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Indirect and Direct Multiuser Hybrid Beamforming for Far-Field and Near-Field Communications: A Deep Learning Approach

Xinyang Li, Songjie Yang, Boyu Ning, Zongmiao He, Xiang Ling, Chau Yuen

Abstract

Hybrid beamforming for extremely large-scale multiple-input multiple-output (XL-MIMO) systems is challenging in the near field because the channel depends jointly on angle and distance, and the multiuser interference (MUI) is strong. Existing deep learning methods typically follow either a decoupled design that optimizes analog beamforming without explicitly accounting for MUI, or an end-to-end (E2E) joint analog-digital optimization that can be unstable under nonconvex constant-modulus (CM), pronounced analog-digital coupling, and gradient pattern of sum-rate loss. To address both issues, we develop a complex-valued E2E framework based on a variant minimum mean square error (variant-MMSE) criterion, where the digital precoder is eliminated in closed form via Karush-Kuhn-Tucker (KKT) conditions so that analog learning is trained with a stable objective. The network employs a grouped complex-convolution sensing front-end for uplink (UL) measurements, a shared complex multi-layer perceptron (MLP) for per-user feature extraction, and a merged constant-modulus head to output the analog precoder. In the indirect mode, the network designs hybrid beamformers from estimated channel state information (CSI). In the direct mode where explicit CSI is unavailable, the network learns the sensing operator and the analog mapping from short pilots, after which additional pilots estimate the equivalent channel and enable a KKT closed-form digital precoder. Simulations show that the indirect mode approaches the performance of iterative variant-MMSE optimization with a complexity reduction proportional to the antenna number. In the direct mode, the proposed method improves spectral efficiency over sparse-recovery pipelines and recent deep learning baselines under the same pilot budget.

Indirect and Direct Multiuser Hybrid Beamforming for Far-Field and Near-Field Communications: A Deep Learning Approach

Abstract

Hybrid beamforming for extremely large-scale multiple-input multiple-output (XL-MIMO) systems is challenging in the near field because the channel depends jointly on angle and distance, and the multiuser interference (MUI) is strong. Existing deep learning methods typically follow either a decoupled design that optimizes analog beamforming without explicitly accounting for MUI, or an end-to-end (E2E) joint analog-digital optimization that can be unstable under nonconvex constant-modulus (CM), pronounced analog-digital coupling, and gradient pattern of sum-rate loss. To address both issues, we develop a complex-valued E2E framework based on a variant minimum mean square error (variant-MMSE) criterion, where the digital precoder is eliminated in closed form via Karush-Kuhn-Tucker (KKT) conditions so that analog learning is trained with a stable objective. The network employs a grouped complex-convolution sensing front-end for uplink (UL) measurements, a shared complex multi-layer perceptron (MLP) for per-user feature extraction, and a merged constant-modulus head to output the analog precoder. In the indirect mode, the network designs hybrid beamformers from estimated channel state information (CSI). In the direct mode where explicit CSI is unavailable, the network learns the sensing operator and the analog mapping from short pilots, after which additional pilots estimate the equivalent channel and enable a KKT closed-form digital precoder. Simulations show that the indirect mode approaches the performance of iterative variant-MMSE optimization with a complexity reduction proportional to the antenna number. In the direct mode, the proposed method improves spectral efficiency over sparse-recovery pipelines and recent deep learning baselines under the same pilot budget.
Paper Structure (26 sections, 33 equations, 14 figures, 3 tables, 2 algorithms)

This paper contains 26 sections, 33 equations, 14 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Prior Works
  3. Main Contributions
  4. System Model
  5. Near- and Far-Field Indirect E2E Beamforming with Perfect CSI
  6. Decoupled Hybrid Beamforming via Sum-MSE Minimization
  7. Proposed Complex-Valued E2E Network Architecture
  8. Grouped Complex-Convolution Sensing Layer
  9. Shared per‑user multiplexing module
  10. Merged Beamforming Output Network
  11. Deep Learning-Based Near- and Far-Field Indirect Multiuser Hybrid Beamforming
  12. Robust Direct End-to-End Hybrid Beamforming with Short Pilots
  13. Problem Reformulation
  14. Effective Channel Estimation and Digital Beamforming Protocol
  15. Numerical Results and Discussion
  16. ...and 11 more sections

Figures (14)

  • Figure 1: Schematic of the XL-MISO hybrid beamforming system serving user equipments (UEs) in mixed near- and far-field regions.
  • Figure 2: Schematic of the proposed complex-valued E2E network. The model comprises: (i) a grouped complex-convolution sensing front-end that emulates the UL measurement process; (ii) a shared per-user complex MLP module for efficient feature extraction; and (iii) a merged output layer imposing CM normalization to generate ${\bf F}_{\rm RF}$.
  • Figure 3: Test sum‑rate with different complex activation functions under varying learning rates.
  • Figure 4: Timeline of signaling protocol, comprising TDMA UL sensing for measurement acquisition, neural network inference for analog precoder generation, effective channel estimation via pilot repetition, and subsequent downlink data transmission.
  • Figure 5: Performance evaluation in the PCSI-based indirect mode ($K=4$). The algorithm-specific complexity parameters are the number of virtual measurements $N$ for DL-IMHB and SU-DNN, distance rings $S$ for LDMA, and iterations $N_{\rm iter}$ for TH-HMP.
  • ...and 9 more figures