Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Performance of Double-Stacked Intelligent Metasurface-Assisted Multiuser Massive MIMO Communications in the Wave Domain

Anastasios Papazafeiropoulos, Pandelis Kourtessis, Symeon Chatzinotas, Dimitra Kaklamani, Iakovos Venieris

TL;DR

This work addresses uplink performance in a multiuser MIMO system by introducing two stacked intelligent metasurfaces (BSIM at the base station and CSIM in the environment) to enable wave-domain processing and environment shaping. It adopts a two-timescale approach, deriving a closed-form uplink sum spectral efficiency and optimizing both SIMs simultaneously via projected gradient ascent (PGAM) using statistical CSI for planning and instantaneous CSI for beamforming. Key contributions include a hybrid BSIM design to reduce RF-chain needs, a CSIM for local environment multiplexing, a single-phase channel estimation method, and a demonstrated performance advantage over alternating optimization, with insights on how metasurface size and layering affect SE. The proposed framework offers a path toward energy-efficient, highly reconfigurable wireless networks for future 6G applications, with potential extensions to active CSIM and varied CSI regimes.

Abstract

Although reconfigurable intelligent surface (RIS) is a promising technology for shaping the propagation environment, it consists of a single-layer structure within inherent limitations regarding the number of beam steering patterns. Based on the recently revolutionary technology, denoted as stacked intelligent metasurface (SIM), we propose its implementation not only on the base station (BS) side in a massive multiple-input multiple-output (mMIMO) setup but also in the intermediate space between the base station and the users to adjust the environment further as needed. For the sake of convenience, we call the former BS SIM (BSIM), and the latter channel SIM (CSIM). Hence, we achieve wave-based combining at the BS and wave-based configuration at the intermediate space. Specifically, we propose a channel estimation method with reduced overhead, being crucial for SIMassisted communications. Next, we derive the uplink sum spectral efficiency (SE) in closed form in terms of statistical channel state information (CSI). Notably, we optimize the phase shifts of both BSIM and CSIM simultaneously by using the projected gradient ascent method (PGAM). Compared to previous works on SIMs, we study the uplink transmission, a mMIMO setup, channel estimation in a single phase, a second SIM at the intermediate space, and simultaneous optimization of the two SIMs. Simulation results show the impact of various parameters on the sum SE, and demonstrate the superiority of our optimization approach compared to the alternating optimization (AO) method.

Performance of Double-Stacked Intelligent Metasurface-Assisted Multiuser Massive MIMO Communications in the Wave Domain

TL;DR

This work addresses uplink performance in a multiuser MIMO system by introducing two stacked intelligent metasurfaces (BSIM at the base station and CSIM in the environment) to enable wave-domain processing and environment shaping. It adopts a two-timescale approach, deriving a closed-form uplink sum spectral efficiency and optimizing both SIMs simultaneously via projected gradient ascent (PGAM) using statistical CSI for planning and instantaneous CSI for beamforming. Key contributions include a hybrid BSIM design to reduce RF-chain needs, a CSIM for local environment multiplexing, a single-phase channel estimation method, and a demonstrated performance advantage over alternating optimization, with insights on how metasurface size and layering affect SE. The proposed framework offers a path toward energy-efficient, highly reconfigurable wireless networks for future 6G applications, with potential extensions to active CSIM and varied CSI regimes.

Abstract

Although reconfigurable intelligent surface (RIS) is a promising technology for shaping the propagation environment, it consists of a single-layer structure within inherent limitations regarding the number of beam steering patterns. Based on the recently revolutionary technology, denoted as stacked intelligent metasurface (SIM), we propose its implementation not only on the base station (BS) side in a massive multiple-input multiple-output (mMIMO) setup but also in the intermediate space between the base station and the users to adjust the environment further as needed. For the sake of convenience, we call the former BS SIM (BSIM), and the latter channel SIM (CSIM). Hence, we achieve wave-based combining at the BS and wave-based configuration at the intermediate space. Specifically, we propose a channel estimation method with reduced overhead, being crucial for SIMassisted communications. Next, we derive the uplink sum spectral efficiency (SE) in closed form in terms of statistical channel state information (CSI). Notably, we optimize the phase shifts of both BSIM and CSIM simultaneously by using the projected gradient ascent method (PGAM). Compared to previous works on SIMs, we study the uplink transmission, a mMIMO setup, channel estimation in a single phase, a second SIM at the intermediate space, and simultaneous optimization of the two SIMs. Simulation results show the impact of various parameters on the sum SE, and demonstrate the superiority of our optimization approach compared to the alternating optimization (AO) method.
Paper Structure (25 sections, 3 theorems, 58 equations, 8 figures, 1 algorithm)

This paper contains 25 sections, 3 theorems, 58 equations, 8 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions
  3. System and Channel Models
  4. System Model
  5. Channel Model
  6. Channel Estimation and Uplink Data Transmission
  7. Channel Estimation
  8. Uplink Data Transmission
  9. Problem Formulation and Optimization
  10. Problem Formulation
  11. Simultaneous Optimization of Both SIMs
  12. Proposed Algorithm-PGAM
  13. Complex-valued Gradients
  14. Projection Operations of PGAM
  15. Convergence Analysis
  16. ...and 10 more sections

Key Result

Lemma 1

The linear MMSE estimated channel ${\mathbf{c}}_{k}$ of user $k$ at the BS is obtained as where $\hat{{\mathbf{R}}}_{k}={\mathbf{W}}^{1^{{\mathsf{H}}}}{\mathbf{P}}^{H}{\mathbf{R}}_{k}{\mathbf{W}}^{1}{\mathbf{P}}$, ${\mathbf{Q}}_{k}\!=\! \left(\!\hat{{\mathbf{R}}}_{k}\!+\!\frac{1}{ \tau \rho }{\bm{\mathrm{I}}}_{M}\!\right)^{\!-1}$, and ${\mathbf{r}}_{k}$ is the noisy channel given by trai

Figures (8)

  • Figure 1: A BSIM and CSIM-assisted mMIMO system with multiple users.
  • Figure 2: Achievable sum SE of the proposed double-SIM mMIMO architecture versus the number of iterations
  • Figure 3: Impact of BCIM and CSIM on the NMSE of UE $k$ versus the SNR.
  • Figure 4: Achievable sum SE of the proposed double-SIM mMIMO architecture.
  • Figure 5: Achievable sum SE of the proposed double-SIM mMIMO architecture.
  • ...and 3 more figures

Theorems & Definitions (7)

  • Remark 1
  • Lemma 1
  • proof
  • Theorem 1
  • proof
  • Proposition 1
  • proof