Deep Learning-Based Tri-Hybrid Multi-User MIMO Precoding: The Blessing of EM-Reconfigurable Antennas

arXiv:2609.39167 · eess.SP, cs.IT, cs.LG, math.IT · Submitted 2026-09-30 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: Today's paper: "Deep Learning-Based Tri-Hybrid Multi-User MIMO Precoding".

Jane: The gist: Tri-PNet, a Conformer-based tri-hybrid precoding network, jointly learns EM, analog,

Tom: First, who's behind it and why it matters.

Title and authors: Tom: So, we're looking at this paper now, "Deep Learning-Based Tri-Hybrid Multi-User MIMO Precoding: The Blessing of EM-Reconfigurable Antennas." It’s by Kaijun Feng and his team.

Jane: Right, so the main idea here is that they take these electromagnetic reconfigurable antennas and combine them with hybrid analog and digital precoding to make a tri-hybrid system that can boost spectral efficiency in wideband MIMO OFDM.

Lu: The authors are tackling the challenge of designing this joint EM, analog, and digital precoding because doing it all at once is really tough.

Meng: What does that mean for us on the ground? Does it just make our existing hybrid systems a little better?

Tom: It’s more than just a little better. They propose this TriPNet network based on Conformer to jointly learn these three precoding variables from the sample-wise channel tensors, mapping them to FbEM, FbRF, and FbBBq.

Jane: So they are using this neural network structure—the Conformer—to handle the complexity of learning how to do all three things simultaneously.

Lu: Specifically, they use a two-module architecture: an RPSNet for radiation pattern selection and an HPNet for hybrid analog-digital precoding.

Meng: Let's talk about that RPSNet part. How does it actually figure out which radiation pattern to use?

Tom: The RPSNet uses a Conformer encoder to capture both local and global frequency-domain correlations, which lets it pick the optimal radiation pattern by processing a feature vector zq, and then projecting that into antenna-wise pattern logits.

Jane: So it’s using this Conformer to see how the whole wideband channel is related across different frequencies at once, not just one frequency at a time.

Lu: The output of the RPSNet is mapped to antenna-wise pattern logits, AEM, which they then use with a differentiable Gumbel-Softmax selector during training to determine the discrete radiation pattern selection matrix FEM.

Meng: Okay, so they are using this selector during training to make sure it picks one of the candidate patterns we have available. That sounds like a lot of tuning for deployment.

Tom: It is, but they get away with it because after offline training, TriPNet just does a single forward inference to produce all the precoders at once, which avoids that iterative pattern search that takes about O(NtNpNcUN2RF).

Title and authors: Jane: That reduction in complexity is pretty significant for real-world hardware deployment when you're dealing with wideband systems.

Lu: And for the analog and digital part, they have the HPNet which uses model-driven priors to design these precoders after the radiation pattern selection is done.

Meng: What are those model-driven priors? Are we talking about something that just looks at a simple prior, or something more complex?

Tom: For the analog part, they construct an SVD-based analog precoder as a model-driven prior by applying SVD to the channel Gram matrix Cuq for each user and subcarrier.

Jane: So they are using Singular Value Decomposition on that Gram matrix to get a starting point for the analog design.

Lu: Then, their neural analog branch uses a Transformer encoder and a gated cross-attention refinement to generate the refined analog precoder FeRF.

Meng: A Transformer and cross-attention for the analog part sounds computationally heavy when you're trying to ship this on embedded hardware. How does that fit into your deployment concerns?

Tom: The digital part uses a normalized-channelbased Zero Forcing digital precoder as another model-driven prior, which they then refine with a dual-path attention block.

Jane: That dual-path attention block sounds like they are looking at the channel in two different ways to make sure the digital part is well-designed.

Lu: The results show that TriPNet outperforms random EM precoding and conventional hybrid MIMO without EM precoding, and it approaches the greedy search scheme with substantially lower online complexity.

Meng: Lower complexity is good for us because we don't want to spend all day on training just to get a slightly better result than what we could find manually.

Tom: It seems they are robust to imperfect CSI because the Conformer-based RPSNet extracts local and global frequency-domain features, while the HPNet uses model-driven analog and digital precoding priors to reduce sensitivity to noisy CSI.

