Organizations: School of Information and Electronics, Beijing Institute of Technology (BIT), Beijing 100081, China · School of Information and Electronics, BIT (Zhuhai), Zhuhai 519088, China · Department of Electronic Engineering, Tsinghua University, Beijing, 100084, China · School of Information and Communication, Guilin University of Electronic Technology (GUET), Guilin 541004, China · Yangtze Delta Region Academy, BIT (Jiaxing), Jiaxing 314019, China, and also with the School of Information and Electronics, Advanced Research Institute of Multidisciplinary Sciences, BIT, Beijing 100081, China
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).
Figures & tables
Architecture
Ref.
Digital precoding
Analog precoding
EM precoding
Spatial reconfiguration
Reconfiguration mechanism
Comments
Hybrid MIMO
[ 2 ]
✓
✓
Fully-connected is impractical; sub-connected has limited spectral efficiency
Movable/fluid antenna
[ 7 , 8 ]
Port selection and index modulation
Low antenna-aperture utilization and slow reconfiguration response
EM: discrete 3GPP TR 38.901 radiation-pattern selection with different directions and HPBWs
[ 18 ]
✓
✓
EM: joint EM-domain precoding and channel estimation
TABLE I: Comparison of reconfiguration domains, mechanisms, and limitations in representative MIMO architectures.
Fig. 1: System model of the proposed tri-hybrid multi-user downlink transmitter, where EM-reconfigurable antennas select radiation states and a sub-connected RF network produces analog and digital precoders.
Fig. 2: Four candidate radiation patterns of the non-regular mode according to [ 11 ] . For each antenna element, the horizontal, vertical, and normal directions are the x , z , and y axes, respectively.
Fig. 3: Nine candidate radiation patterns of the 3GPP TR 38.901 mode adopted in [ 16 ] . With HPBW =90∘ , the elevation and azimuth main-lobe pointing directions are sampled at −60∘ , 0∘ , and 60∘ . For each antenna element, the horizontal, vertical, and normal directions are the x , z , and y axes.
Fig. 4: Overview of the proposed Conformer-based Tri-PNet. RPSNet selects the antenna-wise EM precoding matrix FEM , which gathers the selected channels HEM[q] for HPNet to generate FRF and FBB[q] .
Fig. 5: Detailed architecture of RPSNet. The real and imaginary parts of the pattern-aware CSI are embedded and processed by a Conformer encoder to produce antenna-wise pattern logits. The Gumbel-Softmax selector generates FEM , which gathers HEM[q] for q=1,…,Nc .
Fig. 6: Detailed architecture of HPNet. Its analog branch combines a Transformer channel feature with an SVD prior through gated cross-attention to obtain the quantized FRF . Its digital branch processes HRF[q] using dual-path attention to produce the normalized FBB[q] .
Hyperparameter
Value
Optimizer
Adam
Training epochs
50
Mini-batch size
512
Initial learning rate
10−4
Learning-rate schedule
×0.5 every 10 epochs
Gumbel temperature
max{0.1,2exp(−0.03e)}
TABLE II: Training hyperparameters.
Fig. 7: Performance comparison of tri-hybrid precoding using different schemes under the non-regular and 3GPP TR 38.901 modes at Pt=50 dBm.
Fig. 8: Spectral-efficiency evaluation under the non-regular radiation-pattern mode. The left and right panels show the spectral efficiency versus transmit power and number of users, respectively; the user numbers are U∈{2,4,6,8} .
Fig. 9: Spectral-efficiency evaluation under the 3GPP TR 38.901 radiation-pattern mode. The left and right panels show the spectral efficiency versus transmit power and number of users, respectively. Here the user numbers are U∈{2,4,6,8} .
Fig. 10: Comparison of the proposed sub-connected Tri-PNet, fully-connected Tri-PNet, fully-digital WMMSE, and fixed-Type-0 fully-connected PCA and manifold optimization-based alternating minimization (MO-AltMin) precoding under the non-regular radiation-pattern mode. The fully-connected Tri-PNet uses NRF=8 RF chains connected to all Nt=32 antennas, whereas fully-digital WMMSE uses eight RF chains for eight active antennas. The left and right panels show the spectral efficiency versus transmit power and number of users, respectively. Here the user numbers are U∈{2,4,6,8} .
