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Modeling, Optimization and Electromagnetic Validation of Stacked Intelligent Metasurfaces by Using a Multiport Network Model

Giuseppe Pettanice, Andrea Abrardo, Alberto Toccafondi, Marco Di Renzo

Abstract

Stacked intelligent metasurfaces (SIMs) extend the concept of reconfigurable intelligent surfaces by cascading multiple programmable layers, enabling advanced electromagnetic wave transformations for communication and sensing applications. However, most existing optimization frameworks rely on simplified channel abstractions that may overlook key electromagnetic effects such as multiport coupling, circuit losses, and non-ideal hardware behavior. In this paper, we develop a modeling and optimization framework for SIMs based on a multiport network representation using scattering parameters. The proposed formulation captures realistic circuit characteristics and mutual interactions among SIM ports while remaining amenable to optimization. The resulting models are validated through electromagnetic simulations, enabling a systematic comparison between idealized and practical SIM configurations. Numerical results for communication and sensing scenarios confirm that the proposed framework provides accurate performance predictions and enables the effective design of SIM configurations under realistic electromagnetic conditions.

Modeling, Optimization and Electromagnetic Validation of Stacked Intelligent Metasurfaces by Using a Multiport Network Model

Abstract

Stacked intelligent metasurfaces (SIMs) extend the concept of reconfigurable intelligent surfaces by cascading multiple programmable layers, enabling advanced electromagnetic wave transformations for communication and sensing applications. However, most existing optimization frameworks rely on simplified channel abstractions that may overlook key electromagnetic effects such as multiport coupling, circuit losses, and non-ideal hardware behavior. In this paper, we develop a modeling and optimization framework for SIMs based on a multiport network representation using scattering parameters. The proposed formulation captures realistic circuit characteristics and mutual interactions among SIM ports while remaining amenable to optimization. The resulting models are validated through electromagnetic simulations, enabling a systematic comparison between idealized and practical SIM configurations. Numerical results for communication and sensing scenarios confirm that the proposed framework provides accurate performance predictions and enables the effective design of SIM configurations under realistic electromagnetic conditions.
Paper Structure (28 sections, 61 equations, 16 figures)

This paper contains 28 sections, 61 equations, 16 figures.

Table of Contents

  1. Introduction
  2. Contributions
  3. CEO S-parameter model
  4. S-parameters representation and optimization of a SIM
  5. SIM optimization problem
  6. Gradient evaluation
  7. Simplified SIM models and optimization
  8. S-parameters representation of a layered isolated SIM
  9. Gradient evaluation for a layered isolated SIM
  10. Weakly-coupled SIM
  11. Optimization with discrete cell-state sets
  12. Discrete scattering-cell model
  13. Special case (phase-only quantization)
  14. Initialization via projection onto the codebook
  15. Coordinate-wise discrete descent
  16. ...and 13 more sections

Figures (16)

  • Figure 1: Multiport network representation of the considered CEO scenario, including a transmitting array (T), an $N$-port CEO, and a receiving array (R).
  • Figure 2: Schematic of the considered SIM as a CEO with a layered architecture. The shaded region represents the electromagnetic interactions among all antenna ports due to wave propagation in the surrounding medium.
  • Figure 3: SIM geometry and unit-cell example
  • Figure 4: Illustration of the layer-isolated SIM ($SIM$-$I$) coupling structure. The shaded regions represent electromagnetic coupling only between adjacent arrays: from the transmitter to the receive array of the first layer, between the transmit and receive arrays of consecutive layers, and from the transmit array of the last layer to the receiver. Interactions between non-adjacent layers are neglected
  • Figure 5: Structure of the considered SIM with $Q$ stacked T-RIS layers. Each layer includes planar receive and transmit arrays interconnected by tunable phase-shifting networks.
  • ...and 11 more figures