PaperlayerView exact revision on arXiv

Source-linked AI summary

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

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

arXiv:2609.39167v1eess.SP

TL;DR

Wideband multi-user MIMO precoding must jointly handle radiation-pattern selection and hybrid precoding, a coupled design that can make iterative optimization costly. Tri-PNet learns EM, analog, and digital precoding with a Conformer-based network; simulations report improved spectral efficiency over baselines and performance approaching greedy search with lower online complexity.

  • Problem

    Joint EM, analog, and digital precoding is challenging, and optimization-based methods repeatedly update coupled variables, increasing online computation in wideband multi-user systems.

    Source: §I · p. 2

  • Method

    Tri-PNet jointly learns EM, analog, and digital precoding from sample-wise channel tensors using Conformer-based pattern selection and hybrid analog-digital precoding networks.

    Source: §I · p. 2, §III · p. 6

  • Results

    Tri-PNet improves spectral efficiency over various baseline schemes and approaches the greedy benchmark with substantially lower online complexity through single forward inference.

    Source: §V · p. 13

  • Takeaways & Limitations

    Simulations support one framework across non-regular pixel-antenna and 3GPP TR 38.901 radiation-pattern modes.

    Source: §V · p. 13

Abstract

from arXiv · show

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).

I. INTRODUCTION

Wideband multi-user MIMO precoding must balance spectral efficiency with hardware cost, while existing joint pattern-and-precoder optimization can be computationally burdensome. Tri-PNet combines Conformer-based pattern selection with hybrid precoding, and simulations report performance approaching greedy search with lower online complexity.

I. INTRODUCTION

  • Hybrid precoding reduces RF-chain count but retains substantial phase-shifter and interconnection costs, while static mechanical antenna choices cannot favor every subcarrier in wideband fading.EM-reconfigurable antennas electronically reshape radiation patterns without adding RF chains or enlarging the physical aperture.Source: §I · pp. 1–2
  • Table I compares representative MIMO architectures across reconfiguration domains, implementation mechanisms, and limitations.The overview includes both antenna-hardware prototyping and communication-algorithm work.Source: §I · p. 2, Table I · p. 3
  • Prior tri-hybrid optimization repeatedly updates tightly coupled pattern, analog, and digital variables, while PR-HBFNet does not explicitly model adjacent-subcarrier local correlations.Wideband per-subcarrier variation further increases the iteration burden of optimization-based methods.Source: §I · p. 2
  • Tri-PNet jointly maps sample-wise wideband CSI to EM, analog, and digital precoders using cascaded RPSNet and HPNet modules.RPSNet uses Conformer encoding and Gumbel-Softmax pattern selection; HPNet combines attention modules with SVD and ZF priors.Source: §I · pp. 2–3
  • Validation covers pixel-switching non-regular patterns and 3GPP TR 38.901 patterns parameterized by azimuth, elevation, and HPBW.The two families represent hardware-derived and geometrically parameterized pattern sets.Source: §I · p. 3
  • Tri-PNet approaches greedy-search performance across transmit powers, user numbers, and pattern conditions, maintains advantages under HPBW variation and imperfect CSI, and reduces online latency with one forward pass.The evaluation reports a moderate offline training cost in exchange for significantly reduced online latency.Source: §I · p. 3

II. SYSTEM MODEL AND PROBLEM FORMULATION

The section formulates a downlink multi-user OFDM system in which per-antenna radiation-pattern selection adds an EM-domain choice to sub-connected analog and per-subcarrier digital precoding. It jointly maximizes average sum spectral efficiency over these choices despite discrete, nonconvex, frequency-coupled constraints.

