Inverse design of an ultra-wideband endfire grooved half-mode waveguide (G-HMWG) antenna based on the CNN approach

Abstract

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.

Introduction

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.

To overcome these limitations, several researchers have proposed advanced endfire antenna configurations. Zhang et al.^1,12 reported a grooved half-mode waveguide (HMWG) leaky-wave antenna achieving a narrow bandwidth of 14.3% (2.74–3.17 GHz) with a high gain of 13.37 dBi, but the design lacked frequency stability. Patel et al.² introduced a spoof surface plasmon polariton (SSPP) grooved endfire antenna covering 22–41 GHz with a 62% bandwidth, yet the structure exhibited a very large physical length of approximately five free-space wavelengths. Another wideband planar endfire antenna³ offered a broader 68% bandwidth (1.75–3.55 GHz) but only 8.23 dBi peak gain. Kandwal et al.^4,22,25 proposed a thin SSPP traveling-wave antenna with moderate gain (9.2 dBi) and only 10% bandwidth. These studies highlight an inherent trade-off between gain, size, and bandwidth in endfire antenna design—achieving all three simultaneously remains a major challenge^2,13,23.

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.

Ultra-wideband (UWB) antennas are widely used in modern wireless communication systems due to their wide frequency coverage and high data-rate capabilities. Traditional design methods, including parametric sweeps and conventional optimization techniques, often require extensive computational effort and may not efficiently explore the full design space, particularly for antennas with complex geometrical features such as grooves or tapered feeding structures. Therefore, there is a clear need for a rapid, AI-assisted inverse design approach capable of efficiently estimating optimal antenna dimensions. In this work, we address this gap by proposing a 1D Convolutional Neural Network (1D-CNN) based methodology for the inverse design of a compact grooved half-mode waveguide (G-HMWG) antenna. The proposed approach significantly reduces design cycle time while maintaining high antenna performance.

The proposed AI-optimized G-HMWG end-fire antenna is primarily intended for X-band radar applications operating in the 6–10 GHz frequency range. The antenna’s compact profile, high gain, stable end-fire radiation, and sidelobe suppression make it particularly suitable for radar front-end systems, short-range surveillance, and sensing applications. In addition, the proposed design can be employed in directive point-to-point wireless communication links and ultra-wideband sensing systems where radiation stability and compact size are critical requirements.

Unlike conventional surrogate modeling or optimization-based antenna design approaches, which typically rely on forward mappings and iterative full-wave simulations, the proposed framework introduces a true inverse design strategy that directly maps radiation-pattern features to the optimal geometrical parameters. In this work, the CNN is trained using full angular radiation-pattern vectors as input, rather than scalar performance metrics such as gain or bandwidth. This enables the network to capture spatial radiation characteristics, including beam direction, sidelobe behavior, and pattern stability, which are critical for end-fire leaky-wave antennas. Moreover, once trained, the proposed CNN eliminates the need for iterative optimization loops, providing a rapid and deterministic prediction of optimal design parameters for ultra-wideband end-fire radiation. To the best of the authors’ knowledge, the application of a CNN-based inverse design framework using radiation-pattern-driven learning for compact grooved half-mode waveguide end-fire antennas has not been previously reported.

Despite recent progress in AI-assisted antenna design, most existing studies rely on forward surrogate models or iterative optimizers and focus primarily on scalar performance metrics such as gain or impedance bandwidth. Radiation-pattern-driven inverse design, which directly maps spatial radiation characteristics to antenna geometry, remains largely unexplored—particularly for compact grooved half-mode waveguide end-fire antennas. Moreover, achieving stable ultra-wideband end-fire radiation with simultaneous size reduction has not been reported. This work addresses these gaps by introducing a CNN-based inverse design framework that utilizes full radiation-pattern vectors to directly predict the key geometrical parameters of a compact G-HMWG antenna, enabling wideband, stable end-fire radiation with reduced physical length (Figs. 1, 2 and 3).

Fig. 1.

