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

eess.SPSep 30, 2026

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

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

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 ·

Abstract

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 ]	$\checkmark$	$\checkmark$				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
	[ 4 , 6 ]	$\checkmark$			Antenna position optimization
EM-reconfigurable MIMO	[ 11 ]	$\checkmark$		$\checkmark$		EM: discrete non-regular radiation-pattern selection	Requires low-complexity EM precoding design
	[ 16 ]		$\checkmark$	$\checkmark$		EM: discrete 3GPP TR 38.901 radiation-pattern selection with different directions and HPBWs
	[ 18 ]	$\checkmark$		$\checkmark$		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 $=90^{\circ}$ , the elevation and azimuth main-lobe pointing directions are sampled at $-60^{\circ}$ , $0^{\circ}$ , and $60^{\circ}$ . 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 $\mathbf{F}_{\rm EM}$ , which gathers the selected channels $\mathbf{H}^{\rm EM}[q]$ for HPNet to generate $\mathbf{F}_{\rm RF}$ and $\mathbf{F}_{\rm BB}[q]$ .

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 $\mathbf{F}_{\rm EM}$ , which gathers $\mathbf{H}^{\rm EM}[q]$ for $q=1,\ldots,N_{\rm c}$ .

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

\mathbf{F}_{\rm RF}

. Its digital branch processes

\mathbf{H}_{\rm RF}[q]

using dual-path attention to produce the normalized

\mathbf{F}_{\rm BB}[q]

Hyperparameter	Value
Optimizer	Adam
Training epochs	$50$
Mini-batch size	$512$
Initial learning rate	$10^{-4}$
Learning-rate schedule	$\times 0.5$ every $10$ epochs
Gumbel temperature	$\max\{0.1,2\exp(-0.03e)\}$

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 $P_{\rm t}=50$ 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 $U\in\{2,4,6,8\}$ .

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 $U\in\{2,4,6,8\}$ .

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 $N_{\rm RF}=8$ RF chains connected to all $N_{\rm t}=32$ 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 $U\in\{2,4,6,8\}$ .

Fig. 11: Spectral efficiency versus HPBW under the 3GPP TR 38.901 pattern mode at $P_{\rm t}=50$ 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.

Wireless Communications

Wireless communications studies how information is sent over radio links and how networks manage signals, spectrum, and resources reliably.

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