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • The base station serves U single-antenna users over Nc OFDM subcarriers using Nt reconfigurable antennas and NRF RF chains, with U ≤ NRF ≪ Nt.The transmitter combines an EM precoder, a sub-connected analog precoder, and per-subcarrier digital precoders.Source: §II · pp. 3, 5
  • The two radiation-pattern modes are non-regular pixel-antenna patterns and 3GPP TR 38.901 patterns with HPBW = 90° and nine sampled pointing directions.The non-regular mode selects among four representative patterns; the 3GPP mode samples elevation and azimuth at −60°, 0°, and 60°.Source: §II · p. 4, Figure 2 · p. 4, Figure 3 · p. 5
  • Selecting a pattern changes the complex field gain of propagation paths and forms the pattern-aware effective channel for each subcarrier.Each antenna selects one candidate pattern, represented by a one-hot EM precoding matrix.Source: §II · pp. 4–5
  • The design objective is to maximize average sum spectral efficiency by jointly choosing the EM, analog, and per-subcarrier digital precoders.The EM matrix is binary one-hot, the active analog entries have unit modulus, and one common analog precoder serves all subcarriers.Source: §II · pp. 5–6
  • The resulting problem is mixed-integer, nonconvex, and frequency-coupled, motivating a direct learning-based joint design.The discrete EM choices, constant-modulus analog constraint, and shared analog precoder create these challenges.Source: §II · p. 6

III. PROPOSED CONFORMER-BASED TRI-HYBRID MULTI-USER MIMO PRECODING

Tri-PNet maps wideband CSI through cascaded RPSNet and HPNet modules to jointly produce EM, analog, and digital precoders. Its staged data flow preserves the coupling between pattern selection and hybrid precoding.

III. PROPOSED CONFORMER-BASED TRI-HYBRID MULTI-USER MIMO PRECODING

  • Tri-PNet maps sample-wise wideband CSI end-to-end to EM, analog, and digital precoding variables through cascaded RPSNet and HPNet modules.The network has trainable parameters Θ and implements the cascade F_Θ(·).Source: §III · p. 6
  • RPSNet selects an EM pattern per antenna and gathers the corresponding channel entries; HPNet uses those selected channels to generate the analog precoder and per-subcarrier digital precoders.The selected channel matrices provide the input to HPNet, which designs the sub-connected analog precoder and digital precoders.Source: §III · p. 6
  • Unlike separate pattern search followed by hybrid-precoder optimization, Tri-PNet learns the coupled decisions end-to-end in a flow aligned with the physical signal-processing pipeline.The pipeline proceeds from pattern-aware channel observation to pattern selection, selected-channel construction, precoding, and power normalization.Source: §III · p. 6
  • RPSNet compares candidate patterns using the full-dimensional EM-domain channel, while HPNet processes selected channels in the lower-dimensional RF-chain domain.HPNet’s analog branch extracts frequency-shared information, and its digital branch suppresses subcarrier-dependent multi-user interference.Source: §III · p. 6

A. RPSNet-based EM Precoding

RPSNet learns discrete antenna-wise radiation-pattern choices from pattern-aware CSI across subcarriers. A Conformer encodes the frequency sequence, and a differentiable selector produces the pattern matrix used to gather selected channels.

A. RPSNet-based EM Precoding

  • RPSNet rearranges pattern-aware CSI along the subcarrier dimension and processes its real and imaginary parts as input features.The resulting sequence is embedded and passed to a Conformer encoder.Source: A. RPSNet-based EM Precoding · p. 6
  • The Conformer combines convolution-enhanced local modeling with sequence processing suited to wideband channels, where neighboring subcarriers usually exhibit strong local correlation.Its encoded sequence is flattened and mapped to antenna-wise pattern logits.Source: A. RPSNet-based EM Precoding · p. 6
  • A Gumbel-Softmax selector enables differentiable training of discrete pattern choices, with a straight-through hard decision keeping each antenna’s forward-pass selection one-hot.The temperature progressively sharpens the relaxed probabilities during training; inference obtains the selection from the logits.Source: A. RPSNet-based EM Precoding · p. 7
  • The selected pattern indices determine which channel entries are gathered for every subcarrier and passed onward as selected channel matrices.This keeps pattern selection coupled to each antenna, user, and subcarrier rather than reducing it to a sample-level label.Source: A. RPSNet-based EM Precoding · p. 7

B. HPNet-based Hybrid Analog-Digital Precoding

HPNet jointly designs analog and digital precoding after EM pattern selection. It combines channel features with SVD and ZF priors, attention-based refinements, and hardware constraints.