Jane: So it handles noisy channel information better because of how it learns the structure of those signals across time and frequency.

Lu: The framework is validated under two different radiation-pattern families: the non-regular mode and the 3GPP TR thirty-eight point nine zero one mode, which confirms its hardware generality <ref:2609.39167#pg3>.

Meng: That’s important, because it means this isn't just tuned for one specific type of antenna setup; it works across different physical configurations.

Title and authors: Tom: And they consistently achieve the highest spectral efficiency as the transmit power increases and as more users are served under both radiation-pattern modes.

Jane: So, when you push up the power or add more users, this approach keeps delivering high performance regardless of which specific pattern mode you're using.

Lu: The paper also points out a non-monotonic relationship between the HPBW and spectral efficiency, showing that the best performance is observed near one hundred degrees under the 3GPP TR thirty-eight point nine zero one radiation-pattern mode.

Meng: That’s a useful piece of data for our hardware teams because it tells us where we should focus our beamwidth optimization efforts to get the most out of these antennas.

Tom: Overall, this work on Deep Learning-Based Tri-Hybrid Multi-User MIMO Precoding is about jointly learning EM, analog, and digital precoding from those sample-wise channel tensors.

Jane: It really connects the dots between hardware capabilities—like having EM reconfigurability—and the software approach of using advanced deep learning to design everything together.

Lu: The implication here is that this joint design approach captures the coupling among users, antennas, subcarriers, and radiation pattern modes in a way that previous methods couldn't.

Meng: So for deployment, it means we can build more efficient systems without needing a lot of complex manual optimization loops on the fly.

Tom: It seems like TriPNet is a solid step forward by replacing iterative search with this single forward inference while still hitting high spectral efficiency targets.

Jane: We should keep an eye on how they extend this framework to multi-cell scenarios and more realistic spatially consistent channel models in future work, which the authors mention.

Lu: I agree, extending it to multi-cell scenarios is definitely where the next big challenge lies for this type of representation learning.

Meng: For now, from what we're seeing here with these results on spectral efficiency improvements over baseline schemes, it looks like a promising direction to explore for our current system architecture.

Tom: So that's the rundown on Deep Learning-Based Tri-Hybrid Multi-User MIMO Precoding: The Blessing of EM-Reconfigurable Antennas. We’ve seen how TriPNet uses a Conformer and its hybrid design to tackle the joint learning problem with EM, analog, and digital precoding.

The paper's summary: Tom: So, to recap, this paper is about building a system that combines EM reconfigurable antennas with hybrid analog and digital precoding using a neural network called TriPNet to improve spectral efficiency in wideband MIMO OFDM systems.

Jane: It’s basically taking this hardware capability—the ability for each antenna element to switch between different radiation patterns—and integrating it smartly with the software side of things, the precoders, using a deep learning approach.

Lu: The core idea is that instead of designing the EM part, the analog part, and the digital part separately and hoping they work together well, you use this TriPNet to learn all three at once from a single set of measurements called sample-wise channel tensors.

Meng: I'm still thinking about that joint learning bit. If you’re training something like this on real traffic data, how do you even define the loss function when the EM selection is discrete and the others are continuous?

Tom: The paper says they maximize the average sum spectral efficiency, which is basically a measure of how much data we can send successfully across all users and subcarriers. It’s a straightforward objective function applied to the whole system performance.

Jane: And they structure this learning into two main parts: an RPSNet for picking the radiation pattern, and an HPNet for designing the analog and digital precoders based on that choice.

Lu: The RPSNet uses a Conformer encoder, which is interesting because it’s supposed to handle both local frequency details and long-range dependencies in the wideband channel data simultaneously.

Tom: Yeah, that’s where they get their power—the Conformer structure lets it look at the whole frequency spectrum together, not just one subcarrier at a time.

Jane: And then the HPNet takes that selected information and uses a few clever techniques to refine the analog and digital precoders.

Lu: Specifically, for the analog part, they use an SVD-based analog precoder as a starting point—a model-driven prior—and then put a Transformer encoder with gated cross-attention on top of it for refinement.

Meng: Wait, so you’re using a Transformer and cross-attention just to refine the analog part? That sounds like it could be very slow if we try to run that inference repeatedly on every time slot in real time.

