RISnet: A Domain-Knowledge Driven Neural Network Architecture for RIS Optimization with Mutual Coupling and Partial CSI

TL;DR

The paper tackles joint SDMA precoding and RIS configuration in the presence of mutual coupling and partial CSI. It derives a mutual-coupling–aware RIS channel model and introduces RISnet, a domain-knowledge–driven unsupervised neural network that scales to large RIS deployments and is permutation-invariant. A hybrid approach combines ML-based RIS configuration with analytical precoding to guarantee performance while reducing training complexity. Empirical results across ray-tracing and deterministic channel models show RISnet outperforms baselines, with partial CSI viable when the channel is sparse, and underscore the importance of explicitly modeling mutual coupling. The work advances scalable, real-time RIS optimization by integrating problem-specific architecture design with data-driven learning.

Abstract

Space-division multiple access (SDMA) plays an important role in modern wireless communications. Its performance depends on the channel properties, which can be improved by reconfigurable intelligent surfaces (RISs). In this work, we jointly optimize SDMA precoding at the base station (BS) and RIS configuration. We tackle difficulties of mutual coupling between RIS elements, scalability to more than 1000 RIS elements, and high requirement for channel estimation. We first derive an RIS-assisted channel model considering mutual coupling, then propose an unsupervised machine learning (ML) approach to optimize the RIS with a dedicated neural network (NN) architecture RISnet, which has good scalability, desired permutation-invariance, and a low requirement for channel estimation. Moreover, we leverage existing high-performance analytical precoding scheme to propose a hybrid solution of ML-enabled RIS configuration and analytical precoding at BS. More generally, this work is an early contribution to combine ML technique and domain knowledge in communication for NN architecture design. Compared to generic ML, the problem-specific ML can achieve higher performance, lower complexity and permutation-invariance.

Figures (11)

• Figure 1: The system model of -assisted downlink multi-user broadcasting.
• Figure 2: Information processing (info. proc.) in RISnet. The symmetric information processing along the dimension of users makes RISnet invariant to user permutation.
• Figure 3: Application of 9 information processing units to expand from one anchor RIS element to 9 RIS elements, where $\mathbf{f}_5$ is the channel feature of element 5. Information processing unit 5 is comparable to the information processing units of RISnet with full . Indices of user and layer are omitted for simplicity since the expansion is for elements.
• Figure 4: Expansion of considered RIS elements. Blue: anchor RIS elements. Lower left corner: example of the expansion to extend the anchor RIS elements from the blue element to the adjacent elements (light blue elements in Subfigure (a) and all elements in Subfigure (b)).
• Figure 5: The RISnet architecture with partial , where the information processing of normal layers is given by \ref{['eq:layer_processing']} and the information processing of expansion layers is given by \ref{['eq:expansion_layer_processing']}. Note that this process is only possible with uniformly placed anchor elements.

Theorems & Definitions (9)

• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Definition 1
• Theorem 1
• proof
• Remark 5
• Remark 6