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This study presents an AI-assisted inverse design methodology for a compact and ultra-wideband grooved half-mode waveguide (G-HMWG) end-fire antenna. A parametric dataset was generated using CST full-wave simulations, and the corresponding radiation-pattern vectors were used to train a one-dimensional convolutional neural network (1D-CNN) for predicting the optimal geometrical parameters. The optimized multi-unit-cell antenna achieves stable end-fire radiation across 6–10 GHz, with |S₁₁| < − 10 dB, peak gain above 11 dBi, and sidelobe suppression better than − 13 dB, while reducing the physical length by 34% compared to conventional designs. A fabricated prototype was measured and showed excellent agreement with simulations, validating the effectiveness of the AI-driven optimization approach. The results demonstrate that integrating deep learning with electromagnetic modeling enables rapid, accurate, and scalable development of compact high-performance end-fire antennas for next-generation wireless, radar, and sensing applications.
Mohammad Rezaei1 & Amir Saman Nooramin2
Keywords:
End-fire antenna
Grooved half-mode waveguide
Leaky- wave antenna
CNN optimization
AI-based inverse design
Ultra-wideband antennas
In recent years, the demand for compact, wideband, and high-gain antennas has significantly increased due to the rapid development of modern wireless communication, radar, and sensing systems. Among various radiation configurations, endfire antennas have attracted considerable attention because of their inherent ability to support directional radiation with a low profile and high efficiency[1–4, 19]. However, conventional endfire designs such as Yagi–Uda and classical leaky-wave antennas (LWAs) often suffer from limited operational bandwidth and strong frequency dependence of the beam direction, restricting their applicability in broadband communication systems[5–7, 11].
In this context, artificial intelligence (AI) has emerged as a powerful tool for optimizing electromagnetic structures, providing an alternative to traditional parametric sweeps and manual tuning. Deep learning models, particularly convolutional neural networks (CNNs), can efficiently learn the nonlinear mapping between geometrical parameters and radiation characteristics, thus accelerating the design process while improving performance consistency.[1–4, 8–13]
Building upon this paradigm, this paper presents an AI-optimized grooved half-mode waveguide (G-HMWG) endfire antenna that achieves a significantly improved balance among compactness, bandwidth, and gain. The proposed CNN-based framework automatically adjusts key geometrical parameters to ensure stable endfire radiation across 6–10 GHz with |S₁₁| < − 10 dB, peak gain exceeding 11 dBi, and sidelobe levels below − 13 dB. Compared to prior works, the antenna demonstrates a 34% reduction in length and enhanced radiation stability, confirming the potential of deep learning-driven inverse design for next-generation broadband antenna systems.
Antenna Configuration and Design Principle
The etched grooves extend the path of the maximum surface current along the propagation direction, thereby reducing the effective phase velocity. This engineered wave-slowing mechanism facilitates the transition from a fast-wave to a slow-wave regime, which is essential for achieving efficient endfire radiation [5, 6, 24].
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Figure 1. It illustrates a half-waveguide.[5]In the proposed configuration, each unit cell of the grooved half-mode waveguide (G-HMWG) functions as a fundamental phase-controlling and radiating segment, governing the overall endfire behavior of the antenna. The concept of the unit cell follows the principle of periodic leaky-wave structures, in which each segment contributes simultaneously to guided-wave propagation and controlled radiation leakage. By properly engineering the local geometry of the cell, the propagation constant β and the attenuation constant α can be precisely adjusted to satisfy the slow-wave condition required for efficient endfire radiation [5, 7, 9].
As illustrated in Fig. 3, the unit cell is composed of a metallic half-mode waveguide section with periodically etched grooves along the open edge. The main geometric parameters defining the unit cell include the groove depth D, slot spacing S, groove separation D, and waveguide width W. Each of these parameters plays a distinct electromagnetic role: the groove depth D primarily affects the phase velocity (
) by extending the surface current path, the slot spacing S determines the coupling and radiation leakage rate. In contrast, the waveguide width W influences impedance matching and modal confinement. By fine-tuning these parameters, the phase constant β can be made to approach the free-space wavenumber (
), thus fulfilling the Hansen–Woodyard criterion for maximum endfire directivity [1, 8, 10, 22].
