Edge-Aware, Data-Efficient Fine-Tuning of Progressive GANs for Multiband Antennas

Abstract

This study proposes a data-efficient fine-tuning strategy for multi-band antenna synthesis using a Wasserstein Auxiliary-Guided Progressive Growing GAN (WAG-PGGAN). Starting from a pretrained 512 × 512 dual-band PIFA-like generator trained on 4180 samples at 2.45/5.2 GHz, we introduce three 3.5-GHz wideband seeds augmented to 836 images (new:legacy ≈ 1:5) and fine-tune only the highest-resolution stage on the combined 5016-image corpus. A Hough-transform-based edge-enhancement module with an edge-aware loss preserves conductor boundaries and strengthens frequency–geometry correlation. Across n = 8 fabricated prototypes, all achieve |S11| < −10 dB and collectively span 1.86–5.83 GHz; measured total efficiencies are 52–87% (e.g., 73.6% @ 2.68 GHz, 66.7% @ 3.56 GHz, 69.0% @ 5.83 GHz), with radiation patterns consistent with simulation. The method retains prior 2.45/5.2 GHz performance while adding 3.5-GHz wideband behavior using ≤ 17% new data (836/5016), demonstrating effective transfer from small datasets. On an RTX 3060 Ti, inference is ≈ 3 s/design after ~192 h of training. Simulation–measurement agreement confirms that fine-tuned WAG-PGGAN yields high-resolution, physically valid multi-band antennas with reduced data and computational cost.

1. Introduction

With the rapid advancement of wireless communication technologies, antenna design has become a cornerstone of modern systems, particularly for applications requiring multi-band operation. Multi-band antennas support multiple frequency bands within a single compact structure, making them well suited to mobile devices, satellite communications, and Internet of Things (IoT) sensing networks. Among these, dual-band antennas with embedded wideband characteristics are widely adopted because they operate across two independent bands while retaining extensibility to additional bands [1,2]. Their simple geometries, low production cost, and ease of integration have made them a mainstream industrial solution. Traditional antenna design relies on expert knowledge and iterative full-wave simulations; although accurate, these methods are time-consuming and limited in exploring the vast design space. To address these limitations, artificial intelligence (AI) and machine learning (ML) have emerged as powerful data-driven tools for antenna design and optimization [3,4]. Generative adversarial networks (GANs) can synthesize complex antenna geometries by learning structure–performance relationships from large datasets [5,6]. Prior work demonstrates that GAN-based models generate diverse, physically meaningful designs [7], yet challenges persist in output stability, high-resolution fidelity, and structural diversity—especially for multi-frequency applications. We therefore propose a fine-tuning-centered antenna-generation methodology, inspired by knowledge distillation and built on Progressive Growing of GANs (PGGAN). Introduced by Karras et al. [8], PGGAN improves convergence stability and output quality by gradually increasing the resolution of both generator and discriminator during training. We further develop a Wasserstein Auxiliary-Guided PGGAN (WAG-PGGAN) that enhances training efficiency and performance, making it well suited to high-dimensional structural learning of antennas.

This study extends a previously trained 512 × 512 dual-band PIFA-like generator. The original dataset contained two single-band antennas at 2.45 and 5.2 GHz, expanded by geometric augmentation and full-wave EM simulation to 4180 labeled samples. To improve multi-band and wideband generalization, we add three newly designed wideband antennas centered near 3.5 GHz. Data augmentation yields 836 additional samples, which are merged with the original set to fine-tune the model under the WAG-PGGAN framework at 512 × 512 resolution. To increase sensitivity to conductive boundaries and structural transitions, we introduce a second-stage Hough-transform edge-enhancement module at the highest-resolution layer [9,10]. This module strengthens the coupling between geometrical features and frequency response in the latent space, providing auxiliary supervision that guides the generator toward physically interpretable structures. The complete pipeline—covering data simulation, feature mapping, label enhancement, and progressive image synthesis—produces new Wi-Fi PIFA-like antennas exhibiting dual- and tri-band wideband characteristics.

Simulation and measurement results show that the generated antenna prototypes closely match HFSS (High-Frequency Structure Simulator) predictions, confirming the method’s robustness, generalizability, and practical utility. Integrating fine-tuned machine-learning frameworks [11,12] with high-resolution generative models markedly improves the performance and design diversity of AI-driven antenna synthesis. This provides a scalable paradigm for the intelligent synthesis of complex electromagnetic structures and advances next-generation smart wireless systems.

