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Energy-Efficient Designs for SIM-Based Broadcast MIMO Systems

Nemanja Stefan Perović, Eduard E. Bahingayi, Le-Nam Tran

TL;DR

This work tackles energy-efficiency (EE) optimization for SIM-based broadcast MIMO systems employing both Dirty Paper Coding (DPC) and Linear Precoding (LP). It leverages BC–MAC duality to reformulate the BC EEmax problems into tractable MAC forms and solves them via a two-level alternating optimization: (i) covariance/precoding matrix optimization using successive convex approximation (SCA) and Dinkelbach’s fractional programming for closed-form updates (water-filling), and (ii) SIM phase-shift optimization via a conventional projected gradient method. The paper provides concise complexity and convergence analyses, and demonstrates through simulations that substantial EE gains are achievable with SIM, with the magnitude of improvement depending on the number and distribution of meta-elements across SIM layers; LP offers a strong, lower-complexity alternative to DPC, especially at larger system sizes. Key insights include logarithmic EE growth with the number of meta-elements, the importance of distributing elements across layers, and the need for at least 3 bits of phase quantization per element to maintain EE when many layers are used. Overall, the results highlight the practical potential of SIM-aided broadcast MIMO for energy-efficient wireless systems and chart directions for future exploration (e.g., inter-layer spacing and mobility adaptation).

Abstract

Stacked intelligent metasurface (SIM), which consists of multiple layers of intelligent metasurfaces, is emerging as a promising solution for future wireless communication systems. In this timely context, we focus on broadcast multiple-input multiple-output (MIMO) systems and aim to characterize their energy efficiency (EE) performance. To explore the potential of SIM, we consider both dirty paper coding (DPC) and linear precoding (LP) and formulate the corresponding EE maximization problems. For DPC, we employ the broadcast channel (BC)-multiple-access channel (MAC) duality to obtain an equivalent problem, and optimize users' covariance matrices using the successive convex approximation (SCA) and Dinkelbach's methods. Since the phase shift optimization problem of the SIM meta-elements is one of extremely large size, we adopt a conventional projected gradient-based method for its simplicity. A similar approach is followed for the case of LP. Simulation results show that the proposed optimization methods for the considered SIM-based systems can significantly improve the EE, compared to conventional counterparts. Also, we demonstrate that the number of SIM meta-elements and their distribution across the SIM layers have a significant impact on both the achievable sum-rate and EE performance.

Energy-Efficient Designs for SIM-Based Broadcast MIMO Systems

TL;DR

This work tackles energy-efficiency (EE) optimization for SIM-based broadcast MIMO systems employing both Dirty Paper Coding (DPC) and Linear Precoding (LP). It leverages BC–MAC duality to reformulate the BC EEmax problems into tractable MAC forms and solves them via a two-level alternating optimization: (i) covariance/precoding matrix optimization using successive convex approximation (SCA) and Dinkelbach’s fractional programming for closed-form updates (water-filling), and (ii) SIM phase-shift optimization via a conventional projected gradient method. The paper provides concise complexity and convergence analyses, and demonstrates through simulations that substantial EE gains are achievable with SIM, with the magnitude of improvement depending on the number and distribution of meta-elements across SIM layers; LP offers a strong, lower-complexity alternative to DPC, especially at larger system sizes. Key insights include logarithmic EE growth with the number of meta-elements, the importance of distributing elements across layers, and the need for at least 3 bits of phase quantization per element to maintain EE when many layers are used. Overall, the results highlight the practical potential of SIM-aided broadcast MIMO for energy-efficient wireless systems and chart directions for future exploration (e.g., inter-layer spacing and mobility adaptation).

Abstract

Stacked intelligent metasurface (SIM), which consists of multiple layers of intelligent metasurfaces, is emerging as a promising solution for future wireless communication systems. In this timely context, we focus on broadcast multiple-input multiple-output (MIMO) systems and aim to characterize their energy efficiency (EE) performance. To explore the potential of SIM, we consider both dirty paper coding (DPC) and linear precoding (LP) and formulate the corresponding EE maximization problems. For DPC, we employ the broadcast channel (BC)-multiple-access channel (MAC) duality to obtain an equivalent problem, and optimize users' covariance matrices using the successive convex approximation (SCA) and Dinkelbach's methods. Since the phase shift optimization problem of the SIM meta-elements is one of extremely large size, we adopt a conventional projected gradient-based method for its simplicity. A similar approach is followed for the case of LP. Simulation results show that the proposed optimization methods for the considered SIM-based systems can significantly improve the EE, compared to conventional counterparts. Also, we demonstrate that the number of SIM meta-elements and their distribution across the SIM layers have a significant impact on both the achievable sum-rate and EE performance.
Paper Structure (24 sections, 2 theorems, 66 equations, 9 figures, 1 table, 4 algorithms)

This paper contains 24 sections, 2 theorems, 66 equations, 9 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. Dirty Paper Coding (DPC)
  5. Multi-user MIMO with LP
  6. Problem Formulation
  7. Proposed Solution to DPC-based SIM
  8. Covariance Matrix Optimization
  9. Problem Reformulation
  10. SCA Method: A Tight Lower Bound of Sum Rate
  11. Dinkelbach's Method: Water-filling Solution
  12. SIM Phase Shift Optimization
  13. Proposed Solution to LP
  14. Precoding Matrix Optimization
  15. Problem Reformulation: Dimension Reduction
  16. ...and 9 more sections

Key Result

Theorem 1

The gradient of $h(\boldsymbol{\phi})$ w.r.t. $\boldsymbol{\phi}^{L}$ is given by where where $\boldsymbol{\Theta}^{m:n}=(\mathbf{W}^{m})^{H}(\boldsymbol{\mathbf{\Phi}}^{m})^{H}\cdots(\mathbf{W}^{n})^{H}(\boldsymbol{\mathbf{\Phi}}^{n})^{H}$.

Figures (9)

  • Figure 1: System level diagrams of conventional and SIM-aided broadcast systems.
  • Figure 2: Convergence of the proposed algorithms for different number of SIM layers.
  • Figure 3: EE versus number meta-elements per SIM layer.
  • Figure 4: EE (blue solid lines) and achievable sum-rate (red dashed lines) versus number SIM layer for the constant number of 400 meta-elements.
  • Figure 5: The EE versus the number users.
  • ...and 4 more figures

Theorems & Definitions (3)

  • Remark 1
  • Theorem 1
  • Theorem 2