B. HPNet-based Hybrid Analog-Digital Precoding

  • The analog branch builds an SVD-based prior from user and subcarrier channel directions, aggregates them across subcarriers, and restricts the result to each subarray.The principal subarray direction supplies the RF-chain prior.Source: B. HPNet-based Hybrid Analog-Digital… · p. 7
  • A Transformer channel feature and SVD prior are combined through gated cross-attention to produce the analog precoder.The neural analog branch refines the prior and enforces the sub-connected mask and finite-resolution phase constraint; simulations use 4-bit phase quantization.Source: B. HPNet-based Hybrid Analog-Digital… · p. 7, Figure 6 · p. 8
  • The digital branch processes HRF[q] to produce normalized FBB[q], with the analog and digital precoders normalized together to satisfy the transmit-power constraint.The constraint is enforced independently on every subcarrier.Source: Figure 6 · p. 8, B. HPNet-based Hybrid Analog-Digital… · p. 8
  • For digital precoding, dual-path attention captures cross-subcarrier correlation and uses the RF-chain-domain channel representation to refine digital features.The normalized-channel ZF prior first normalizes each user channel vector to unit norm, reducing the influence of unequal user channel gains under the sub-connected architecture.Source: B. HPNet-based Hybrid Analog-Digital… · pp. 7–8
  • Combining model-driven beamforming priors with learnable attention modules improves training stability while retaining deep learning-based precoding flexibility.The precoding matrices are normalized to satisfy the transmit-power constraint.Source: B. HPNet-based Hybrid Analog-Digital… · p. 8

C. Training Objective

Tri-PNet is trained without labels from exhaustive search, using negative average sum spectral efficiency as its objective to jointly optimize the three precoding stages.

C. Training Objective

  • The network is trained without supervised labels generated by exhaustive search.For each mini-batch, the loss is the negative average sum spectral efficiency.Source: C. Training Objective · p. 8
  • The objective directly matches the communication performance metric and enables joint optimization of EM, analog, and digital precoding.Each mini-batch loss averages spectral efficiency across its channel realizations.Source: C. Training Objective · p. 8
  • Gumbel-Softmax temperature is annealed independently of the learning-rate schedule; Adam starts at 10^-4 and the learning rate halves every 10 epochs without warmup.Source: C. Training Objective · p. 8

IV. SIMULATION RESULTS

The simulations use a wideband multi-user MIMO setup with a sub-connected array and evaluate two radiation-pattern modes; three datasets support training and testing.

IV. SIMULATION RESULTS

  • The default setup uses 32 planar-array antennas, eight RF chains, two users, 60 OFDM subcarriers, and six paths per user.The 4 × 8 array is partitioned into eight contiguous 2 × 2 subarrays; transmit power varies from 10 to 50 dBm.Source: §IV · p. 8
  • The non-regular mode uses four candidate patterns per antenna, while the 3GPP TR 38.901 mode uses nine patterns at HPBW = 90°.The 3GPP patterns are generated from elevation and azimuth samples at −60°, 0°, and 60° on both axes.Source: §IV · p. 9
  • Three independent datasets each contain 10,000 channel samples; two are used for training and the remaining dataset for testing.The core training configuration is summarized in Table II.Source: §IV · p. 9, Table II · p. 9

A. Spectral Efficiency Evaluation

Across the tested radiation-pattern modes and power and user ranges, Tri-PNet achieves the strongest spectral-efficiency results, including performance competitive with greedy pattern selection. It also outperforms conventional fixed-pattern hybrid precoding under a sub-connected architecture.

