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Hybrid Beamforming with Widely-spaced-array for Multi-user Cross-Near-and-Far-Field Communications

Heyin Shen, Yuhang Chen, Chong Han, Jinhong Yuan

TL;DR

This work introduces cross-near-and-far-field CNFF communications with a widely-spaced array (MU-WSA) to enable distance-domain resolution for THz multi-user MIMO. It develops a CNFF channel model and analyzes how the number of subarrays $K$ and subarray spacing $d_s$ affect capacity, deriving a maximum- spacing rule under aperture constraints. For hybrid beamforming, it proposes a BD-based digital design with two analog schemes: S-AO for sub-connected MU-WSA and SVR for fully-connected MU-WSA, achieving efficient interference suppression and steering-vector based orchestration. Numerical results show MU-WSA can boost SE by over 60% at 20 dBm and that the SVR method attains over 95% of the SE upper bound with substantially reduced computation, highlighting the practical benefits of CNFF MU-WSA in dense THz networks.

Abstract

With multi-GHz bandwidth, Terahertz (THz) beamforming has drawn increasing attention in the sixth generation (6G) and beyond communications. Existing beamforming designs mainly focus on a compact antenna array where typical communication occurs in the far-field. However, in dense multi-user scenarios, only relying on far-field angle domain fails to distinguish users at similar angles. Therefore, a multi-user widely-spaced array (MU-WSA) is exploited in this paper, which enlarges the near-field region to introduce the additional distance domain, leading to a new paradigm of cross-near-and-far-field (CNFF) communication. Under this paradigm, the CNFF channel model is investigated, based on which the subarray spacing $d_s$ and the number of subarrays $K$ in MU-WSA are optimized to maximize the channel capacity. Then, in sub-connected systems, an alternating optimization (AO) beamforming algorithm is proposed to deal with the special block-diagonal format of the analog precoder. For fully-connected systems, a low-complexity steering-vector reconstruction (SVR)-based algorithm is proposed by constructing specialized steering vectors of MU-WSA. Numerical evaluations show that due to distance domain resolutions, the MU-WSA can improve the SE by over $60$% at a power of $20$dBm compared to the compact array. Additionally, the proposed AO algorithm in the SC system can achieve over 80% of the sum (SE) of the FC system while reducing the number of phase shifters by $K^2$, thereby lowering power consumption. The SVR algorithm in the FC system can achieve over 95% of the upper bound of SE but takes only 10% of the running time of the singular vector decomposition (SVD)-based algorithms.

Hybrid Beamforming with Widely-spaced-array for Multi-user Cross-Near-and-Far-Field Communications

TL;DR

This work introduces cross-near-and-far-field CNFF communications with a widely-spaced array (MU-WSA) to enable distance-domain resolution for THz multi-user MIMO. It develops a CNFF channel model and analyzes how the number of subarrays and subarray spacing affect capacity, deriving a maximum- spacing rule under aperture constraints. For hybrid beamforming, it proposes a BD-based digital design with two analog schemes: S-AO for sub-connected MU-WSA and SVR for fully-connected MU-WSA, achieving efficient interference suppression and steering-vector based orchestration. Numerical results show MU-WSA can boost SE by over 60% at 20 dBm and that the SVR method attains over 95% of the SE upper bound with substantially reduced computation, highlighting the practical benefits of CNFF MU-WSA in dense THz networks.

Abstract

With multi-GHz bandwidth, Terahertz (THz) beamforming has drawn increasing attention in the sixth generation (6G) and beyond communications. Existing beamforming designs mainly focus on a compact antenna array where typical communication occurs in the far-field. However, in dense multi-user scenarios, only relying on far-field angle domain fails to distinguish users at similar angles. Therefore, a multi-user widely-spaced array (MU-WSA) is exploited in this paper, which enlarges the near-field region to introduce the additional distance domain, leading to a new paradigm of cross-near-and-far-field (CNFF) communication. Under this paradigm, the CNFF channel model is investigated, based on which the subarray spacing and the number of subarrays in MU-WSA are optimized to maximize the channel capacity. Then, in sub-connected systems, an alternating optimization (AO) beamforming algorithm is proposed to deal with the special block-diagonal format of the analog precoder. For fully-connected systems, a low-complexity steering-vector reconstruction (SVR)-based algorithm is proposed by constructing specialized steering vectors of MU-WSA. Numerical evaluations show that due to distance domain resolutions, the MU-WSA can improve the SE by over % at a power of dBm compared to the compact array. Additionally, the proposed AO algorithm in the SC system can achieve over 80% of the sum (SE) of the FC system while reducing the number of phase shifters by , thereby lowering power consumption. The SVR algorithm in the FC system can achieve over 95% of the upper bound of SE but takes only 10% of the running time of the singular vector decomposition (SVD)-based algorithms.
Paper Structure (19 sections, 1 theorem, 56 equations, 10 figures, 3 tables, 2 algorithms)

This paper contains 19 sections, 1 theorem, 56 equations, 10 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. System and Channel Models
  3. Cross Near-and-Far-Field (CNFF) Channel Model
  4. System Model for MU-WSA
  5. Fully-connected MU-WSA
  6. Sub-connected MU-WSA
  7. Problem Formulation
  8. Design of MU-WSA Architecture
  9. Design of Hybrid Beamforming Algorithm
  10. Digital Precoder and Combiner
  11. Analog Precoder and Combiner
  12. Alternating-Optimization-based Analog Beamforming in Sub-connected MU-WSA
  13. Low-complexity Subarray-based Analog Beamforming in Fully-connected MU-WSA
  14. Performance Evaluation
  15. Cross Field Analysis of MU-WSA and Compact Array
  16. ...and 4 more sections

Key Result

Theorem 1

For a given number of subarrays $K$, the capacity of the LoS channel increases monotonically with the subarray distance $d_s$ when the transmission distance satisfies $D^{uk} \geq 2\sqrt{2}(\sqrt{N_r}-1) S_t, \forall u,k$.

Figures (10)

  • Figure 1: Block diagram of the MU-WSA system with hybrid beamforming architecture.
  • Figure 2: Impact of subarray spacing $d_s$ and the number of subarrays $k$ on the sum SE.
  • Figure 3: Beamforming gain for 2D users at the same angle.
  • Figure 4: 2D scenario: optimal sum SE versus transmission distance.
  • Figure 5: Beamforming gain for 3D users with similar angles.
  • ...and 5 more figures

Theorems & Definitions (1)

  • Theorem 1