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Fig. 2
Geometry of the designed structure modeled in CST Microwave Studio.
Physically, the periodic grooves act as reactive discontinuities that alter the boundary conditions of the propagating mode, effectively reducing the local phase velocity and enabling radiation in the endfire direction. This engineered slowing-down mechanism ensures that the surface current distribution remains concentrated near the open aperture, resulting in high aperture efficiency and reduced backward radiation. The corresponding electric field distribution, shown in Fig. 3, confirms the strong field confinement and the gradual phase progression along the propagation axis.
When multiple optimized unit cells are cascaded to form the complete structure (as later depicted in Fig. 8), the cumulative phase shift introduced by each cell produces a uniform phase gradient across the aperture. This controlled phase progression allows for constructive interference of the radiated fields in the endfire direction, yielding a highly directive beam with suppressed sidelobes. Furthermore, the modular nature of the unit-cell-based configuration facilitates scalability of gain without increasing the overall antenna profile, which is a critical advantage in compact system implementations.[5, 6, 9]
From a design and optimization standpoint, the parametric sensitivity of the unit cell provides a flexible platform for performance enhancement. In this work, the parameters S and D were selected as the principal optimization variables, since they have the most significant impact on the radiation efficiency, beam alignment, and impedance bandwidth. These parameters were systematically varied through CST-based full-wave simulations to generate a comprehensive dataset, which was subsequently utilized in the AI-driven optimization framework described in the next section. The trained Convolutional Neural Network (CNN) predicted the optimal geometric configuration for each unit cell, leading to an enhanced bandwidth, stabilized endfire beam, and improved overall gain performance of the proposed antenna.
Fig. 3
Geometry of the unit cell with optimized dimensions.
To achieve a wider operational bandwidth while preserving the desired endfire radiation pattern, the key design parameters must be carefully analyzed and optimized. For a more detailed understanding, a single unit cell of the antenna is examined, as shown in Fig. 3. The analysis reveals that one of the most influential factors affecting antenna performance is the waveguide width (W), which governs both the phase constant and the leaky rate. As W increases, the phase constant also increases, thereby reducing the phase velocity and allowing for more effective control of endfire radiation [5, 10, 21].
Moreover, the parameters S and D — or more generally, the effective radiating surface area — play a crucial role in shaping the radiation characteristics of the antenna. Hence, through precise and targeted engineering of these parameters, the radiation properties of the antenna can be effectively controlled.
To overcome the narrow bandwidth limitation of the conventional design, artificial intelligence (AI) techniques can be employed to enhance the operational bandwidth without distorting the desired endfire pattern. By applying AI-based optimization to the antenna geometry and physical parameters, a broader bandwidth, higher gain, and improved beam stability can be achieved while maintaining the integrity of the endfire radiation.
General Architecture of CNNs
AI-Based Optimization Framework
To achieve the desired structure, an initial model (Fig. 3) was first designed using CST software. Subsequently, a MATLAB-CST link was established, enabling dimensional modifications of the structure within CST through MATLAB scripting. These modifications, applied via MATLAB, allowed for precise adjustments to the antenna structure's dimensions in the relevant sections.[14, 16, 20]
In the MATLAB code, an appropriate and controlled range was defined for varying the dimensions S and D. At each iteration, these dimensional changes were applied to the structure, followed by simulating CST. As a result, the two-dimensional radiation pattern of the structure was obtained. The coordinate data of each generated two-dimensional radiation pattern was then stored in a dedicated dataset. This process was repeated multiple times using a 'for' loop implemented in the MATLAB code.
Ultimately, a structured dataset was created, serving as training data for the neural network. This dataset contains the corresponding dimensional parameters along with the coordinate data of the two-dimensional radiation patterns, as illustrated in Fig. 9.