2. Methodology and System Architecture Description

This section outlines the proposed multiband antenna-generation methodology and system architecture, covering the data-augmentation pipeline, antenna feature-extraction techniques, the training mechanism of the Weighted and Attention-Guided Progressive Growing GAN, and a label-enhanced high-dimensional feature-mapping strategy. The complete workflow is shown in Figure 1. Building on prior single- and dual-band generative models, we fine-tune and extend the framework to synthesize multiband and wideband antenna structures. We retain the Nadam optimizer (learning rate = 0.001) from a previously trained 512 × 512 dual-band PIFA-like model. Hyperparameters follow earlier experiments with multiple configurations and are adjusted to the available computational resources. Each stage of the workflow includes data organization, inference, and model-evaluation procedures to quantify the probability of successful antenna generation. The end-to-end design flow is summarized in Figure 1.

2.1. Augmentation of Three Wideband Antenna Samples

We simulated three wideband antennas in HFSS to generate high-quality training data. Centered near 3.5 GHz, the designs were constrained to maintain a return loss (S₁₁) below −10 dB across the target band. As shown in Figure 2, the S-parameter responses and corresponding geometries confirm distinct resonances and adequate bandwidth for each structure. These simulation-validated designs provide a solid foundation for subsequent data-driven learning.

Three additional wideband antennas centered near 3.5 GHz were employed to strengthen the model’s capacity for complex multiband structures. Covering a broader frequency range, these designs serve as key exemplars for multiband feature learning. To improve data diversity and generalization, geometric augmentations—flipping, shifting, rotation, and structural morphing—were applied to each validated design (Figure 3), yielding 5016 training samples while preserving core EM traits. This dataset was then used to fine-tune the WAG-PGGAN, enabling high-fidelity synthesis of novel multiband antennas with improved control of frequency response.

These transformations yielded structurally diverse yet label-consistent samples. A total of 836 augmented images were generated from the three new antennas. Examples appear in Figure 4, and Figure 5 summarizes all ten antenna designs used in this study.

Augmentation operations:

• Horizontal/vertical flips
• Image translations (shifts)
• Structural mirroring/swapping
• Local geometric morphing
• Arbitrary-angle rotations

To ensure that augmentation does not distort frequency-band labeling, all transformations are restricted to conformal operations (translation, mirroring, arbitrary-angle rotation, and local geometric perturbation) without scaling, while maintaining the 1:1 pixel-to-physical mapping and feed-point relationship. The newly added 3.5 GHz samples were verified using HFSS, and their augmented data inherit the original band and −10 dB labeling to preserve geometry–frequency semantic consistency. To preserve edge integrity and geometry–EM consistency, an edge-aware regularization based on the Hough-transform features is introduced in the training objective (see Section 2.4).

2.2. Image Format Standardization and Dataset Integration

To ensure compatibility with the WAG-PGGAN fine-tuning workflow, all antenna images were converted to a standardized 512 × 512-pixel PNG format. This preprocessing step aligned the new samples with the original set of 4180 single- and dual-band images. The new and existing samples were then merged into a consolidated dataset of 5016 images, which served as input to the training stage.

2.3. Feature Enhancement and Latent Space Sampling

Before training, a Hough transform was applied to each image to extract geometric edges and annotate key conductor contours, supplying additional structural cues to the generator and discriminator and improving associations between physical features and electromagnetic properties (e.g., trace length, current paths) [13].

To promote diverse and well-distributed latent samples, Latin hypercube sampling (LHS) was used for latent-variable selection [14,15], enabling broader exploration of the structural design space.

2.4. WAG-PGGAN Training Process (4 × 4 to 512 × 512)

To generate multiband antenna structures, this work fine-tunes a previously trained 512 × 512 dual-band model using a 1:5 ratio of new to legacy samples, preserving prior knowledge while introducing new frequency characteristics. All images were standardized to 512 × 512 PNG for compatibility with the WAG-PGGAN framework. The final dataset comprised 5016 samples, including 836 new images derived from three HFSS-verified wideband designs and augmented via geometric transformations. To enhance recognition of structural boundaries, a second Hough-transform pass is applied at the highest resolution to emphasize edges. An edge-alignment loss, L_edge, is introduced to guide the generator to match synthetic boundaries with ground-truth structural annotations, primarily on the new samples. The loss is defined in (1).

$${\lambda }_{edge}\cdot L_{edge}\left(X_{new}\right)$$

(1)