Tom: The authors address complexity by showing that after the offline training is done, TriPNet produces all these variables—EM, analog, and digital precoders—in just a single forward inference pass. That’s what brings the online complexity down significantly compared to searching for patterns iteratively.

Jane: So they manage to get this high-quality design without needing constant, slow recalculations during live operation because the network has learned the mapping already.

Lu: And they show it works across two different radiation pattern modes, non-regular and 3GPP TR thirty-eight point nine zero one mode, which proves it’s not just tuned for one specific antenna geometry but is actually general <ref:2609.39167#pg3>.

Meng: That hardware generality is key for us because we don't want to be locked into one type of antenna array just because it was easiest to test initially.

Tom: And they confirm that under both modes, TriPNet delivers the highest spectral efficiency as the transmit power goes up and more users are added. That’s a solid result against those baseline schemes we looked at before.

Jane: It suggests that this joint learning framework is a very effective way to unlock the potential of EM-reconfigurable antennas in wideband systems, provided you can get that initial training done correctly.

Lu: The main thing is that it captures the interaction between the users, the antennas, and all those different radiation pattern possibilities simultaneously through this representation learning approach.

Meng: So what’s missing? I wonder if they show how this framework handles scenarios where the CSI is really bad—like when there's a lot of noise or interference—beyond just saying it’s robust to imperfect CSI.

Tom: They do mention that because the Conformer encoder captures both local and global frequency-domain features, and because the HPNet uses those model-driven priors, it handles noisy channel information better than simpler methods.

Jane: It’s a big leap for how we design these complex systems; instead of engineers manually tweaking different parts, you train one unified network to figure out the optimal configuration for all three domains.

Lu: The authors also flag that there's this non-monotonic relationship between the HPBW and spectral efficiency, showing that the best beamwidth setting depends heavily on whether you are using the 3GPP TR thirty-eight point nine zero one mode or not <ref:2609.39167#pg3>.

Meng: That’s a practical piece of info for our hardware team—it tells us exactly where to optimize that beamwidth tuning for maximum gain in different operating conditions.

Tom: The paper is basically showing how to replace iterative search, which is computationally expensive, with this single forward inference pass while still achieving the efficiency gains we were aiming for.

Jane: So this TriPNet framework really connects the physical flexibility of reconfigurable hardware with a unified AI design approach for hybrid precoding.

The paper's improvements: Tom: So, we’re looking at how TriPNet actually improves things compared to those baseline systems we talked about earlier—random EM precoding and conventional hybrid MIMO without EM precoding.

Jane: It’s a big step up because it doesn't just offer a marginal gain; it shows superior spectral efficiency as the transmit power increases and more users get served under both radiation pattern modes.

Lu: The real improvement is the structure of this joint learning. TriPNet captures that coupling between the users, the antennas, those subcarriers, and all those different radiation pattern possibilities in a way that previous methods just couldn't manage effectively.

Meng: I’m focusing on the complexity again—the paper claims after offline training you only need a single forward inference pass to get all three precoders—that is what matters for us at scale.

Tom: Exactly, because the online complexity of iterative pattern search scales roughly as O(NtNpNcUN2RF, but TriPNet bypasses that by doing it all in one go. That’s a major operational win for deploying these things on hardware.

Jane: That single inference makes the system much more practical for real-time applications because you aren't waiting around for the network to "search" or "solve" something during transmission.

Lu: And they show this robustness against imperfect CSI—the noisy channel information—because that Conformer encoder is good at picking up both local and global frequency-domain features, which helps the whole thing stay stable even when the measurements aren't perfect.

Tom: That’s a clean ablation for me; it means you don't need a perfect channel to get good results, which is always a win in real-world deployments.

Jane: It really changes how we think about designing these systems; instead of optimizing each component in isolation, you train one unified network to handle all three layers of complexity at once.

Lu: And they validated it across two different physical patterns, proving the methodology is general and doesn't just work for one specific antenna setup.

Meng: That hardware generality is important because it means we aren't locked into a specific antenna array type; the software approach works for more of our product line.

Tom: So, the implication here is that this learning framework provides a path to much higher spectral efficiency than what we could achieve with conventional methods using these EM reconfigurable antennas.