Finally, this dataset, comprising both the feature vectors (radiation pattern coordinates) and the label vectors (structural dimensions), was exported as a CSV file. This file was used as the input for the neural network training process, which is described in detail in the following sections.
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Fig. 4
Designing the structure with the new predicted dimensions in CST software
To optimize both the dimensions and the slot spacing in the Endfire antenna structure, a deep learning approach based on a Convolutional Neural Network (CNN) was implemented. The primary objective of this method was improving the overall radiation gain along the propagation axis.[14–16]
For this purpose, a series of electromagnetic simulations was performed with varying slot dimensions and inter-slot distances. In each simulation, the corresponding radiation pattern vectors were extracted and utilized as input data for training the CNN. These radiation patterns effectively capture the essential spatial characteristics of the antenna's emission behavior in response to structural variations, making them suitable for data-driven optimization.
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The CNN architecture consisted of multiple convolutional layers designed to extract spatial features from the input radiation data. These layers utilized learnable filters to identify local patterns such as beam direction, lobe width, and field intensity. Following the convolutional layers, pooling layers were employed to reduce the spatial dimensions and eliminate irrelevant noise, thereby lowering computational complexity and enhancing generalization.The output from the feature extraction stage was passed to a set of fully connected (dense) layers that modeled nonlinear relationships between the extracted features and the target output—the optimal slot spacing. Finally, a softmax or regression output layer (depending on the formulation of the problem) was used to generate the predicted value.
To improve model accuracy and prevent overfitting, several regularization techniques were employed, including dropout, L2 regularization, and early stopping. Optimization of network parameters was carried out using advanced gradient-based algorithms such as Adam and RMSprop.[17–20]
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The results demonstrated that the trained CNN was capable of accurately predicting the optimal slot spacing based on spatial radiation features. This approach not only accelerated the antenna design process but also provided a robust framework for automated optimization of complex photonic structures with minimal human intervention.The following section provides an analysis of the architecture and operational stages of the neural network used in this study, detailing its structure and functionality.
The Fig. 5 illustrates the architecture of the neural network employed in this study. It represents a customized Convolutional Neural Network (CNN) designed specifically for processing structured, tabular (non-image) data. Unlike conventional CNN models that typically accept two-dimensional grayscale or RGB images as input, this architecture processes one-dimensional or single-channel tabular vectors.
To enable compatibility with deeper convolutional layers, the input vector is first passed through a 1×1 convolutional layer that maps it into a three-channel tensor. This transformation is not intended for spatial feature extraction but serves to expand the feature space, thereby facilitating the application of deeper convolutional operations.
Following the channel expansion, a MaxPooling layer is employed to reduce the spatial dimensions of the feature maps. This is followed by several convolutional layers with 3×3 filters and ReLU activation functions, which progressively extract higher-level features from the input data. The network leverages a combination of convolutional layers, batch normalization, and ReLU activations to enhance training stability and accelerate convergence.
In the final stage of the network, the extracted features are flattened and fed into a fully connected layer consisting of seven output neurons. Depending on the problem formulation, this output can represent either seven continuous values in a regression task or the class probabilities across seven categories in a classification task. The architecture, though structurally simple, is capable of deep and effective feature extraction, making it highly suitable for analyzing structured data such as sensor signals, statistical descriptors, or simulation outputs. [17–20]
Ultimately, the output of the fully connected layer corresponds to the optimal dimensions and slot spacing, namely S and D, which are predicted by the network and provided as the final output of the neural network.
Fig. 5
Block diagram of the neural network.
The model was trained using the Mean Squared Error (MSE) loss function and the Adam optimizer for 200 epochs, achieving convergence with a final error below 0.1[17, 18]. This approach provides a reliable and efficient framework for the accurate prediction of key design parameters (S and D), offering a powerful data-driven tool for antenna design.