Fig. 11: Spectral efficiency versus HPBW under the 3GPP TR 38.901 pattern mode at Pt=50 dBm.
Fig. 12: Spectral efficiency versus NCPE under the non-regular mode. The NCPE values range from −20 to 20 dB.
Fig. 13: Spectral efficiency versus NCPE under the 3GPP TR 38.901 mode. The NCPE values range from −20 to 20 dB.
Configuration
Parameters
FLOPs
PR-HBFNet [ 23 ]
8.65M
481.03M
RPSNet + HBN [ 23 ]
10.83M
619.79M
PRN [ 23 ] + HPNet
11.56M
696.80M
Our Tri-PNet
13.74M
835.55M
Greedy [ 11 ] + HPNet
7.98M
544.75M
TABLE III: Parameter number and FLOPs under the non-regular mode.
Configuration
Parameters
FLOPs
PR-HBFNet [ 23 ]
13.12M
487.92M
RPSNet + HBN [ 23 ]
15.30M
626.67M
PRN [ 23 ] + HPNet
16.03M
703.68M
Our Tri-PNet
18.21M
842.43M
Greedy [ 11 ] + HPNet
7.98M
555.24M
TABLE IV: Parameter number and FLOPs under the 3GPP TR 38.901 mode.
The integration of terahertz communications and ultra-massive multiple-input multiple-output (UM-MIMO) systems in 6G networks is motivated by their ability to enable unprecedented data rates, mitigate spectrum congestion, and enhance overall network performance. However, the enlarged antenna apertures and higher carrier frequencies in these systems increase the Rayleigh distance, causing users to span both the near-field and conventional far-field regions. Accurate spatial precoding thus requires exact channel estimation at the base station - a task made more challenging by the hybrid coexistence of near- and far-field effects and the limited number of digital chains available in hybrid beamforming architectures. In this paper, we propose a block recurrent transformer model to address this challenge. We demonstrate that a single transformer block equipped with state memory can be trained once and then iteratively applied for hybrid-field channel estimation. Furthermore, we train the model such that it generalizes to wireless channels with varying scatterer distances, different numbers of propagation paths, and wideband operation. Simulation results show that the proposed method achieves performance gains of approximately 5 dB and 7.5 dB in normalized mean squared error (NMSE) over state-of-the-art solutions in narrowband and wideband scenarios, respectively.
Dmitry Artemasov, Alexander Shmatok, Kirill Andreev +3
Center for Next Generation Wireless and IoT, Skolkovo Institute of Science and Technology, Moscow, Russia · Department of IEOR, Indian Institute of Technology Bombay, India · Faculty of Computer and Engineering Sciences, Innopolis University, Innopolis, Russia
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.
Zijiu Yang, Zixiang Zhang, Shunpu Tang +2
College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China
Predicting electromagnetic field (EMF) strength in urban environments is essential for cellular network planning but computationally expensive with physics-based simulators. We propose a multi-conditioned dense prediction framework that generates 500 500 EMF maps from building layout images and antenna configurations. Our architecture uses a High-Resolution Transformer (HRFormer) backbone with two complementary conditioning mechanisms: Feature-wise Linear Modulation (FiLM) injects scalar antenna parameters into all backbone stages, while cross-attention fuses 1-D radiation pattern tokens with spatial features at the deepest stage. We further introduce transmitter-relative spatial channels encoding distance, proximity, and bearing from the antenna, enabling coordinate-consistent test-time augmentation (TTA) that reduces test MAE by 6.3%. To address the prediction difficulty imbalance across EMF maps, we design a composite loss combining masked L1, multi-scale structural similarity (MS-SSIM), and a focal L1 term that upweights high-signal pixels, outperforming individual loss components in all metrics. Our best model achieves a test MAE of 0.0461, a 25.2% improvement over a plain UNet baseline and 31.8% over an HRFormer-only baseline.Do-
Do-Eon Kim, Dongryul Park, Seungyoung Ahn +3
Soongsil University, Seoul 06978, Republic of Korea · Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology, Daejeon 34051, Republic of Korea · Department of Intelligent Semiconductors, Soongsil University, Seoul 06978, Republic of Korea