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Hashing Beam Training for Integrated Ground-Air-Space Wireless Networks

Yuan Xu, Chongwen Huang, Wei Li, Zhaohui Yang, Ahmed Al Hammadi, Jun Yang, Zhaoyang Zhang, Chau Yuen, Mérouane Debbah

TL;DR

This work tackles the high training overhead of beam training in integrated ground-air-space networks by introducing Hashing Multi-Arm Beam (HMB) training. It designs an IGAS-specific single-beam codebook that leverages polar-domain sparsity, then constructs per-AP multi-arm codebooks via independent hash functions, enabling simultaneous traversal of multiple beams across APs. A soft-decision and voting mechanism identifies aligned beams with a theoretical guarantee of logarithmic traversal complexity, and simulations show about 96.4% identification accuracy relative to exhaustive training while dramatically reducing overhead. The approach is validated in near-field and shown to remain effective under far-field conditions, indicating practical utility for sensing-enabled IGAS systems in future 6G networks.

Abstract

In integrated ground-air-space (IGAS) wireless networks, numerous services require sensing knowledge including location, angle, distance information, etc., which usually can be acquired during the beam training stage. On the other hand, IGAS networks employ large-scale antenna arrays to mitigate obstacle occlusion and path loss. However, large-scale arrays generate pencil-shaped beams, which necessitate a higher number of training beams to cover the desired space. These factors motivate our investigation into the IGAS beam training problem to achieve effective sensing services. To address the high complexity and low identification accuracy of existing beam training techniques, we propose an efficient hashing multi-arm beam (HMB) training scheme. Specifically, we first construct an IGAS single-beam training codebook for the uniform planar arrays. Then, the hash functions are chosen independently to construct the multi-arm beam training codebooks for each AP. All APs traverse the predefined multi-arm beam training codeword simultaneously and the multi-AP superimposed signals at the user are recorded. Finally, the soft decision and voting methods are applied to obtain the correctly aligned beams only based on the signal powers. In addition, we logically prove that the traversal complexity is at the logarithmic level. Simulation results show that our proposed IGAS HMB training method can achieve 96.4% identification accuracy of the exhaustive beam training method and greatly reduce the training overhead.

Hashing Beam Training for Integrated Ground-Air-Space Wireless Networks

TL;DR

This work tackles the high training overhead of beam training in integrated ground-air-space networks by introducing Hashing Multi-Arm Beam (HMB) training. It designs an IGAS-specific single-beam codebook that leverages polar-domain sparsity, then constructs per-AP multi-arm codebooks via independent hash functions, enabling simultaneous traversal of multiple beams across APs. A soft-decision and voting mechanism identifies aligned beams with a theoretical guarantee of logarithmic traversal complexity, and simulations show about 96.4% identification accuracy relative to exhaustive training while dramatically reducing overhead. The approach is validated in near-field and shown to remain effective under far-field conditions, indicating practical utility for sensing-enabled IGAS systems in future 6G networks.

Abstract

In integrated ground-air-space (IGAS) wireless networks, numerous services require sensing knowledge including location, angle, distance information, etc., which usually can be acquired during the beam training stage. On the other hand, IGAS networks employ large-scale antenna arrays to mitigate obstacle occlusion and path loss. However, large-scale arrays generate pencil-shaped beams, which necessitate a higher number of training beams to cover the desired space. These factors motivate our investigation into the IGAS beam training problem to achieve effective sensing services. To address the high complexity and low identification accuracy of existing beam training techniques, we propose an efficient hashing multi-arm beam (HMB) training scheme. Specifically, we first construct an IGAS single-beam training codebook for the uniform planar arrays. Then, the hash functions are chosen independently to construct the multi-arm beam training codebooks for each AP. All APs traverse the predefined multi-arm beam training codeword simultaneously and the multi-AP superimposed signals at the user are recorded. Finally, the soft decision and voting methods are applied to obtain the correctly aligned beams only based on the signal powers. In addition, we logically prove that the traversal complexity is at the logarithmic level. Simulation results show that our proposed IGAS HMB training method can achieve 96.4% identification accuracy of the exhaustive beam training method and greatly reduce the training overhead.
Paper Structure (12 sections, 3 theorems, 57 equations, 11 figures, 1 algorithm)

This paper contains 12 sections, 3 theorems, 57 equations, 11 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related works
  3. Contributions
  4. System Model
  5. IGAS Codebook Generation
  6. IGAS Single-Beam Codebook
  7. Hashing Multi-Arm Beam Codebook Generation
  8. integrated ground-air-space Beam Traning
  9. Beam Identification Phase
  10. Complexity Analysis
  11. Simulation Results
  12. Conclusion

Key Result

Theorem 1

For the Galois field $GF(N_C)$, we construct a $k$-wise independent map from $\mathcal{U}$ to $\mathcal{T}$ as follows: Pick $k$ random numbers $a_0,a_1,...,a_{k-1}\in GF(N_C)$. For any $x\in\mathcal{U}$, where the calculations are done over the field $GF(N_C)$, and $|\mathcal{H}|=N_C^{k}-N_C$, because $a_1,a_2,... . a_{k-1}$ cannot equal to zero at the same time.

Figures (11)

  • Figure 1: Downlink IGAS mmWave scenario with $K$ APs and several users.
  • Figure 2: The schematic diagram for hashing implementation.
  • Figure 3: Success beam identification accuracy versus the SNR.
  • Figure 4: Success beam identification accuracy versus the number of buckets $B$ at different SNRs.
  • Figure 5: Success beam identification accuracy versus the SNR when considering soft and hard decisions.
  • ...and 6 more figures

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2
  • Lemma 1