Jane: It points toward a future where designing complex multi-user systems isn't just about solving one optimization problem at a time, but about training an AI to understand the whole system's behavior together.

Lu: And they are looking ahead by saying they plan to extend TriPNet to multi-cell scenarios and investigate its performance under more realistic spatially consistent channel models.

Tom: That’s where the next big challenge lies—moving it from a single base station setup to a whole network environment.

Conclusion: Tom: So, to wrap up on "Deep Learning-Based Tri-Hybrid Multi-User MIMO Precoding: The Blessing of EM-Reconfigurable Antennas," this paper essentially shows how a joint deep learning approach can learn EM, analog, and digital precoding from raw channel data.

Jane: It’s a really neat way to integrate the physical capabilities of reconfigurable antennas with advanced AI to boost spectral efficiency in wideband OFDM systems.

Lu: The main implication is that this unified representation learning captures the coupling among users, antennas, subcarriers, and radiation pattern modes better than any previous approach we've seen.

Meng: It means for us in the field of deploying these things that we can move away from those slow, iterative search methods toward a single fast inference pass for production systems.

Tom: That’s the operational win—trading a complex, time-consuming search loop for one forward pass that gives you all three precoders at once.

Jane: And they proved it works well even with imperfect CSI because of how the network learns those local and global frequency features to be robust against noise.

Lu: The authors are looking ahead by planning to extend this TriPNet framework to multi-cell scenarios, which is definitely the next big hurdle in applying this representation learning.

Meng: I'm still thinking about what it costs for us to run a model like TriPNet constantly, but the efficiency gains they show suggest it might be worth that computational overhead for high-throughput applications.

Tom: The paper confirms that TriPNet consistently achieves the highest spectral efficiency under both radiation pattern modes, which is a strong performance metric against those various baseline schemes.

Jane: It really connects the dots between having flexible hardware and using deep learning to design the software side of things together.

Lu: The finding about non-monotonic relationship between HPBW and spectral efficiency under the 3GPP TR thirty-eight point nine zero one mode is a specific piece of data that will guide hardware designers on where to set their beamwidth <ref:2609.39167#pg3>.

Meng: That kind of specific tuning advice is exactly what we need when moving from simulation to actual prototype testing.

Tom: Overall, TriPNet provides a solid framework for jointly learning these three precoding variables from the sample-wise channel tensors.

Jane: It’s a very strong piece of work because it manages to combine complex domain knowledge with deep learning to solve a really difficult joint design problem in wireless communication.

Kaijun Feng, Jiaxin He, Hongrui Yu, Zhen Gao, Anwen Liao, Ziwei Wan

Beijing Institute of Technology (BIT) · Tsinghua University · Guilin University of Electronic Technology (GUET)

eess.SP, cs.IT, cs.LG, math.IT

Submitted: 2026-09-30

Updated: 2026-09-30

Comments: 14 pages, 13 figures, 4 tables

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 82/100

The gist: The gist: Tri-PNet, a Conformer-based tri-hybrid precoding network, jointly learns EM, analog, and digital precoding from sample-wise channel tensors to substantially improve the spectral efficiency

Key concepts

Tri-hybrid Precoding: This technique combines three types of precoding: electromagnetic (EM) domain, analog, and digital. EM precoding allows antennas to choose from multiple physical radiation patterns, adding a new degree of freedom for signal shaping. This combination is used to optimize how signals are transmitted across different users and frequency bands in MIMO systems.
Conformer Encoder: A neural network architecture that merges the strengths of Convolutional Neural Networks (CNNs) and Transformers. It is used in TriPNet's Radiation Pattern Selection Network (RPSNet) to effectively capture both local frequency-domain patterns and long-range dependencies across wideband channels simultaneously, which is crucial for accurate precoding decisions.
Radiation Pattern Selection Network (RPSNet): This module within TriPNet uses a Conformer encoder to process the channel information. Its goal is to determine which specific EM radiation pattern should be used by each antenna element based on the input channel tensor, effectively mapping complex channel data into discrete antenna-wise pattern logits.
Hybrid Analog-Digital Precoding (HPNet): This network jointly designs analog and digital precoders. The analog part uses SVD on the channel Gram matrix as a prior, refined by a Transformer encoder. The digital part uses ZF precoding, both guided by attention mechanisms to ensure optimal signal transmission while respecting power constraints.