It illustrates a half-waveguide⁵.

Fig. 2.

Surface current distribution on the structure in two cases: (a) without the groove, and (b) with the groove introduced on the structure.

Fig. 3.

Geometry of the designed structure modeled in CST Microwave Studio.

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. The basic concept of the half-mode waveguide is illustrated in Fig. 1.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.

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.The surface current distribution for both configurations is shown in Fig. 2.

As illustrated in Fig. 4, 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.The overall geometry of the designed structure modeled in CST is presented in Fig. 3.

Fig. 4.

Geometry of the unit cell with optimized dimensions.

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. 4, confirms the strong field confinement and the gradual phase progression along the propagation axis (Figs. 5, 6, 7, and 8).

Fig. 5.

Designing the structure with the new predicted dimensions in CST software.

Fig. 6.

Block diagram of the neural network.

Fig. 7.

Training loss curve for the target parameters.

Fig. 8.

Example of the simulated responses obtained for the unit cell.

When multiple optimized unit cells are cascaded to form the complete structure (as later depicted in Fig. 9), 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.

Fig. 9.

Geometry of the final antenna structure without the feed.

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.

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. 4. 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. 4) 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. No artificial data augmentation techniques or symmetry-based transformations were applied to the dataset. Instead, a uniform distribution approach was used to sample the two-dimensional parameter space defined by slot spacing (S) and groove depth (D). The dimensional search ranges for the slot spacing (S = 4–15 mm) and groove depth (D = 12–30 mm) were identified through a combination of electromagnetic feasibility analysis and structural constraints. Preliminary CST simulations were carried out to determine the limits at which the leaky-wave mechanism is preserved and stable end-fire radiation can be maintained. Values of S below 4 mm produced extremely tight groove spacing, leading to excessive capacitive coupling and strong impedance mismatch at the feeding region. On the other hand, S values above 15 mm significantly weakened periodic radiation leakage and resulted in beam broadening and loss of end-fire characteristics.

Similarly, the groove depth range was physically constrained by wave-slowdown and manufacturability criteria. D values below 12 mm did not provide sufficient phase delay required for achieving the slow-wave regime and resulted in forward-beam degradation. Conversely, D values larger than 30 mm excessively slowed the wave, causing backward radiation and increased dielectric loading. From the fabrication perspective, groove depths above 30 mm also violate mechanical stability limits in aluminium milling.

Therefore, these ranges were selected to guarantee radiation feasibility, structural integrity, and CNN training stability within a physically meaningful leaky–wave parameter space.

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. To construct the training dataset, approximately 400 full-wave electromagnetic simulations were performed over the target ultra-wideband frequency range. The groove spacing (S) and groove depth (D) were systematically varied within predefined ranges using a MATLAB–CST co-simulation framework. Each simulation produced a corresponding two-dimensional radiation pattern, resulting in a dataset of 400 input–output samples. The dataset was randomly divided into 80% for training and 20% for testing the 1D-CNN model.

Although the size of the generated dataset is limited to 400 samples, the risk of overfitting was carefully addressed through several design choices. First, the dimensionality of the optimization problem was intentionally restricted to two dominant physical parameters (slot spacing S and groove depth D), resulting in a low-complexity regression task. Second, the CNN architecture was kept relatively shallow and was regularized using dropout layers, L2 weight regularization, batch normalization, and early stopping based on validation loss. These techniques effectively prevent memorization and improve generalization performance. No data augmentation was applied, as the radiation-pattern data represent physically meaningful electromagnetic responses rather than images, and artificial transformations could distort the underlying physical relationships. The close agreement between training and validation errors, as well as the high prediction accuracy reported in Table 1, confirms that overfitting was successfully mitigated despite the moderate dataset size.

Table 1.

Training and validation performance metrics of the neural network.

Output	MSE (Train)	MSE (Validation)	R2 (Train)	R2 (Validation)
S	0.61	0.074	0.92	0.89
D	0.053	0.068	0.93	0.93

This dataset contains the corresponding dimensional parameters along with the coordinate data of the two-dimensional radiation patterns, as illustrated in Fig. 10.

