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Stacked Intelligent Metasurfaces-Based Electromagnetic Wave Domain Interference-Free Precoding

Hetong Wang, Yashuai Cao, Tiejun Lv, Jintao Wang, Ni Wei, Jiancheng An, Chau Yuen

TL;DR

This work introduces a wave-domain, SIM-enabled interference-exploitation precoding framework for MU-MISO systems, explicitly modeling and compensating power amplifier nonlinear distortion (NLD) within the EM domain. It advances a frame-level IEP design supported by a Recursive Oblique Manifold (ROM) algorithm to optimize multi-layer SIM phase shifts and an ROM-AO framework to jointly handle transmit antenna selection, SIM phase design, and power allocation. The key contributions include NLD-aware IEP, layer-wise ROM for phase shifts, and a greedy AS with ROM-AO for flexible DoF, all validated by simulations showing substantial gains over benchmarks and substantial SER/sum-rate improvements as SIM layers and AS become richer. The results demonstrate that SIM-enabled IEP can outperform traditional precoding while effectively mitigating hardware impairments, offering a scalable path toward high-efficiency, interference-exploitation wireless systems.

Abstract

This paper introduces an interference-free multi-stream transmission architecture leveraging stacked intelligent metasurfaces (SIMs), from a new perspective of interference exploitation. Unlike traditional interference exploitation precoding (IEP) which relies on computational hardware circuitry, we perform the precoding operations within the analog wave domain provided by SIMs. However, the benefits of SIM-enabled IEP are limited by the nonlinear distortion (NLD) caused by power amplifiers. A hardware-efficient interference-free transmitter architecture is developed to exploit SIM's high and flexible degree of freedom (DoF), where the NLD on modulated symbols can be directly compensated in the wave domain. Moreover, we design a frame-level SIM configuration scheme and formulate a maxmin problem on the safety margin function. With respect to the optimization of SIM phase shifts, we propose a recursive oblique manifold (ROM) algorithm to tackle the complex coupling among phase shifts across multiple layers. A flexible DoF-driven antenna selection (AS) scheme is explored in the SIM-enabled IEP system. Using an ROM-based alternating optimization (ROM-AO) framework, our approach jointly optimizes transmit AS, SIM phase shift design, and power allocation (PA), and develops a greedy safety margin-based AS algorithm. Simulations show that the proposed SIM-enabled frame-level IEP scheme significantly outperforms benchmarks. Specifically, the strategy with AS and PA can achieve a 20 dB performance gain compared to the case without any strategy under the 12 dB signal-to-noise ratio, which confirms the superiority of the NLD-aware IEP scheme and the effectiveness of the proposed algorithm.

Stacked Intelligent Metasurfaces-Based Electromagnetic Wave Domain Interference-Free Precoding

TL;DR

This work introduces a wave-domain, SIM-enabled interference-exploitation precoding framework for MU-MISO systems, explicitly modeling and compensating power amplifier nonlinear distortion (NLD) within the EM domain. It advances a frame-level IEP design supported by a Recursive Oblique Manifold (ROM) algorithm to optimize multi-layer SIM phase shifts and an ROM-AO framework to jointly handle transmit antenna selection, SIM phase design, and power allocation. The key contributions include NLD-aware IEP, layer-wise ROM for phase shifts, and a greedy AS with ROM-AO for flexible DoF, all validated by simulations showing substantial gains over benchmarks and substantial SER/sum-rate improvements as SIM layers and AS become richer. The results demonstrate that SIM-enabled IEP can outperform traditional precoding while effectively mitigating hardware impairments, offering a scalable path toward high-efficiency, interference-exploitation wireless systems.

Abstract

This paper introduces an interference-free multi-stream transmission architecture leveraging stacked intelligent metasurfaces (SIMs), from a new perspective of interference exploitation. Unlike traditional interference exploitation precoding (IEP) which relies on computational hardware circuitry, we perform the precoding operations within the analog wave domain provided by SIMs. However, the benefits of SIM-enabled IEP are limited by the nonlinear distortion (NLD) caused by power amplifiers. A hardware-efficient interference-free transmitter architecture is developed to exploit SIM's high and flexible degree of freedom (DoF), where the NLD on modulated symbols can be directly compensated in the wave domain. Moreover, we design a frame-level SIM configuration scheme and formulate a maxmin problem on the safety margin function. With respect to the optimization of SIM phase shifts, we propose a recursive oblique manifold (ROM) algorithm to tackle the complex coupling among phase shifts across multiple layers. A flexible DoF-driven antenna selection (AS) scheme is explored in the SIM-enabled IEP system. Using an ROM-based alternating optimization (ROM-AO) framework, our approach jointly optimizes transmit AS, SIM phase shift design, and power allocation (PA), and develops a greedy safety margin-based AS algorithm. Simulations show that the proposed SIM-enabled frame-level IEP scheme significantly outperforms benchmarks. Specifically, the strategy with AS and PA can achieve a 20 dB performance gain compared to the case without any strategy under the 12 dB signal-to-noise ratio, which confirms the superiority of the NLD-aware IEP scheme and the effectiveness of the proposed algorithm.
Paper Structure (30 sections, 1 theorem, 43 equations, 13 figures, 1 table, 3 algorithms)

This paper contains 30 sections, 1 theorem, 43 equations, 13 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Symbol-Level and Frame-Level Precoding
  4. Single-Layer Intelligent Metasurface-Assisted Precoding
  5. Stacked Intelligent Metasurface-Assisted Precoding
  6. Contributions and Organization
  7. System Model and Problem Formulation
  8. Transmission System
  9. NLD model for modulated symbols
  10. Channel model for SIM-assisted MU-MISO downlink communication system
  11. Scattering Model of Stacked Intelligent Surfaces
  12. Transmission Strategy and Problem Formulation
  13. SIM Phase Shift Optimization
  14. Problem Transformation and Decomposition
  15. Problem Decoupling via Layer-Wise Reformulation
  16. ...and 15 more sections

Key Result

Lemma 1

The smooth log-sum-exp approximation $f(\boldsymbol{\Theta}_{l})$ is a smooth maximum approximation function by leveraging the properties of the exponential and logarithmic functions. It satisfies $f(\boldsymbol{\Theta}_{l}) \geq g_{\mu^*,k^*}$, and $f(\boldsymbol{\Theta}_{l}) \to g_{\mu^*,k^*}$ whe

Figures (13)

  • Figure 1: SIM-empowered integrated modulation and precoding framework in the EM wave domain.
  • Figure 2: IEP design for QPSK signals: (a) CI region and safety margin for a first-quadrant QPSK point; (b) diagram from Fig. 2(a) after a clockwise rotation by $\angle s_{\mu,k}$.
  • Figure 3: Simulation setup of SIM-empowered MU-MISO communication system.
  • Figure 4: Constellation diagrams for different SIM layers under NLD-aware and NLD-unaware schemes, with $K = 5$, $N = 36$: (a) NLD-aware; (b) NLD-unaware.
  • Figure 5: SER and sum rate vs. SNR, with $K = 5$, $N = 36$.
  • ...and 8 more figures

Theorems & Definitions (1)

  • Lemma 1