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Stacked Intelligent Metasurface-Enhanced Wideband Multiuser MIMO OFDM-IM Communications

Zheao Li, Jiancheng An, Chau Yuen

Abstract

Leveraging the multilayer realization of programmable metasurfaces, stacked intelligent metasurfaces (SIM) enable fine-grained wave-domain control. However, their wideband deployment is impeded by two structural factors: (i) a single, quasi-static SIM phase tensor must adapt to all subcarriers, and (ii) multiuser scheduling changes the subcarrier activation pattern frame by frame, requiring rapid reconfiguration. To address both challenges, we develop a SIM-enhanced wideband multiuser transceiver built on orthogonal frequency-division multiplexing with index modulation (OFDM-IM). The sparse activation of OFDM-IM confines high-fidelity equalization to the active tones, effectively widening the usable bandwidth. To make the design reliability-aware, we directly target the worst-link bit-error rate (BER) and adopt a max-min per-tone signal-to-interference-plus-noise ratio (SINR) as a principled surrogate, turning the reliability optimization tractable. For frame-rate inference and interpretability, we propose an unfolded projected-gradient-descent network (UPGD-Net) that double-unrolls across the SIM's layers and algorithmic iterations: each cell computes the analytic gradient from the cascaded precoder with a learnable per-iteration step size. Simulations on wideband multiuser downlinks show fast, monotone convergence, an evident layer-depth sweet spot, and consistent gains in worst-link BER and sum rate. By combining structural sparsity with a BER-driven, deep-unfolded optimization backbone, the proposed framework directly addresses the key wideband deficiencies of SIM.

Stacked Intelligent Metasurface-Enhanced Wideband Multiuser MIMO OFDM-IM Communications

Abstract

Leveraging the multilayer realization of programmable metasurfaces, stacked intelligent metasurfaces (SIM) enable fine-grained wave-domain control. However, their wideband deployment is impeded by two structural factors: (i) a single, quasi-static SIM phase tensor must adapt to all subcarriers, and (ii) multiuser scheduling changes the subcarrier activation pattern frame by frame, requiring rapid reconfiguration. To address both challenges, we develop a SIM-enhanced wideband multiuser transceiver built on orthogonal frequency-division multiplexing with index modulation (OFDM-IM). The sparse activation of OFDM-IM confines high-fidelity equalization to the active tones, effectively widening the usable bandwidth. To make the design reliability-aware, we directly target the worst-link bit-error rate (BER) and adopt a max-min per-tone signal-to-interference-plus-noise ratio (SINR) as a principled surrogate, turning the reliability optimization tractable. For frame-rate inference and interpretability, we propose an unfolded projected-gradient-descent network (UPGD-Net) that double-unrolls across the SIM's layers and algorithmic iterations: each cell computes the analytic gradient from the cascaded precoder with a learnable per-iteration step size. Simulations on wideband multiuser downlinks show fast, monotone convergence, an evident layer-depth sweet spot, and consistent gains in worst-link BER and sum rate. By combining structural sparsity with a BER-driven, deep-unfolded optimization backbone, the proposed framework directly addresses the key wideband deficiencies of SIM.

Paper Structure

This paper contains 23 sections, 32 equations, 10 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. The Proposed SIM-enhanced Wideband Multiuser MIMO OFDM-IM System Model
  3. SIM–Enhanced OFDM-IM Transceiver Architecture
  4. Multiuser OFDM–IM Module Construction at the BS
  5. Wideband Channel and Received Signal Model
  6. Optimization Problem Formulation
  7. Single-Subblock BER Derivation
  8. Network-Level Worst‑Link BER and Distance‑Weighted SINR
  9. Final Optimization Problem
  10. DUN Solution for SIM Phase Optimization
  11. Motivation and Design Principle
  12. UPGD Network Architecture
  13. Forward Propagation:
  14. Backward Propagation:
  15. Complexity Analysis
  16. ...and 8 more sections

Figures (10)

  • Figure 1: Transceiver structure of the SIM-enhanced wideband multiuser MIMO OFDM-IM wideband communication system.
  • Figure 2: OFDM index modulators at the $k$-th branch of the TX.
  • Figure 3: UPGD-Net for optimizing the phase shifts of the $L$-layer SIM over $T$ projected-gradient iterations. Columns denote successive iterations $t=0:T-1$, and rows correspond to SIM layers $l=1:L$. In each cell, the analytic gradient $\nabla$ is scaled by the trainable step size $-\eta^{(t)}$, added to the current phase-shift tensors, and then projected to $[0,2\pi)$. A vertical coupling bus delivers the worst-link SINR gradient, computed from the cascade precoder of all layers, to every $\nabla$-block within the same iteration. All modules are model-driven and fully differentiable.
  • Figure 4: Convergence performance of the worst-link loss $\mathcal{L} = - \gamma_{\rm{min}}$ versus the iteration index $T$.
  • Figure 5: Convergence performance of the worst-link loss $\mathcal{L}$ for different numbers of SIM layers $L$ with $M=100$ meta-atoms.
  • ...and 5 more figures

Theorems & Definitions (9)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • Remark 7
  • Remark 8
  • Remark 9