Fig. 10.

(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.

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. The input features of the 1D-CNN were constructed from the normalized two-dimensional radiation patterns extracted in the E-plane (yz-plane). The radiation patterns were sampled over an angular range of − 90° to + 90° with a resolution of 1°, resulting in 181 angular samples per radiation pattern. This angular sampling resolution provides sufficient spatial accuracy to capture the main beam direction, sidelobe levels, and beamwidth variations required for effective CNN-based optimization (Figs. 11 and 12).The redesigned structure using the predicted dimensions is illustrated in Fig. 5.

Fig. 11.

Feeding configuration of the proposed structure using a transmission line and a coaxial cable.

Fig. 12.

Simulated scattering parameters versus frequency.

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.

In this study, two geometrical parameters were selected for CNN-driven optimisation: the slot spacing S and the groove depth D. These parameters were identified as the dominant physical variables governing the end-fire leaky-wave behaviour of the antenna. The groove depth D primarily controls the phase velocity within each unit cell, enabling the slow-wave condition required for efficient end-fire radiation. Meanwhile, the slot spacing S determines the radiation leakage rate along the propagation axis, influencing the sidelobe level, impedance bandwidth, and beamwidth characteristics. Other geometrical parameters, such as the metal width, thickness, and taper profile, were kept constant as their variation exhibited limited influence on the end-fire mechanism and unnecessarily increased the dimensionality of the optimisation problem (Figs. 13 and 14).

Fig. 13.

Simulated antenna gain versus frequency.

Fig. 14.

Radiation efficiency plot.

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 (Figs. 15 and 16).

Fig. 15.

Fabricated antenna and measurement setup in the antenna laboratory.

Fig. 16.

(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.

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.

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 integration of CNN-based inverse modelling provides several advantages over conventional parametric scanning and manual optimisation techniques. First, the CNN eliminates the need for exhaustive full-wave re-simulation during parameter tuning, which reduces the design time by approximately 80%. Second, the model provides a highly nonlinear mapping between the radiation response and the structural parameters, enabling accurate prediction of the optimal geometry without human intervention. Third, the proposed approach ensures excellent stability over the 6–10 GHz bandwidth while maintaining consistent end-fire radiation behaviour, which is challenging to achieve through classical optimisation methods. In addition, the data-driven optimisation framework improves repeatability and reproducibility of the design process, offering a scalable solution for future multi-band or multi-parameter antenna systems.

The primary advantage of the proposed AI-based optimization over the built-in CST optimizer lies in the design philosophy. CST optimizers operate through iterative forward simulations that search for optimal values within user-defined constraints. Each optimization attempt requires dozens to hundreds of CST evaluations, making the method computationally expensive for multi-dimensional antenna problems.

In contrast, the CNN performs a deterministic inverse prediction without requiring any electromagnetic re-simulation. Once trained, the network instantly predicts optimized geometrical parameters, eliminating iterative tuning and reducing computational cost significantly. Additionally, the CNN learns nonlinear relationships between the radiation behaviour and geometry, which the CST optimizer cannot exploit since it only evaluates numerical performance metrics rather than spatial radiation patterns.

Despite these advantages, certain limitations must also be acknowledged. The CNN requires a sufficiently large number of high-fidelity electromagnetic samples to avoid overfitting, and the dataset generation step remains computationally expensive. Moreover, the trained model is architecture-dependent and cannot generalise beyond the physical geometry used during training. Finally, the optimisation process relies on supervised learning and therefore does not guarantee a globally optimal design outside the predefined parameter search space.

These strengths and limitations have now been discussed in the revised manuscript to offer a balanced view of the proposed AI-assisted design framework. To further clarify the practical advantages of the proposed approach, a direct comparison with conventional optimization techniques is discussed below.