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Fig. 6
Training loss curve for the target parameters
The CNN model was evaluated under two configurations (S and D) using MSE and accuracy metrics on both training and validation datasets. In configuration S, the model achieved MSE values of 0.61 (training) and 0.074 (validation), with accuracies of 0.92 and 0.89, respectively, showing strong generalization capability. Configuration D demonstrated superior performance with MSE values of 0.053 (training) and 0.068 (validation), and an accuracy of 0.93 for both datasets. These results confirm the effectiveness of the proposed 1D CNN in achieving high accuracy and robust generalization across diverse data.
Output | MSE (Train) | MSE (Validation) | (Train) | (Validation) |
|---|---|---|---|---|
S | 0.61 | 0.074 | 0.92 | 0.89 |
D | 0.053 | 0.068 | 0.93 | 0.93 |
Optimized Antenna Structure & Results
The optimized dimensions are summarized in Table 2. With these dimensions, the antenna exhibits a high-gain Endfire radiation pattern over a wide frequency range.
Initially, a single unit cell was analyzed in detail, and subsequently, multiple unit cells were arranged side by side to realize the final structure and achieve the intended design objectives.
With the chosen dimensions, the surface current distribution ensures that variations in frequency do not alter the beam shape of the antenna. This characteristic represents the key advantage of the proposed structure, and the use of a neural network in the design process has been instrumental in attaining this performance.
Parameter | Values | Parameter | Values |
|---|---|---|---|
S | 4 mm | R | 4 mm |
D | 3 mm | 10 mm | |
W | 10 mm | 14 mm | |
2 mm | 5 mm | ||
10 mm | T | 1 mm | |
Z | 2 mm |
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Fig. 7
Example of the simulated responses obtained for the unit cell
The results indicate that the proposed structure exhibits radiation at undesired angles, corresponding to unwanted sidelobes. This issue can be effectively mitigated by arranging multiple unit cells in proximity, thereby suppressing the undesired radiation components.
By connecting the unit cells, the following results are obtained. The length of each unit cell is 22 mm, and by placing nine of the designed unit cells side by side, the final design objectives can be achieved. This configuration results in an overall antenna length of 198 mm (19.8 cm), which is significantly shorter than the initial antenna (over 30 cm in length) that exhibited Endfire radiation only at a single frequency of 3 GHz. In contrast, the proposed structure not only has smaller dimensions and higher efficiency but also maintains Endfire radiation over a wide frequency range from 6 GHz to 10 GHz.
Fig. 8
Geometry of the final antenna structure without the feed
Fig. 9
a)Simulated result of the proposed antenna at 6 GHz,b) Simulated result of the proposed antenna at 7 GHz, C) Simulated result of the proposed antenna at 8 GHz, c) Simulated result of the proposed antenna at 9 GHz, d) Simulated result of the proposed antenna at 10 GHz
The proposed structure is excited using a 10 mm long and 2 mm thick transmission line made of Teflon, in conjunction with an RG402 coaxial cable.
The results for the scattering parameters and the antenna gain at different frequencies are presented.
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Fig. 10
Feeding configuration of the proposed structure using a transmission line and a coaxial cable
It should be noted that, in the antenna geometry, the aperture at both ends (at the feeding region) is gradually tapered, and the antenna width is reduced. This design ensures a proper and low-loss connection to the feeding element, which can be either a coaxial cable or a transmission line.
To minimize return loss and considering the operational frequency band, it is recommended to first use a transmission line and then connect it to the coaxial cable through proper impedance matching. This feeding method has no significant impact on the shape of the antenna’s radiation pattern.
In this design, the initial transmission line section is 5 mm long and has the same width as the antenna aperture, after which the line width increases. This width adjustment is implemented to achieve impedance matching between the transmission line and the coaxial cable, thereby significantly reducing mismatch losses.
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Fig. 11
Simulated scattering parameters versus frequency
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Fig. 12
Simulated antenna gain versus frequency
In the following, the measured results of the fabricated antenna obtained through laboratory testing are presented. Furthermore, the radiation characteristics of the antenna in the E-plane and H-plane are reported and analyzed.