Summary

The gist: Tri-PNet, a Conformer-based tri-hybrid precoding network, jointly learns EM, analog, and digital precoding from sample-wise channel tensors to substantially improve the spectral efficiency of wideband multi-user MIMO OFDM systems <ref:2609.39167#pg11>.

System Model and Problem Formulation

The system considers a downlink multi-user MIMO system where a base station serves U single-antenna users over an OFDM waveform with Nc subcarriers <ref:2609.39167#pg5>. The BS is equipped with a uniform planar array containing Nt = NxNz radiation-pattern-reconfigurable (RPR) antennas and NRF RF chains, with U ≤ NRF ≪ Nt <ref:2609.39167#pg6>. To exploit the EM-domain degree of freedom, each antenna can select one radiation pattern from a set of Np candidate EM radiation patterns <ref:2609.39167#pg5>. The paper investigates two representative radiation-pattern modes: the non-regular mode [11] and the 3GPP TR 38.901 mode [16] <ref:2609.39167#pg5>.

TriPNet Architecture

TriPNet maps the samplewise wideband CSI tensor to EM, analog, and digital precoding variables as FbEM, FbRF, and FbBB[q] = FΘ(HEM) <ref:2609.39167#pg4>. The architecture is cascaded into two modules: the Radiation Pattern Selection Network (RPSNet) and the Hybrid Analog-Digital Precoding Network (HPNet) <ref:2609.39167#pg5>. RPSNet uses a Conformer encoder to capture both local and global frequency-domain correlations, enabling it to capture both local frequency-domain structures and long-range wideband dependencies simultaneously <ref:2609.39167#pg4>. The HPNet takes the selected channel matrices HEM[q] as input to jointly design the analog and digital precoders <ref:2609.39167#pg5>.

RPSNet-based EM Precoding

The RPSNet processes the input CSI tensor by first rearranging it along the subcarrier dimension, concatenating real and imaginary parts, and then projecting it to a latent dimension before processing by a Conformer encoder <ref:2609.39167#pg6>. The output is mapped to antenna-wise pattern logits, AEM = reshape (Wpvec(URPSNet) + bp) ∈ R Nt×Np <ref:2609.39167#pg8>. A differentiable Gumbel-Softmax selector is used during training to determine the discrete radiation pattern selection matrix FEM, which is then used to gather the selected channels HEM[q] for each subcarrier q <ref:2609.39167#pg9>.

HPNet-based Hybrid Analog-Digital Precoding

The HPNet jointly designs analog and digital precoding after radiation pattern selection <ref:2609.39167#pg9>. For the analog part, it constructs an SVD-based analog precoder as a model-driven prior by applying SVD to the channel Gram matrix Cu[q] for each user and subcarrier <ref:2609.39167#pg9>. The neural analog branch uses a Transformer encoder and a gated cross-attention refinement to generate the refined analog precoder FeRF <ref:2609.39167#pg9>. For the digital part, it uses a normalized-channelbased ZF digital precoder as another model-driven prior, which is then refined by a dual-path attention block <ref:2609.39167#pg9>. The final precoding matrices are normalized together to satisfy the transmit power constraint independently on every subcarrier <ref:2609.39167#pg9>.

Performance and Robustness

TriPNet 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 CSI <ref:2609.39167#pg5>. The framework is validated under two complementary radiation-pattern families: the non-regular mode and the 3GPP TR 38.901 mode, confirming its hardware generality <ref:2609.39167#pg6>. TriPNet consistently achieves the highest spectral efficiency as the transmit power increases and as more users are served under both radiation-pattern modes <ref:2609.39167#pg5>. Furthermore, TriPNet maintains advantages under HPBW variation and imperfect CSI because the Conformer-based RPSNet extracts local and global frequency-domain features, while the HPNet uses model-driven analog and digital precoding priors to reduce sensitivity to noisy CSI <ref:2609.39167#pg9>.