Unlike evolutionary optimizers such as Genetic Algorithms (GA) and Particle Swarm Optimization (PSO), which rely on iterative forward electromagnetic simulations, the proposed CNN-based framework performs a deterministic inverse mapping from radiation patterns to geometrical parameters. For a fair comparison, we consider a typical optimization scenario involving two design variables (S and D) over a wideband frequency range. GA and PSO optimizers generally require 20–40 individuals or particles per generation and 30–50 generations to converge, resulting in approximately 600–1200 full-wave CST simulations. On our workstation, this corresponds to a total computational time exceeding 300 h.

In contrast, the proposed CNN approach requires the same 400 electromagnetic simulations only once during the offline dataset generation stage. After training, the optimized geometrical parameters are predicted in under 1 s without any additional electromagnetic simulations. This leads to a design-cycle time reduction of approximately 95%, while simultaneously ensuring stable end-fire radiation across the entire 6–10 GHz band.

Furthermore, unlike surrogate-based optimizers that still operate within an iterative optimization loop and depend heavily on predefined objective functions, the proposed method directly learns radiation-pattern-driven inverse relationships. This enables the CNN to capture spatial radiation features such as beam alignment, sidelobe suppression, and pattern stability, which are difficult to encode explicitly in conventional optimization frameworks.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. 6 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. It should be emphasized that the AI-based optimization loop was applied exclusively to the radiating unit-cell parameters (S and D). The impedance matching network, including the tapered transition and feeding lines, was not included in the optimization loop. These feeding structures were designed separately using conventional electromagnetic simulations, with special consideration given to fabrication feasibility and practical implementation. This approach ensures reliable impedance matching while simplifying the manufacturing process.

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. The CNN model was trained using the Mean Squared Error (MSE) loss function, which is suitable for regression-based inverse design problems. The MSE loss is defined as

1

where ​ and denote the target and predicted values of the geometrical parameters (slot spacing S and groove depth D), respectively, and N represents the number of training samples. The Adam optimizer was employed for network training with a learning rate of 0.001 to ensure stable and fast convergence. The network was trained for 200 epochs, and early stopping was applied to prevent overfitting.

In addition to the MSE metric, a tolerance-based regression accuracy was used to evaluate prediction performance. The accuracy is defined as the percentage of predicted geometrical parameters whose absolute error lies within ± 5% of the corresponding ground-truth value.

The use of a convolutional neural network is motivated by the structured and spatially ordered nature of the input radiation-pattern data. Unlike scalar performance metrics, radiation patterns contain local angular features such as main-beam direction, sidelobe structure, and angular symmetry. CNNs are particularly effective in extracting such spatial features through convolutional filtering, enabling a physically meaningful inverse mapping between radiation behavior and antenna geometry. This makes the proposed CNN-based framework more suitable than simpler regression models for radiation-pattern-driven inverse antenna design.

Although CNN models are commonly associated with 2-D image processing, the ability of convolutional filters to extract spatially ordered features applies equally to 1-D structured radiation-pattern vectors. In this application, the radiation data consist of 181 sequential angular samples per pattern, which form a one-dimensional spatial signal. CNNs are therefore suitable due to their capability to extract localized spatial features such as beam direction, sidelobe depth, pattern symmetry, and shape variation. Other models, such as multilayer perceptrons (MLPs), cannot capture spatial locality and performed worse in our comparative tests.The training loss curve of the CNN model is presented in Fig. 7.

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.

In conventional parametric scanning, approximately 400 full-wave simulations were required to reach near-optimal S and D values, resulting in a total computational time of ~220 hours on our workstation (Intel i9 processor, 64 GB RAM). In contrast, the CNN approach required the same 400 simulations only once for dataset generation, after which the inverse design process provided optimized geometry values in under 1 second with no further CST simulations. Therefore, the total design-cycle time was reduced by ~95%. This confirms that the CNN method is significantly faster than parametric sweeps or GA-based optimizers, which typically require hundreds of electromagnetic solves to converge.

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.

Table 2.

Geometrical parameters of the designed structure.

