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Coupling-Aware RHS Beamforming for Wideband Multi-User Sum Rate Maximization

Liangshun Wu, Wen Chen

Abstract

Wideband multi-user transmission assisted by reconfigurable holographic surfaces (RHSs) is fundamentally limited by mutual coupling effect among densely packed sub-wavelength radiation elements. This paper develops a coupling-aware wideband RHS model and an efficient joint beamforming framework to maximize the multi-user sum rate under practical feeder power and RHS excitation power constraints. We establish an electromagnetic equivalent model based on magnetic-dipole elements and a physically interpretable coupling decomposition into free space near field coupling and guided surface wave coupling. For optimization, we employ a weighted minimum mean square error (WMMSE)-based block coordinate method with a closed-form digital precoder update and introduce a Jacobian-aided coupling consistent hologram update that preserves coupling sensitivity via a first-order surrogate while keeping the hologram subproblem convex and efficiently solvable by projected first-order methods. Meep experiments verify the correctness of the proposed coupling model, and the simulations for a 28~GHz, 1~GHz-bandwidth RHS downlink prove the effectiveness of Jacobian-aided WMMSE-based method.

Coupling-Aware RHS Beamforming for Wideband Multi-User Sum Rate Maximization

Abstract

Wideband multi-user transmission assisted by reconfigurable holographic surfaces (RHSs) is fundamentally limited by mutual coupling effect among densely packed sub-wavelength radiation elements. This paper develops a coupling-aware wideband RHS model and an efficient joint beamforming framework to maximize the multi-user sum rate under practical feeder power and RHS excitation power constraints. We establish an electromagnetic equivalent model based on magnetic-dipole elements and a physically interpretable coupling decomposition into free space near field coupling and guided surface wave coupling. For optimization, we employ a weighted minimum mean square error (WMMSE)-based block coordinate method with a closed-form digital precoder update and introduce a Jacobian-aided coupling consistent hologram update that preserves coupling sensitivity via a first-order surrogate while keeping the hologram subproblem convex and efficiently solvable by projected first-order methods. Meep experiments verify the correctness of the proposed coupling model, and the simulations for a 28~GHz, 1~GHz-bandwidth RHS downlink prove the effectiveness of Jacobian-aided WMMSE-based method.
Paper Structure (33 sections, 4 theorems, 31 equations, 15 figures, 1 table, 1 algorithm)

This paper contains 33 sections, 4 theorems, 31 equations, 15 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Modeling
  3. RHS Beamforming in Wideband
  4. Mutual Coupling
  5. Free-space near-field coupling $\boldsymbol{\Xi}_{\mathrm{fs},u}$
  6. Surface-wave mediated coupling $\boldsymbol{\Xi}_{\mathrm{wg},u}$
  7. Multi-User Sum Rate Maximization Problem
  8. Solution
  9. WMMSE Equivalence
  10. Digital Precoding Subproblem for $\{\mathbf{V}_u\}$
  11. Holographic Amplitude Subproblem for $\mathbf{m}$
  12. Jacobian-Aided Coupling-Consistent Hologram Update
  13. Coupling-consistent first-order surrogate
  14. Convex quadratic WMSE and QCQP update
  15. Simulation
  16. ...and 18 more sections

Key Result

Theorem 1

For any fixed $(\mathbf{m},\{V_u\})$, consider the MSE $e_{k,u}$ associated with the linear equalizer $g_{k,u}\in\mathbb{C}$ and the WMSE cost $\xi_{k,u}$. Then the minimizers of $\xi_{k,u}$ are given by $g_{k,u}^{\star} = \frac{\overline{\mathbf{h}}_{k,u}(\mathbf{m})\,\mathbf{v}_{k,u}}{\sum_{i=1}^{

Figures (15)

  • Figure 1: Working principle of RHS.
  • Figure 2: Mutual coupling with equivalent dipole.
  • Figure 3: Geometric relationship and $(r_k,\theta_k)$ to $(\psi_k,\nu_k)$ field conversion.
  • Figure 4: Unified near- and far- filed representation with $(\psi_k,\nu_k)$: near-field, $\nu_k\neq 0$; far-field, $\nu_k\to 0$.
  • Figure 5: RHS beamforming for multi users.
  • ...and 10 more figures

Theorems & Definitions (8)

  • Theorem 1: WSR--WMMSE equivalence
  • proof
  • Theorem 2: Convex QP and KKT closed-form update for $\{\mathbf{V}_u\}$
  • proof
  • Theorem 3: Convex quadratic form of the $\mathbf{m}$ subproblem
  • proof
  • Theorem 4: Monotonic decrease and convergence of WMMSE block coordinate descent (BCD)
  • proof