3D aperture-engineered diffractive neural networks for super-resolution electromagnetic wave computing

Sheng Gao; Songtao Yang; Haiou Zhang; Yuan Shen; Xing Lin

physics.app-phMar 1, 2026

3D aperture-engineered diffractive neural networks for super-resolution electromagnetic wave computing

Authors: Sheng Gao, Songtao Yang, Haiou Zhang, Yuan Shen, Xing Lin

Organizations: Department of Electronic Engineering, Tsinghua University, Beijing, 100084, China. · Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing, 100084, China.

Abstract

The rapid progress in 6G communication and high-bandwidth radar has driven an unprecedented surge in the spatial density of signal sources, resulting in an increasingly congested electromagnetic (EM) environment. When resolving closely spaced signals and interference, existing architectures are strictly bounded by the inherent diffraction limits of two-dimensional (2D) physical apertures, hindering super-resolution sensing and multi-interference mitigation in complex scenarios. Here, we present a 3D aperture-engineered diffractive neural network (AE-DNN) that achieves super-resolution sensing and computing by extending the traditional 2D aperture into 3D. The 3D aperture engineering framework is realized by constructing deep cascaded metasurface layers so that the diffractive propagation from oblique incident fields can be layer-wise modulated and piecewise encoded for perceiving EM fields far exceeding physical aperture limits. The N-layer AE-DNN has the capability to achieve ~N times higher angular resolution than the 2D aperture diffraction limit. The multi-dimensional synthetic aperture (MSA) training is developed to achieve speed-of-light coherent synthesis of the 3D aperture and integrate neural network-based modeling of multi-dimensional metasurface modulation. By orthogonalizing array response vectors in the analog domain, AE-DNN performs parallel super-resolution angle estimation, source number estimation, and source separation for up to 10 independent coherent or incoherent sources. Experimental results across the 36-41 GHz band demonstrate that AE-DNN resolves and suppresses closely spaced multi-interference by ~20 dB, enhances communication capacity by 13.5X, and reduces latency by three orders of magnitude. AE-DNN heralds a paradigm shift in signal processing for advanced radar and 6G communications.

Figures & tables

Figure 1: AE-DNN using 3D aperture engineering. ( A ) The traditional electronic architecture comprises an antenna array with a limited 2D aperture , phase shifters, RF mixers, ADCs, and DSPs, which leads to high processing complexity. ( B ) SAR enlarges the aperture size and enhances the resolution through time-consuming mechanical scanning and virtual aperture synthesis processing. ( C ) AE-DNN architecture utilizes deep cascaded metasurfaces to extend the perception aperture size with oblique incident waves and directly perform layer-wise modulation and coherent synthesis on the 3D extended aperture in the analog domain, thereby achieving array response vector orthogonalization and super-resolution sensing. ( D ) AE-DNN performs sensing and computing tasks at the speed of light, with high parallelism and low power consumption.

Figure 2: MSA training of AE-DNN for super-resolution sensing. ( A ) Both input fields within and outside apertures are utilized to train the model to achieve light-speed aperture synthesis for super-resolution sensing. ( B ) MSA training method is accelerated with the neuro-augmented forward model that integrates mini-FCNNs to characterize the high-dimensional modulation of meta-atoms. Meta-atom geometries are updated by minimizing the loss function during training. ( C ) As the number of layers increases, the phase of output fields exhibit higher-order nonlinear responses to the incident angle. ( D ) AE-DNN achieves scalable super-resolution for DOA estimation. Increasing the number of layers continuously improves the angular resolution while maintaining high energy efficiency and CSR. ( E ) Confusion matrix for two-target DOA estimation in simulation. ( F ) Full-wave simulation showing EM field distribution in the AE-DNN. ( G ) A five-layer AE-DNN comprising metasurface layers. ( H ) Experimental confusion matrix for two-target DOA estimation.