The overall loss follows the WGAN-GP framework to ensure stable training and high-resolution synthesis. The discriminator (critic) loss is

$$\begin{array}{ll}{L}_{\mathrm{PGGAN}-\mathrm{D}}=& E_{z\sim p_{g\left(z\right)}}\left[D\left(G\left(z\right)\right)\right]-E_{x\sim p_{\mathrm{d}\mathrm{a}\mathrm{t}\mathrm{a}}}\left[D\left(x\right)\right]\\ & +\lambda E_{\widehat{x}\sim p_{\widehat{x}}}\left[{\left(\left|\right|{\nabla }_{\widehat{x}}D\left(\widehat{x}\right){\left|\right|}_2-1\right)}^2\right] \end{array}$$

(2)

where $D\left(·\right)$ is the discriminator (critic) and $G\left(·\right)$ is the generator; ${z~p}_z$ denotes latent inputs, ${x~p}_{data}$ denotes real antenna images, and $\widehat{x}$ are points interpolated between real and generated samples (used for the gradient penalty). The coefficient $\lambda$ controls the strength of the gradient penalty and enforces the 1-Lipschitz constraint.

The loss components are:

• $E_{z\sim p_{g\left(z\right)}}\left[D\left(G\left(z\right)\right)\right]$: Discriminator’s expected score on generated images; minimized by the generator.
• $\left(E_{x\sim p_{\mathrm{data}}}\left[D\left(x\right)\right]\right)$: Discriminator’s expected score on real images; maximized to separate real from generated.
• $\lambda E_{\widehat{x}\sim p_{\widehat{x}}}\left[{\left(\left|\right|{\nabla }_{\widehat{x}}D\left(\widehat{x}\right){\left|\right|}_2-1\right)}^2\right]$: Gradient penalty enforcing 1-Lipschitz continuity and stabilizing training. This interpolation $\widehat{x}$ is used in the gradient penalty term to ensure smooth transitions between real and generated samples, improving training stability.

The interpolation $\widehat{x}$ between real and generated images is calculated as (3):

$$\widehat{x}=ϵx+\left(1-ϵ\right)\tilde{x},\hspace{1em}ϵ\sim U\left[\mathrm{0,1}\right]$$

(3)

where $x$ is a real antenna image and $\tilde{x}$ is a generated antenna image. $ϵ$ is sampled from a uniform distribution $U\left[\mathrm{0,1}\right]$. When $ϵ=1$, $\widehat{x}=x$ (real sample). When $ϵ=0$, $\widehat{x}=\tilde{x}$ (generated sample). When $ϵ$ is between 0 and 1, $\widehat{x}$ is a linear combination of the real and generated images. This interpolation is used in the gradient penalty term to ensure smooth transitions between real and generated samples, improving training stability.

• Combining the above components, the total fine-tuning loss is

$$L_{total}=L_{PGGAN}+{\lambda }_{edge}\cdot L_{edge}\left(X_{new}\right)$$

(4)

• $L_{PGGAN}$: WGAN-GP-based adversarial objective (Wasserstein distance + gradient penalty) to stabilize training and improve fidelity.
• ${\lambda }_{edge}$: Edge-loss weight, tuned on a validation set (typically 0.01–0.1).
• $L_{edge}\left(X_{new}\right)$: Hough-annotated, edge-guided term on new samples $X_{new}$ that preserves conductive boundaries and promotes physically meaningful structures.

The Hough-transform-derived term ${ L}_{edge}$ serves as a high-resolution regularization component that maintains conductive-boundary integrity and physical realizability, ensuring that the generated designs exhibit both geometric stability and electromagnetic consistency.

While the classical Hough transform is originally a line-detection method, in this study it is redefined as a physics-aware structural proxy. It summarizes conductive boundaries into a compact parameter space where features that directly govern surface-current paths—and hence resonances, bandwidth, and coupling—become measurable.

Unlike conventional edge detectors that only capture local gradients, the Hough-transform-based features summarize global edge orientation and density, which are directly related to effective current paths, resonance lengths, and capacitive coupling. This makes the edge-aware loss a physics-aligned regularizer rather than a purely image-based constraint.

For planar PIFA-like and slot-like conductors, dominant surface currents concentrate along edges and discontinuities.

This motivates three geometry–EM correspondences:

(i)

the resonant frequency relates to the effective current-path length

$$f_r={\displaystyle \frac{c}{4\hspace{0.17em}{L}_{\mathrm{eff}\hspace{0.17em}}\sqrt{{\mathsf{\epsilon }}_{\mathrm{eff}}}}}$$

(5)

(ii)

bandwidth correlates with edge density and parallelism (which affect capacitive coupling and the quality factor), and

(iii)

multiband behavior arises from multiple distinct edge orientations and branch lengths.

