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Hemispherical Antenna Array Architecture for High-Altitude Platform Stations (HAPS) for Uniform Capacity Provision

Omid Abbasi, Halim Yanikomeroglu, Georges Kaddoum

Abstract

In this paper, we present a novel hemispherical antenna array (HAA) designed for high-altitude platform stations (HAPS). A significant limitation of traditional rectangular antenna arrays for HAPS is that their antenna elements are oriented downward, resulting in low gains for distant users. Cylindrical antenna arrays were introduced to mitigate this drawback; however, their antenna elements face the horizon leading to suboptimal gains for users located beneath the HAPS. To address these challenges, in this study, we introduce our HAA. An HAA's antenna elements are strategically distributed across the surface of a hemisphere to ensure that each user is directly aligned with specific antenna elements. To maximize users minimum signal-to-interference-plus-noise ratio (SINR), we formulate an optimization problem. After performing analog beamforming, we introduce an antenna selection algorithm and show that this method achieves optimality when a substantial number of antenna elements are selected for each user. Additionally, we employ the bisection method to determine the optimal power allocation for each user. Our simulation results convincingly demonstrate that the proposed HAA outperforms the conventional arrays, and provides uniform rates across the entire coverage area. With a $20~\mathrm{MHz}$ communication bandwidth, and a $50~\mathrm{dBm}$ total power, the proposed approach reaches sum rates of $14~\mathrm{Gbps}$.

Hemispherical Antenna Array Architecture for High-Altitude Platform Stations (HAPS) for Uniform Capacity Provision

Abstract

In this paper, we present a novel hemispherical antenna array (HAA) designed for high-altitude platform stations (HAPS). A significant limitation of traditional rectangular antenna arrays for HAPS is that their antenna elements are oriented downward, resulting in low gains for distant users. Cylindrical antenna arrays were introduced to mitigate this drawback; however, their antenna elements face the horizon leading to suboptimal gains for users located beneath the HAPS. To address these challenges, in this study, we introduce our HAA. An HAA's antenna elements are strategically distributed across the surface of a hemisphere to ensure that each user is directly aligned with specific antenna elements. To maximize users minimum signal-to-interference-plus-noise ratio (SINR), we formulate an optimization problem. After performing analog beamforming, we introduce an antenna selection algorithm and show that this method achieves optimality when a substantial number of antenna elements are selected for each user. Additionally, we employ the bisection method to determine the optimal power allocation for each user. Our simulation results convincingly demonstrate that the proposed HAA outperforms the conventional arrays, and provides uniform rates across the entire coverage area. With a communication bandwidth, and a total power, the proposed approach reaches sum rates of .
Paper Structure (19 sections, 7 theorems, 31 equations, 16 figures, 1 table, 3 algorithms)

This paper contains 19 sections, 7 theorems, 31 equations, 16 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. State of the Art
  4. Motivation and Contributions
  5. Outline and Notations
  6. System Model and Channel Model
  7. System Model
  8. Channel Model
  9. Transmitter Scheme Proposed for the HAPS
  10. Optimization problem
  11. Steering Vector-Based Analog Beamforming
  12. Antenna Selection Based on the Gains of the Antenna Elements
  13. Optimal Power Allocation via the Bisection Method
  14. Numerical Results
  15. Conclusion
  16. ...and 4 more sections

Key Result

Proposition 1

The achievable rate of user $k$ in the proposed HAA scheme for HAPS is given by where where $\beta_k^2$ represents large-scale fading, $p_k$ indicates the power allocated to user $k$, $\mathbf{G}_k \in \mathbb{R}^{M\times M}$ represents user $k$'s diagonal antenna gain matrix at the HAPS, $\mathbf{A}_k \in \mathbb{R}^{M\times M}$ represents user $k$'s diagonal antenna selection matri

Figures (16)

  • Figure 1: System model for the proposed HAA.
  • Figure 2: The proposed transmitter structure at the HAPS.
  • Figure 3: Polar coordinates for antenna element $m$ expressed as $(d_m,\theta_m,\phi_m)$ and for user $k$ denoted as $(d_k,\theta_k,\phi_k)$. In this figure, $d_{km}$ is the distance between antenna element $m$ and user $k$, while $\theta_{km}$ represents the angle between them.
  • Figure 4: Heatmaps depicting the spectral efficiencies of three individual antenna elements in the proposed HAA, showcasing the impact of two distinct $3~\mathrm{dB}$ beamwidth settings. Each element is allocated a fixed power of $1~\mathrm{Watt}$.
  • Figure 5: CDF of spectral efficiency for a user uniformly distributed across $10,000$ different locations in two square urban areas with dimensions of $200~\mathrm{km} \times 200~\mathrm{km}$ and $60~\mathrm{km} \times 60~\mathrm{km}$. The user is allocated a fixed power of $1~\mathrm{Watt}$ and served by 64 antenna elements ($M_k=64$).
  • ...and 11 more figures

Theorems & Definitions (14)

  • Proposition 1
  • proof
  • Corollary 1
  • proof
  • Corollary 2
  • proof
  • Proposition 2
  • proof
  • Lemma 1
  • proof
  • ...and 4 more