Figure 3: AE-DNN for parallel sensing and computing tasks. ( A ) AE-DNN selectively maps coherent and incoherent sources from different angles to the corresponding receiving antennas (top). The manufactured metasurfaces and a representative experimental output field of a single source is shown (bottom). ( B ) Experimental system utilizes AWG to generate independent source signals with FSW to analyze the processed signals. ( C ) Experimental confusion matrix evaluated on the single-source testing dataset. ( D ) MSA training enables the DOA estimation under broader wavelength range. ( E ) Experimental energy distribution matrix for 3 ∘ super-resolution DOA estimation of two sources under 45 angular interval permutations. ( F ) Experimental confusion matrix (left) and numerically evaluated confidence values (right) for source number estimation with $m$ varying from 1 to 10. ( G ) Eye diagrams and EVMs of QAM-16 and BPSK signals received by spectrum analyzer with and without AE-DNN. ( H ) EVMs of received QAM-16 source signals from different angles (left) and at different symbol rates (right). AE-DNN substantially improve the communication capacity.

Figure 4: Radar Anti-Jamming with Multiple Separation Channels. ( A ) Time domain waveform and pulse compression results of the mixed LFM signal and the DFTJ (top). After AE-DNN source separation, the SNR of the LFM signal is improved, and the DFTJ is effectively suppressed (bottom). ( B ) When the angular interval is increased from 3° to 6°, the jamming suppression ratio of the demixed LFM channel reaches 35 dB. ( C ) Before separation, the LFM signal is overwhelmed by the high-power NSJ (left); after separation, the LFM signal waveform and pulse compression spikes are detectable (right). ( D ) Waveform and spectrum of the mixture of the LFM, DFTJ, and single-tone signal when three signals are simultaneously transmitted (top). After multi-channel source separation, the LFM, DFTJ, and single-tone signal are successfully demixed in both the time and frequency domains (bottom).

Processor Type	Total Neurons	Computing Paradigm	Aperture	Resolution	Channels	Nonlinear	Gain/ Loss	Sensing and Computing Tasks
AE-DNN	6075	Fully-analog (1.67 µs)	3D	Scalable super-resolution	10	Encoding nonlinear	+13 dB	Source number and DOA estimation, source separation.
MRR Array [ 29 ]	4	Optoelectronic (33 ms)	1D	Diffraction-limited	2	None	-15 dB	Blind source separation
MZI Array [ 30 ]	30	Optoelectronic (50 ms)	1D	Diffraction-limited	2	None	-2 dB	Source separation
Holographic RIS [ 39 ]	1024	Optoelectronic (6.2 ms)	2D	Diffraction-limited	2	None	-0.5 dB	DOA estimation
S-DNN [ 34 ]	4096	Fully-analog	2D	Super-resolution	2	None	N/A	DOA estimation
Classic MUSIC [ 43 ]	N/A	Electronic (1 ms)	2D	Super-resolution	N/A	Electronic nonlinear	N/A	DOA estimation

Table 1: Comparison AE-DNN with state-of-the-art optoelectronic and electronic computing architectures

Figure S1 : Mini-FCNN for predicting meta-atom modulations. ( A ) The mini-FCNN structure comprises a Fourier feature extraction layer and two fully-connected layers followed by ReLU activation. ( B ) Comparison between mini-FCNN predictions and CST simulations for meta-atom amplitude and phase responses. The high similarity between the modulation values across different geometric settings demonstrates the effectiveness of the proposed neural network for multi-dimensional modulation prediction. ( C ) The mean absolute errors of amplitude and phase modulation predictions under different frequencies using mini-FCNN.

Figure S2 : AE-DNN performance under varying network settings. ( A ) Relationship between AE-DNN angular resolution and aperture size. ( B ) Relationship between AE-DNN energy efficiency and aperture size. ( C ) Relationship between AE-DNN energy efficiency and number of layers. The energy efficiency of AE-DNN does not decrease significantly with increasing layer number and propagation distance.

Figure S3 : Super-resolution DOA estimation results for 5-layer AE-DNN. ( A ) CST simulation energy distribution matrix of AE-DNN performing 1.6° super-resolution DOA estimation for 45 two-source angular permutations. ( B ) Experimental energy matrix of AE-DNN performing 1.6° super-resolution DOA estimation.

