Unlocking Symbol-Level Precoding Efficiency Through Tensor Equivariant Neural Network

2025-10-02

AI Summary

To address the high computational complexity of symbol-level precoding (SLP) arising from constructive interference exploitation, this paper proposes an end-to-end tensor-equivariant deep learning framework. We first uncover the tensor-equivariant structure inherent in the optimal closed-form solution of SLP; leveraging this insight, we design parameter-sharing equivariant network modules that jointly incorporate instantaneous channel state information and statistical channel knowledge to directly map to symbol-level auxiliary variables. An attention mechanism is further integrated to enhance representational capacity. The resulting method achieves linear time complexity—reducing inference latency by approximately 80× compared to conventional SLP solvers—while maintaining strong generalization across varying numbers of users, symbol block lengths, and imperfect channel conditions. Empirically, it attains performance closely approaching that of optimal SLP.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Although symbol-level precoding (SLP) based on constructive interference (CI) exploitation offers performance gains, its high complexity remains a bottleneck. This paper addresses this challenge with an end-to-end deep learning (DL) framework with low inference complexity that leverages the structure of the optimal SLP solution in the closed-form and its inherent tensor equivariance (TE), where TE denotes that a permutation of the input induces the corresponding permutation of the output. Building upon the computationally efficient model-based formulations, as well as their known closed-form solutions, we analyze their relationship with linear precoding (LP) and investigate the corresponding optimality condition. We then construct a mapping from the problem formulation to the solution and prove its TE, based on which the designed networks reveal a specific parameter-sharing pattern that delivers low computational complexity and strong generalization. Leveraging these, we propose the backbone of the framework with an attention-based TE module, achieving linear computational complexity. Furthermore, we demonstrate that such a framework is also applicable to imperfect CSI scenarios, where we design a TE-based network to map the CSI, statistics, and symbols to auxiliary variables. Simulation results show that the proposed framework captures substantial performance gains of optimal SLP, while achieving an approximately 80-times speedup over conventional methods and maintaining strong generalization across user numbers and symbol block lengths.

Problem

• Reducing high computational complexity in symbol-level precoding systems
• Designing tensor equivariant neural networks for efficient precoding solutions
• Maintaining performance gains under imperfect channel state information conditions

Innovation

• Tensor equivariant neural network for precoding
• Attention-based module with linear complexity
• TE network handles imperfect CSI scenarios