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Cell-Free Massive MIMO-Assisted SWIPT Using Stacked Intelligent Metasurfaces

Thien Duc Hua, Mohammadali Mohammadi, Hien Quoc Ngo, Michail Matthaiou

Abstract

This study explores a next-generation multiple access (NGMA) framework for cell-free massive MIMO (CF-mMIMO) systems enhanced by stacked intelligent metasurfaces (SIMs), aiming to improve simultaneous wireless information and power transfer (SWIPT) performance. A fundamental challenge lies in optimally selecting the operating modes of access points (APs) to jointly maximize the received energy and satisfy spectral efficiency (SE) quality-of-service constraints. Practical system impairments, including a non-linear harvested energy model, pilot contamination (PC), channel estimation errors, and reliance on long-term statistical channel state information (CSI), are considered. We derive closed-form expressions for both the achievable SE and the average sum harvested energy (sum-HE). A mixed-integer non-convex optimization problem is formulated to jointly optimize the SIM phase shifts, APs mode selection, and power allocation to maximize average sum-HE under SE and average harvested energy constraints. To solve this problem, we propose a centralized training, decentralized execution (CTDE) framework based on deep reinforcement learning (DRL), which efficiently handles high-dimensional decision spaces. A Markovian environment and a normalized joint reward function are introduced to enhance the training stability across on-policy and off-policy DRL algorithms. Additionally, we provide a two-phase convex-based solution as a theoretical robust performance. Numerical results demonstrate that the proposed DRL-based CTDE framework achieves SWIPT performance comparable to convexification-based solution, while significantly outperforming baselines.

Cell-Free Massive MIMO-Assisted SWIPT Using Stacked Intelligent Metasurfaces

Abstract

This study explores a next-generation multiple access (NGMA) framework for cell-free massive MIMO (CF-mMIMO) systems enhanced by stacked intelligent metasurfaces (SIMs), aiming to improve simultaneous wireless information and power transfer (SWIPT) performance. A fundamental challenge lies in optimally selecting the operating modes of access points (APs) to jointly maximize the received energy and satisfy spectral efficiency (SE) quality-of-service constraints. Practical system impairments, including a non-linear harvested energy model, pilot contamination (PC), channel estimation errors, and reliance on long-term statistical channel state information (CSI), are considered. We derive closed-form expressions for both the achievable SE and the average sum harvested energy (sum-HE). A mixed-integer non-convex optimization problem is formulated to jointly optimize the SIM phase shifts, APs mode selection, and power allocation to maximize average sum-HE under SE and average harvested energy constraints. To solve this problem, we propose a centralized training, decentralized execution (CTDE) framework based on deep reinforcement learning (DRL), which efficiently handles high-dimensional decision spaces. A Markovian environment and a normalized joint reward function are introduced to enhance the training stability across on-policy and off-policy DRL algorithms. Additionally, we provide a two-phase convex-based solution as a theoretical robust performance. Numerical results demonstrate that the proposed DRL-based CTDE framework achieves SWIPT performance comparable to convexification-based solution, while significantly outperforming baselines.
Paper Structure (31 sections, 2 theorems, 61 equations, 15 figures, 6 tables, 2 algorithms)

This paper contains 31 sections, 2 theorems, 61 equations, 15 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. RIS-assisted CF-mMIMO
  4. SIM-assisted CF-mMIMO
  5. SIMs versus RISs
  6. Research Gap and Summarized Contributions
  7. System Model
  8. Channel Model
  9. Uplink Channel Estimation
  10. Downlink Wireless Information and Power Transmission
  11. Protective Partial Zero Forcing Precoding
  12. Performance Analysis and Problem Formulation
  13. Ergodic Downlink Spectral Efficiency with PPZF
  14. Average Non-Linear Harvested Energy with PPZF
  15. Problem Formulation
  16. ...and 16 more sections

Key Result

Proposition 1

The SE of IR $k_i$ is given by eq:SEk:Ex, where while $\mathrm{PC}_{k_i} = \sum\nolimits_{k_{i}'\in \mathcal{P}_{k} \setminus k_i } (\sum\nolimits_{m \in \mathop{\mathrm{\mathcal{M}}}\nolimits} \alpha_{m k'_i}^{\mathsf{ZF}} \!\sqrt{a_m \rho_{d} \eta_{m k_{i}'}^{\mathtt{I}} } )^{\!\!2},$ and with $\bar{e}_{m k_i} = \bar{\beta}^{\mathtt{I}}_{m k_i} \mathrm{tr}({\bf F}_{m} {\bf F}_{m}^{\dag} )\! -\

Figures (15)

  • Figure 1: The CTCE CF-mMIMO-assisted SWIPT using SIMs.
  • Figure 2: The CTDE CF-mMIMO-assisted SWIPT using SIMs.
  • Figure 3: Minimum SE versus $T_{\mathrm{SIM}}$ ($S=36$, $M = 10, N = 20, \mathrm{PRF}^{\mathtt{I}} = 0, \mathrm{PRF}^{\mathtt{I}} = 3$).
  • Figure 4: Sum-HE versus $T_{\mathrm{SIM}}$ ($S=36$, $M = 10, N = 20, \mathrm{PRF}^{\mathtt{I}} = 0, \mathrm{PRF}^{\mathtt{I}} = 3$).
  • Figure 5: Minimum SE versus $S$ ($T_{\mathrm{SIM}}\!=\!4\lambda$, $M\!=\!10, \mathrm{PRF}^{\mathtt{I}} = 0, \mathrm{PRF}^{\mathtt{I}} = 3$).
  • ...and 10 more figures

Theorems & Definitions (9)

  • Remark 1
  • Remark 2
  • Remark 3
  • Proposition 1
  • proof
  • Remark 4
  • Proposition 2
  • proof
  • Remark 5