Figure S4 : Numerical evaluations of three-layer AE-DNN. ( A ) Schematic diagram of each meta-atom of the metasurface. The geometric parameters $\left(d_{a},\,d_{b},\,\alpha\right)$ affect the EM wave modulation effect. ( B ) AE-DNN’s CST model and the structure of each metasurface. ( C ) Example inference results for a single source (angle of -7.5°) using both MSA simulation and CST evaluations. ( D ) CST energy distribution matrix evaluated on the single-source testing dataset. ( E ) AE-DNN can perform source number estimation tasks on up to 10 sources. ( F ) CST energy distribution matrix of AE-DNN performing 3° super-resolution DOA estimation of two sources under 45 angular interval permutations.

Figure S5 : Experimental performance of AE-DNN for source number estimation and super-resolution DOA estimation in ISCC applications. ( A ) The confusion matrix of the DOA estimation task was evaluated on 51 sets of two-source experimental samples, with the angular interval between the BPSK and QAM16 being 3°or 6°. The confidence value of the DOA estimation task was $98\%$ . ( B ) The calibrated and normalized antenna detection energy for the source number estimation task was measured on the same experimental samples, with a threshold of 0.37 and a confidence value of $96\%$ .

Figure S6 : Experimental performance of AE-DNN for source number estimation and super-resolution DOA estimation in radar anti-jamming applications. ( A ) The confusion matrix of the DOA estimation task is evaluated on 51 sets of two-source experimental samples, with the angular interval between the radar signal and the jamming being 3°or 6°. The confidence value of the DOA estimation task was $98\%$ . ( B ) The calibrated and normalized antenna detection energy for the source number estimation task was measured on the same experimental samples, with a threshold of 0.5 and a confidence value of $94.2\%$ .

Figure S7 : Experimental performance of AE-DNN for source separation in radar anti-jamming applications. ( A ) The jamming suppression ratio (JSR) of source separation was evaluated on multiple sets of two-source experimental samples. When the angular separation between the LFM signal and the DFTJ was 3°, the average JSR was 14.6 dB. ( B ) When the angular separation between the LFM signal and the DFTJ was 6°, the average JSR was 20 dB. ( C ) Below are screenshots of the spectrum analyzer for different demixing channels.

Figure S8 : Simulation proves that AE-DNN supports up to 10 source separation channels. ( A ) The simulation generates ten LFM signals with different angles and time delays, and the time domain waveform and pulse compression of the mixed signal after coherent superposition. ( B ) After AE-DNN source separation, the waveforms and pulse compression results of the demixed signals in the ten separated channels are shown. The average channel crosstalk suppression ratio is 17.6 dB.

Figure S9 : Experimental setup for testing AE-DNN. ( A ) Overview of the microwave anechoic chamber, including the vector network analyzer (VNA), the AE-DNN fixed on an angle rotating stage, and waveguide probe mounted on an XY translation stage. ( B ) Multiple transmitting horn antennas are located at the far field distance of the AE-DNN. ( C ) The R&S spectrum analyzer for demodulating and analyzing radar and communication signals. ( D ) Keysight Technologies’ M8198 arbitrary waveform generator, capable of simultaneously transmitting two signals, including radar signals and jamming, or communication signals with different modulation formats.