Complexity Analysis

The online complexity of greedy pattern selection scales approximately as O(NtNpNcUN2RF), whereas after offline training, TriPNet jointly produces its radiation pattern selection for EM precoding and hybrid precoders through a single forward inference <ref:2609.39167#pg4>. This single forward inference avoids iterative pattern search [11] while providing the spectral-efficiency gains demonstrated in the preceding simulations <ref:2609.39167#pg5>. The computational complexity under both radiation-pattern modes is summarized in Tables III and IV in terms of the number of trainable parameters and FLOPs per inference <ref:2609.39167#pg5>.

Conclusion

TriPNet develops a Conformer-based tri-hybrid precoding framework that jointly learns EM precoding, analog precoding, and digital precoding from sample-wise channel tensors <ref:2609.39167#pg4>. By combining the Conformer-based RPSNet with crossattention analog precoding and dual-path digital precoding in the HPNet, TriPNet captures the coupling among users, antennas, subcarriers, and radiation pattern modes <ref:2609.39167#pg5>. Simulation results demonstrate that TriPNet improves spectral efficiency over various baseline schemes while approaching the greedy benchmark with substantially lower online complexity by replacing iterative pattern search with a single forward inference <ref:2609.39167#pg5>. The results further reveal a non-monotonic relationship between the HPBW and spectral efficiency, with the best performance observed near 100◦ under the 3GPP TR 38.901 radiation-pattern mode, highlighting the importance of properly selecting the radiation-pattern beamwidth <ref:2609.39167#pg5>. The paper will extend TriPNet to multi-cell scenarios and investigate its performance under more realistic spatially consistent channel models <ref:2609.39167#pg5>.

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Deep Learning-Based Tri-Hybrid Multi-User MIMO Precoding: The Blessing of EM-Reconfigurable Antennas Kaijun Feng, Jiaxin He, Hongrui Yu, Zhen Gao <ref:2609.39167#pg2>. Abstract—Electromagnetic (EM)-reconfigurable antennas provide multiple candidate radiation patterns per element, thereby introducing an additional EM-domain degree of freedom <ref:2609.39167#pg2>. Integrating radiation-pattern reconfigurability, realized as EMdomain 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 <ref:2609.39167#pg2>. However, the joint design of EM, analog, and digital precoding remains challenging <ref:2609.39167#pg2>. To address this challenge, we propose a tri-hybrid precoding network (TriPNet) based on Conformer, an emerging neural architecture that combines the local modeling strength of convolutional neural networks with the global dependency modeling of Transformers <ref:2609.39167#pg2>. 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 <ref:2609.39167#pg5>. Tri-PNet is trained in an unsupervised manner to jointly learn EM, analog, and digital precoding by maximizing the average sum spectral efficiency <ref:2609.39167#pg5>. 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-valuedecomposition (SVD) and zero-forcing (ZF) priors <ref:2609.39167#pg5>.

Improvements for AI systems

Bold header: End-to-end Tri-hybrid precoding via Conformer (TriPNet)

The improved system can jointly infer the EM, analog, and digital precoding variables by mapping the sample-wise wideband CSI tensor to the EM, analog, and digital precoding variables as FbEM, FbRF, and FbBB[q] in a single forward pass.

Bold header: Enhanced radiation pattern selection via Conformer encoder (RPSNet)

The RPSNet utilizes a Conformer encoder to capture both local and global frequency-domain correlations, allowing it to select the optimal radiation pattern by processing the feature vector zq, which is then projected into antenna-wise pattern logits.

Bold header: Model-driven analog precoding via SVD prior (HPNet)

The HPNet designs the sub-connected analog precoder by applying an SVD-based analog precoder as a model-driven prior, specifically extracting the dominant right singular vector from the channel Gram matrix Cu[q] to guide the optimization.

Bold header: Dual-path digital precoding refinement

The digital branch of HPNet uses a dual-path attention block to process the real-valued representation of HRF[q], which captures both cross-subcarrier correlation via self-attention and refines the feature with cross-attention on the RF-chain domain.

Bold header: Robustness against imperfect CSI

TriPNet maintains performance under imperfect CSI because the Conformerbased RPSNet extracts local and global frequency-domain features, while the HPNet uses model-driven analog and digital precoding priors to reduce sensitivity to noisy CSI.