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

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.An example of the simulated responses obtained for the unit cell is shown in Fig. 8.

The improved radiation performance obtained using the CNN-optimized geometrical parameters can be physically interpreted in the context of leaky-wave antenna theory. In the proposed grooved half-mode waveguide structure, the groove depth (D) primarily controls the phase constant of the guided mode by extending the effective surface current path, thereby reducing the phase velocity. The CNN-optimized value of D brings the phase constant closer to the free-space wavenumber over a wide frequency range, satisfying the Hansen–Woodyard condition for efficient and stable end-fire radiation.

In parallel, the optimized slot spacing (S) regulates the radiation leakage rate along the propagation direction. Proper balancing of the leakage rate ensures that energy is radiated progressively along the aperture without excessive attenuation or premature radiation. This leads to a more uniform phase progression across the antenna length, resulting in constructive interference in the end-fire direction and suppressed sidelobe levels.

The combined optimization of D and S enables a favorable trade-off between phase control and radiation leakage, which explains the observed wideband behavior and radiation stability from 6 to 10 GHz. Rather than acting as a black-box optimizer, the CNN effectively identifies geometrical configurations that enforce physically meaningful leaky-wave conditions, leading to enhanced bandwidth, stable beam direction, and improved aperture efficiency.

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 to 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.The feeding configuration of the proposed antenna is presented in Fig. 11.

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.The simulated scattering parameters are shown in Fig. 12 and the variation of antenna gain with frequency is illustrated in Fig. 13.

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.The radiation efficiency of the antenna is shown in Fig. 14.

Compared to Ref², the proposed antenna achieves a more compact structure, improved radiation stability with sidelobe levels below –13 dB, and stable end-fire radiation across the 6–10 GHz band. In addition, the CNN-based inverse design accelerates the optimization process, reducing the design-cycle time compared to conventional approaches.

To enable a fair and normalized comparison with existing end-fire antennas, the physical length and radiation performance of the proposed antenna have been normalized with respect to wavelength and physical aperture. The total electrical length of the antenna at 6 GHz is L ≈ 5.28 λ₀, confirming that the design remains significantly more compact than most reported SSPP-based or grooved end-fire structures, which typically exceed 6–8 λ₀. The peak directivity achieved at 10 GHz is 11.5 dBi with only 5.28 λ₀ physical length, producing a normalized radiation performance of ≈ 2.17 dBi/λ, which exceeds the performance efficiency of references^2–4 in Table 3.

Table 3.

Performance comparison of the proposed antenna with previous works.

References	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 (5.28 × λ₀)	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	~ 5 × λ₀	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
26	CNN cavity-based antennas	3–6	40	5.5 × λ₀	9.8	AI design – not endfire
27	ML-UWB antenna	5–10	45	–	10.1	ML dimension prediction

Furthermore, aperture efficiency was estimated using

2

where A is the physical aperture area, G is the linear gain (not in dBi!) and is the wavelength. For the proposed structure (19.8 cm × 1.4 cm), is calculated to be approximately 63–67% across 6–10 GHz, confirming that the antenna efficiently uses its radiation aperture despite its compact electrical footprint.

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.

Author contributions

Mohammad Rezaei Department 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)]. Performed the simulations, collected and analyzed the data, and edited the manuscript. Professor Amir Saman NoorAmin Department of Electrical Engineering, Iran University of Science and Technology (IUST), Tehran, Iran. Email: [[a_nooramin@iust.ac.ir](mailto:a_nooramin@iust.ac.ir)]. Served as scientific advisor and provided valuable guidance throughout the study.

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Data availability

The raw source code and the complete dataset used for training and validating the Convolutional Neural Network (CNN) model in this study are publicly available at: [https://github.com/MohammadRezaei40/G-HMWG-CNN-Inverse-Design]. All data were generated through full-wave electromagnetic simulations conducted by the authors. The repository contains the executable training script, dataset, and documentation required to reproduce the reported results.

Declarations

Competing interests

The authors declare no competing interests.