Neural Precoding in Complex Projective Spaces

Precoding is a key technique for interference management and performance improvement in multi-antenna wireless systems. However, existing precoding methods are typically developed for specific system models, objectives, and constraint sets, which limits their adaptability to the heterogeneous and evolving scenarios expected in future 6G networks. To address this limitation, we propose AgenticPrecoding, a universal multi-agent framework that automates end-to-end precoding derivation directly from user-level communication requirements. Specifically, AgenticPrecoding decomposes the derivation process into four coordinated stages: problem formulation, solver selection, prompt upsampling, and code generation, assigning each stage to a specialized agent tailored to its specific reasoning demands. We employ two LoRA-adapted reasoning agents to inject precoding-specific domain knowledge for problem formulation and solver selection, while two general-purpose Large Language Models (LLMs) handle prompt refinement and executable code generation. Furthermore, a feedback-driven refinement mechanism is incorporated to enhance code executability, constraint feasibility, and solution quality. Extensive experiments across 10 representative precoding scenarios demonstrate that AgenticPrecoding achieves superior cross-scenario adaptability compared to conventional optimization-based and LLM-based baselines.

For multi-input and multi-output (MIMO) channels, the optimal channel estimation (CE) based on linear minimum mean square error (LMMSE) requires three-dimensional (3D) filtering. However, the complexity is often prohibitive due to large matrix dimensions. Suboptimal estimators approximate 3DCE by decomposing it into time, frequency, and spatial domains, while yields noticeable performance degradation under correlated MIMO channels. On the other hand, recent advances in deep learning (DL) can explore channel correlations in all domains via attention mechanisms. Building on this capability, we propose a dual attention mechanism based 3DCE network (3DCENet) that can achieve accurate estimates.

Electromagnetic (EM)-reconfigurable antennas provide multiple candidate radiation patterns per element, thereby introducing an additional EM-domain degree of freedom. Integrating radiation-pattern reconfigurability, realized as EM-domain precoding, with conventional hybrid analog-digital precoding yields tri-hybrid multiple-input multiple-output (MIMO) precoding, which can substantially improve the spectral efficiency of wideband multi-user MIMO orthogonal frequency-division multiplexing (OFDM) systems. However, the joint design of EM, analog, and digital precoding remains challenging. To address this challenge, we propose a tri-hybrid precoding network (Tri-PNet) based on Conformer, an emerging neural architecture that combines the local modeling strength of convolutional neural networks with the global dependency modeling of Transformers. Furthermore, two representative radiation-pattern modes, i.e., the non-regular mode and the 3rd Generation Partnership Project (3GPP) Technical Report (TR) 38.901 mode, are investigated. Tri-PNet is trained in an unsupervised manner to jointly learn EM, analog, and digital precoding by maximizing the average sum spectral efficiency. Its radiation-pattern selection network (RPSNet) employs a Conformer encoder to capture both local and global frequency-domain correlations, whereas its hybrid analog-digital precoding network (HPNet) combines cross-attention and dual-path processing with singular-value-decomposition (SVD) and zero-forcing (ZF) priors. Simulation results under both radiation-pattern modes demonstrate that Tri-PNet outperforms random EM precoding and conventional hybrid MIMO without EM precoding, approaches the greedy EM precoding search scheme with substantially lower online complexity, and remains robust to imperfect channel state information (CSI).