A. Spectral Efficiency Evaluation

  • Tri-PNet achieves the highest spectral efficiency among the compared schemes under both radiation-pattern modes in the Fig. 7 comparison.The comparison is at Pt = 50 dBm.Source: Figure 7 · p. 10, A. Spectral Efficiency Evaluation · p. 10
  • The Fig. 7 comparison combines PR-HBFNet and component-swapped configurations, and reports the highest spectral efficiency for the complete Tri-PNet.The reported trend indicates that EM and hybrid analog-digital precoding should be optimized together because selected patterns change the channel seen by later precoding stages.Source: A. Spectral Efficiency Evaluation · p. 10
  • Under the non-regular mode, Tri-PNet consistently achieves the highest spectral efficiency as transmit power increases and more users are served.The gap over random-selection curves indicates that learned EM precoding exploits instantaneous CSI.Source: A. Spectral Efficiency Evaluation · p. 10
  • Under 3GPP TR 38.901, Tri-PNet remains competitive with greedy selection and outperforms learning-based and fixed-pattern alternatives over the tested power and user ranges.As user numbers grow, its persistent advantage also supports its ability to use cross-user and cross-subcarrier structure.Source: A. Spectral Efficiency Evaluation · p. 10
  • Tri-PNet outperforms PCA- and MO-AltMin-based fully-connected hybrid precoding with fixed Type-0 patterns, while fully-connected Tri-PNet provides an architecture-aware reference for the sub-connected constraint.The gap between the two Tri-PNet variants characterizes the spectral-efficiency loss imposed by restricting each RF chain to a local subarray; fully-digital WMMSE is included as a reduced-aperture reference.Source: A. Spectral Efficiency Evaluation · p. 10

B. Spectral Efficiency Versus HPBW

Under the 3GPP TR 38.901 pattern mode, Tri-PNet remains the best-performing method across the tested HPBW range. Spectral efficiency peaks near 100° HPBW and then decreases slightly at 110°.

B. Spectral Efficiency Versus HPBW

C. Robustness Under Imperfect CSI

Tri-PNet retains spectral-efficiency gains under imperfect CSI in both radiation-pattern modes. The robustness evaluation uses channel perturbations measured by NCPE.

C. Robustness Under Imperfect CSI

  • To evaluate robustness under imperfect CSI, the study uses the normalized channel perturbation error (NCPE) metric, modeling the perturbed candidate channel with Gaussian perturbation noise for both radiation-pattern modes.Source: C. Robustness Under Imperfect CSI · pp. 11–12
  • Under the non-regular mode, Tri-PNet remains above baselines as NCPE increases and channel features become less accurate.The authors attribute the gain to RPSNet's local and global frequency-feature extraction and HPNet's model-driven precoding priors.Source: C. Robustness Under Imperfect CSI · p. 12
  • Under the 3GPP TR 38.901 mode, Tri-PNet gains over PR-HBFNet and greedy selection throughout the tested perturbation range.Source: C. Robustness Under Imperfect CSI · p. 12

D. Complexity Analysis

Tri-PNet replaces iterative greedy pattern search with one post-training forward inference while retaining spectral-efficiency gains. The conclusion reports gains over baselines, near-greedy performance, and best 3GPP-mode performance near 100° HPBW.

D. Complexity Analysis

  • More candidate patterns in 3GPP mode increase RPSNet parameters and FLOPs, while HPNet complexity stays unchanged because it is independent of candidate-pattern number and source.Source: D. Complexity Analysis · pp. 12–13
  • Greedy selection scales approximately as O(NtNpNcUN^2_RF), while Tri-PNet replaces iterative pattern search with one forward inference after offline training.Source: D. Complexity Analysis · p. 13

V. CONCLUSION

  • Tri-PNet jointly learns EM, analog, and digital precoding from sample-wise channel tensors using Conformer-based RPSNet and cross-attention, dual-path HPNet processing.Source: §V · p. 13
  • Tri-PNet improves spectral efficiency over baselines and approaches greedy search with substantially lower online complexity; 3GPP-mode performance peaks near 100° HPBW.Source: §V · p. 13
  • Future work will extend Tri-PNet to multi-cell scenarios and investigate more realistic spatially consistent channel models.Source: §V · p. 13
Loading 2609.39167v1…