limited channel variability. Consequently, users who are geographically distant from a terrestrial perspective appear closely spaced from the HAPS viewpoint, resulting in highly similar channel conditions and intensified inter-user interference.

The specific problem addressed in this work involves a single HAPS serving multiple ground users via multiple beams over a limited number of orthogonal Resource Blocks (RBs). Since the number of users ($U$) exceeds the available RBs ($R$), multiple users must share the same RB, leading to severe intra-RB interference. Traditional approaches using user-specific beams are often impractical given the HAPS altitude and user proximity. Therefore, the challenge lies in effectively managing interference when users are grouped into geographic clusters served by a single beam, while simultaneously allocating limited RBs and optimizing transmission strategies to maximize spectral efficiency (SE).

Methodology

The authors propose a three-stage framework to manage interference: Angular-Aware Clustering, Interference-Aware RB Allocation, and Rate-Splitting Multiple Access (RSMA).

1. Angular-Aware Clustering and Beam Steering

The system assumes the HAPS forms beams toward geographic clusters rather than individual users.

• Clustering Strategy: Users are grouped into $L = \lceil U/R \rceil$ clusters based on their angular positions (elevation $\theta$ and azimuth $\phi$). The authors utilize a capacity-constrained K-means algorithm to ensure no cluster exceeds size $R$.
• Beam Steering (WU-Clustering): Unlike centroid-based approaches, the proposed "Worst-User" (WU) clustering strategy steers each beam to the direction that maximizes the minimum effective antenna gain among all users in that cluster. This ensures fairness and protects users with the poorest channel conditions within the cluster.
• RB Allocation: Within each cluster, RBs are allocated orthogonally to avoid intra-cluster interference. However, since RBs are reused across different clusters, inter-cluster interference remains. The allocation algorithm assigns RBs to users to minimize the accumulated interference leakage from already scheduled users in other clusters.

2. RSMA-Based Inter-Cluster Interference Management

To mitigate the inevitable inter-cluster interference caused by RB reuse, the authors employ Rate-Splitting Multiple Access (RSMA) on a per-RB basis.

• Message Splitting: The message for each user is split into a common part and a private part.
• Transmission Structure:
  • The common parts of all users sharing a specific RB are combined into a single common stream ($s^{(c)}_r$), transmitted with power $p^{(c)}_{r,\ell}$ per cluster beam.
  • The private parts are encoded into individual private streams ($s^{(p)}_u$), transmitted with power $p^{(p)}_u$.
• Reception: Users first decode the common stream (treating private streams as noise), perform Successive Interference Cancellation (SIC), and then decode their private stream. This allows for flexible interference management by treating interference as noise or decoding it partially.

3. Optimization Formulation

The authors formulate a Max-Min Fairness (MMF) optimization problem to jointly design the power allocation for common and private streams ($p^{(c)}$ and $p^{(p)}$) and the common rate allocation ($C_u$). The objective is to maximize the minimum achievable data rate across all users, subject to total transmit power constraints and decoding constraints.

• Solution Approach: Due to the non-convex nature of the problem (involving Signal-to-Interference-plus-Noise Ratio (SINR) ratios), the authors employ a Successive Convex Approximation (SCA) technique. They introduce slack variables and use first-order Taylor approximations to transform the problem into a tractable convex form, solved iteratively.

Key Contributions

1. Novel Clustering Framework: The paper introduces an angular-aware clustering algorithm that groups users based on angular similarity and employs a worst-user beam steering strategy. This contrasts with prior works that often assume user-specific beams or centroid-based steering, offering a more practical approach for HAPS geometry.
2. Integrated RSMA Strategy: The work integrates RSMA into HAPS networks specifically to manage inter-cluster interference arising from RB reuse, a scenario where traditional orthogonal allocation fails.
3. Joint Optimization: The authors develop an iterative algorithm (MMF-RSMA-PA) that jointly optimizes beam steering, RB allocation, and power/rate splitting to maximize fairness and spectral efficiency.
4. Comprehensive Evaluation: The study provides a detailed analysis of the trade-offs between beamforming gain and interference mitigation, specifically examining the impact of HAPS antenna array configurations (UPA size).

Numerical Results

Simulations were conducted with a HAPS at 20 km altitude serving 60 users over 10 RBs using an 8x8 Uniform Planar Array (UPA).

• Convergence: The proposed iterative SCA algorithm (Algorithm 2) demonstrates monotonic convergence, stabilizing within fewer than 13 iterations.
• Spectral Efficiency Gains:
  • RSMA Impact: Comparing the proposed scheme (WU-Clustering + RSMA) against a baseline without RSMA (WU-Clustering without RSMA) reveals a substantial improvement. The median Spectral Efficiency (SE) increased from approximately 0.12 b/s/Hz to 0.55 b/s/Hz (a fourfold increase), highlighting RSMA's effectiveness in managing inter-cluster interference.
  • Clustering Impact: The proposed WU-Clustering consistently outperformed a centroid-based clustering approach (C-Clustering + RSMA). By explicitly accounting for the worst-user channel conditions during beam steering, the WU strategy improved fairness and minimum rates.
• Antenna Configuration Trade-off: Increasing the number of antenna elements (e.g., from 2x2 to 8x8) improved performance by narrowing beams and suppressing interference. However, further increasing the array size (e.g., to 16x16 or larger) led to performance degradation. Narrower beams reduced the gain for users located away from the beam center, negatively impacting the overall system performance.

Significance and Claims

The paper claims that the proposed framework of angular-aware clustering combined with RSMA significantly outperforms baseline schemes in terms of achievable per-user spectral efficiency. The authors emphasize that their approach addresses the specific propagation characteristics of HAPS networks (strong LoS, limited channel variability) which render traditional interference management strategies less effective.

The significance of the work lies in demonstrating that:

1. Practical Beamforming: Steering beams based on the "worst-user" within a cluster is superior to centroid-based steering for ensuring fairness in HAPS networks.
2. RSMA Efficacy: RSMA is a powerful tool for managing the specific type of inter-cluster interference generated by RB reuse in HAPS scenarios, offering a bridge between treating interference as noise and fully decoding it.
3. System Design Balance: There is a critical trade-off in HAPS antenna design; simply increasing the number of antenna elements does not guarantee better performance due to the narrowing of beam coverage, necessitating a balanced design approach.

The paper concludes that this integrated approach effectively manages interference in HAPS networks, enhancing the performance of ground users in terms of spectral efficiency without requiring complex user-specific beamforming hardware.