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Fig. 13
Fabricated antenna and measurement setup in the antenna laboratory
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Fig. 14
a)Radiation pattern in the E-plane at 6 GHz, b) Radiation pattern in the E-plane at 7 GHz, c) Radiation pattern in the E-plane at 8 GHz, d) Radiation pattern in the E-plane at 9 GHz, e) Radiation pattern in the E-plane at 10 GHz
Ref. | Structure Type | Frequency Range (GHz) | Bandwidth (%) | Antenna Length | Peak Gain (dBi) | Special Features |
|---|---|---|---|---|---|---|
This work | AI-optimized multi-unit cell grooved HMWG endfire antenna | 6–10 | 50 | 19.8 cm | 11–11.5 | Compact profile, wide bandwidth, stable endfire beam, sidelobe suppression < − 13 dB, CNN-based optimization |
[1] | Grooved HMWG LWA | 2.74–3.17 | 14.3 | ~λ₀ × 3 | 13.37 | High gain, narrowband, no AI optimization |
[2] | SSPP grooved endfire antenna | 22–41 | 62 | ~ 5λ₀ | 13 | Wideband, mmWave, large physical length |
[3] | Wideband planar endfire antenna | 1.75–3.55 | 68 | N/A | 8.23 | Wideband, low gain |
[4] | SSPP traveling-wave antenna | 7.5–8.5 | 10 | Very thin | 9.2 | Narrow bandwidth, moderate gain |
Conclusion
In this work, a compact, wideband, and high-gain endfire antenna based on a multi-unit cell grooved half-mode waveguide structure was presented. The design leverages an AI-driven optimization process using a convolutional neural network (CNN) to precisely tune the key geometric parameters, enabling significant improvements in gain, bandwidth, and radiation stability.
Simulation and measurement results demonstrated that the proposed antenna achieves stable endfire radiation across the 6–10 GHz frequency range with a peak gain exceeding 11 dBi, side-lobe levels below − 13 dB, and excellent impedance matching (|S₁₁| < − 10 dB). Compared to conventional high-gain endfire antennas, the proposed design offers a reduced physical profile (19.8 cm length), broader operational bandwidth, and improved radiation performance without compromising efficiency.
The combination of leaky-wave antenna principles with deep learning-based optimization provides a robust and scalable design methodology for next-generation wireless, radar, and sensing applications. This approach not only accelerates the design process but also ensures performance consistency across a wide range of operating conditions. Future work may explore further miniaturization, integration with reconfigurable feeding networks, and extension of the proposed methodology to millimeter-wave and terahertz frequency bands.
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Data Availability
All data generated or analyzed during this study are of our own work and it is our pleasure to be available on reasonable request. Contact M.S. via email: [mohammad_rezaei40@elec.iust.ac.ir](mailto:mohammad_rezaei40@elec.iust.ac.ir) .
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Funding
This research received no specific grant from any funding agency in the public, commercial,or not-for-profit sectors.
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Author Contribution
Mohammad RezaeiDepartment of Electrical Engineering, Iran University of Science and Technology (IUST), Tehran, Iran. *Email:* [ [Mohammad_rezaei40@elec.iust.ac.ir](mailto:Mohammad_rezaei40@elec.iust.ac.ir) ] *Author contributions:* Performed the simulations, collected and analyzed the data, and edited the manuscript.Professor Amir Saman NoorAminDepartment of Electrical Engineering, Iran University of Science and Technology (IUST), Tehran, Iran. *Email:* [ [a_nooramin@iust.ac.ir](mailto:a_nooramin@iust.ac.ir) ] *Author contributions:* Served as scientific advisor and provided valuable guidance throughout the study.
Professor Amir Saman NoorAmin
Department of Electrical Engineering, Iran University of Science and Technology (IUST), Tehran, Iran.
Email
[a_nooramin@iust.ac.ir]
Author contributions
Served as scientific advisor and provided valuable guidance throughout the study.
Competing interests
The authors declare no competing interests.
Additional information
Correspondence and requests for materials should be addressed to A.N.