Deep Complex-valued Neural-Network Modeling and Optimization of Stacked Intelligent Surfaces

2025-08-29

AI Summary

To address the challenge of jointly maximizing spectral efficiency and minimizing detection error in stacked intelligent surfaces (SIS) for multi-antenna systems, this paper proposes an end-to-end differentiable complex-valued neural network framework. We innovatively model each SIS unit as a complex neuron subject to modulus constraints—bypassing conventional SVD-based orthogonal decomposition—and thereby enable non-orthogonal beam design and hybrid analog-digital beamforming. Leveraging GPU-accelerated automatic differentiation and deep training under Rician fading channels, our approach achieves rapid configuration optimization and near-online deployment. Experiments demonstrate significant improvements over state-of-the-art methods in throughput, symbol error rate, and channel robustness. This work establishes a novel, efficient, and flexible paradigm for wave-domain intelligent control in 6G wireless systems.

Technology Category

• Intelligent Robots: Learning & Optimization for ROB
• Search and Optimization: Mixed Discrete/Continuous Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Personalized, context-aware and across-device search
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

We propose a complex-valued neural-network (CV-NN) framework to optimally configure stacked intelligent surfaces (SIS) in next-generation multi-antenna systems. Unlike conventional solutions that separately tune analog metasurface phases or rely strictly on SVD-based orthogonal decompositions, our method models each SIS element as a unit-modulus complex-velued neuron in an end-to-end differentiable pipeline. This approach avoids enforcing channel orthogonality and instead allows for richer wavefront designs that can target a wide range of system objectives, such as maximizing spectral efficiency and minimizing detection errors, all within a single optimization framework. Moreover, by exploiting a fully differentiable neural-network formulation and GPU-based auto-differentiation, our approach can rapidly train SIS configurations for realistic, high-dimensional channels, enabling near-online adaptation. Our framework also naturally accommodates hybrid analog-digital beamforming and recovers classical SVD solutions as a special case. Numerical evaluations under Rician channels demonstrate that CV-NN SIS optimization outperforms state-of-the-art schemes in throughput, error performance, and robustness to channel variation, opening the door to more flexible and powerful wave-domain control for future 6G networks.

Problem

• Optimizing stacked intelligent surfaces for multi-antenna systems
• Modeling SIS elements as complex-valued neurons in differentiable pipeline
• Maximizing spectral efficiency and minimizing detection errors

Innovation

• Complex-valued neural network for SIS optimization
• End-to-end differentiable pipeline without orthogonality constraints
• GPU-based auto-differentiation enabling rapid training adaptation