Incident Angle	Normalized Output Energy Response Vector (Unit: a.u.)
$\theta_{1}=-13.5^{\circ}$	$\mathbf{P}_{y}=\left[\mathbf{1},\,0.01,\,0.01,\,0.01,\,0.01,\,0.01,\,0.01,\,0.01,\,0.01,\,0.01\right]$
$\theta_{2}=-10.5^{\circ}$	$\mathbf{P}_{y}=\left[0.1,\,\mathbf{0.74},\,0.05,\,0.01,\,0.01,\,0.01,\,0.01,\,0.01,\,0.01,\,0.01\right]$
$\theta_{3}=-7.5^{\circ}$	$\mathbf{P}_{y}=\left[0.02,\,0.03,\,\mathbf{0.36},\,0.01,\,0.01,\,0.01,\,0.01,\,0.01,\,0.01,\,0.01\right]$
$\theta_{4}=-4.5^{\circ}$	$\mathbf{P}_{y}=\left[0.01,\,0.01,\,0.01,\,\mathbf{0.39},\,0.01,\,0.01,\,0.01,\,0.01,\,0.01,\,0.01\right]$
$\theta_{5}=-1.5^{\circ}$	$\mathbf{P}_{y}=\left[0.01,\,0.01,\,0.01,\,0.05,\,\mathbf{0.64},\,0.01,\,0.01,\,0.01,\,0.01,\,0.01\right]$
$\theta_{6}=1.5^{\circ}$	$\mathbf{P}_{y}=\left[0.01,\,0.01,\,0.01,\,0.01,\,0.01,\,\mathbf{0.63},\,0.02,\,0.01,\,0.01,\,0.01\right]$

Table S1 : Output Energy Response Vector of AE-DNN (Experiment)

Incident Angle	Normalized Output Energy Response Vector (Unit: a.u.)
$\theta_{1}=-13.5^{\circ}$	$\mathbf{P}_{y}=\left[\mathbf{1},0.02,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01\right]$
$\theta_{2}=-10.5^{\circ}$	$\mathbf{P}_{y}=\left[0.02,\mathbf{0.88},0.03,0.01,0.01,0.01,0.01,0.01,0.01,0.01\right]$
$\theta_{3}=-7.5^{\circ}$	$\mathbf{P}_{y}=\left[0.01,0.02,\mathbf{0.7},0.02,0.01,0.01,0.01,0.01,0.01,0.01\right]$
$\theta_{4}=-4.5^{\circ}$	$\mathbf{P}_{y}=\left[0.01,0.01,0.02,\mathbf{0.76},0.03,0.01,0.01,0.01,0.01,0.01\right]$
$\theta_{5}=-1.5^{\circ}$	$\mathbf{P}_{y}=\left[0.01,0.01,0.01,0.02,\mathbf{0.98},0.03,0.01,0.01,0.01,0.01\right]$
$\theta_{6}=1.5^{\circ}$	$\mathbf{P}_{y}=\left[0.01,0.01,0.01,0.01,0.02,\mathbf{0.9},0.02,0.01,0.01,0.01\right]$

Table S2 : Output Energy Response Vector of AE-DNN (Simulation)

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Wireless Communications Edge Inference Energy-Efficient ML Reconfigurable Intelligent Surfaces

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The upcoming sixth Generation (6G) of wireless networks envisions ultra-low latency and energy efficient Edge Inference (EI) for diverse Internet of Things (IoT) applications. However, traditional digital hardware for machine learning is power intensive, motivating the need for alternative computation paradigms. Over-The-Air (OTA) computation is regarded as an emerging transformative approach assigning the wireless channel to actively perform computational tasks. This article introduces the concept of Metasurfaces-Integrated Neural Networks (MINNs), a physical-layer-enabled deep learning framework that leverages programmable multi-layer metasurface structures and Multiple-Input Multiple-Output (MIMO) channels to realize computational layers in the wave propagation domain. The MINN system is conceptualized as three modules: Encoder, Channel (uncontrollable propagation features and metasurfaces), and Decoder. The first and last modules, realized respectively at the multi-antenna transmitter and receiver, consist of conventional digital or purposely designed analog Deep Neural Network (DNN) layers, and the metasurfaces responses of the Channel module are optimized alongside all modules as trainable weights. This architecture enables computation offloading into the end-to-end physical layer, flexibly among its constituent modules, achieving performance comparable to fully digital DNNs while significantly reducing power consumption. The training of the MINN framework, two representative variations, and performance results for indicative applications are presented, highlighting the potential of MINNs as a lightweight and sustainable solution for future EI-enabled wireless systems. The article is concluded with a list of open challenges and promising research directions.

Abstract

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