To provide geometry-aware and numerically stable supervision for the generator, we introduce an edge-alignment loss that enforces consistency between the generated sample and the reference antenna geometry. Since the dataset used in this study consists solely of 2-D conductor images without thickness or height information, the height reference is defined as $H_{\mathrm{ref}}=0$, and thus the corresponding term acts only as a weak regularizer. The complete loss is formulated as

$$L_{\mathrm{edge}}=\alpha \parallel A_{\mathrm{gen}}-A_{\mathrm{ref}}{\parallel }_1+ \beta \parallel H_{\mathrm{gen}}-H_{\mathrm{ref}}{\parallel }_1+\gamma \hspace{0.17em}\mathrm{C}\mathrm{h}\mathrm{a}\mathrm{m}\mathrm{f}\mathrm{e}\mathrm{r}\left(E_{\mathrm{gen}},E_{\mathrm{ref}}\right)$$

(6)

To construct reliable geometric targets, each reference image is smoothed using a Gaussian kernel, converted to grayscale, and processed with the Canny operator to obtain an initial edge map. Based on this map, we compute the line Hough accumulator $A(\rho ,\theta )$, which encodes the global distribution of edge orientations and spatial frequencies. Major conductor boundaries are further enhanced through probabilistic Hough line detection; for each detected line segment $\mathcal{l}=(x_1,y_1,x_2,y_2)$, the corresponding pixels are redrawn onto an enhanced reference image $I_{\mathrm{enh}}$. The area term $A_{\mathrm{ref}}$, height term $H_{\mathrm{ref}}$, and boundary set $E_{\mathrm{ref}}$ are derived from these HFSS-validated seeds, including the new 3.5-GHz wideband exemplars.

The incorporation of Hough-domain features provides global structural cues that complement local edge detection. Specifically, the edge-regularization loss constrains the generator to reproduce correct edge orientation, length, continuity, and inter-segment spacing—properties directly tied to conductive path integrity and electromagnetic behavior. The use of global Hough accumulators stabilizes high-resolution training by preventing fragmented or jagged edges that would otherwise break current continuity, a phenomenon further verified in the ablation experiments.

An additional edge-aware regularization term is incorporated during fine-tuning, derived from Hough-transform edge features (Figure 6). Although not expressed in a closed form, its contribution is denoted as ${\lambda }_{edge}\cdot L_{edge}\left(X_{new}\right)$. This term:

• Performs a structural comparison between the original wideband sample $X_{new}$ and the generated image using Hough-based edge attributes (e.g., orientation, density, and line segments).
• Provides guidance that steers the generator toward physically meaningful geometric patterns in the latent space.

The value of ${\lambda }_{edge}$ was determined through manual adjustment and empirical experimentation rather than relying solely on automated hyperparameter optimization methods such as grid search or Bayesian optimization. During the preliminary training phase, a range of ${\lambda }_{edge}$ values was systematically explored to evaluate their impact on the trade-off between edge-preserving detail enhancement and global image stability. Each candidate was assessed through both quantitative metrics (e.g., loss convergence rate, peak signal-to-noise ratio) and qualitative evaluations of generated samples to detect potential artifacts or boundary distortions.

Through iterative refinement, the final ${\lambda }_{edge}$ was selected as the value that consistently yielded stable convergence and visually coherent results across multiple training runs. Consequently, the ${\lambda }_{edge}$ adopted in this study represents an empirically optimized parameter, derived from hands-on experimentation to ensure optimal performance for the 512 × 512 generation model.

Conceptually, this regularization term enforces alignment between antenna geometry and its corresponding frequency response, with the weight ${\lambda }_{edge}$ governing the contribution of the edge loss and being tuned empirically. The resulting objective function integrates global adversarial learning with local geometric regularization: while maintaining the training stability of WGAN-GP fine-tuning, it guides the model toward generating structures that adhere to electromagnetic principles, achieving high structural fidelity and frequency-aware multiband synthesis. After several high-resolution training epochs, the model consistently produces novel antenna images exhibiting dual-band or higher-order multiband characteristics.

According to the results obtained in this study, without applying the Hough-based edge enhancement mechanism, the antenna learning model exhibits severe structural distortion and irreversible deformation in its generated forms (Figure 7). The model fails to preserve the geometric continuity and physical realism of the antenna profile, resulting in irregular, non-functional structures. Although certain iterations may occasionally demonstrate partial generalization capability, these instances remain inconsistent and lack reproducibility. Ultimately, without edge-enhanced feature extraction, the network is unable to generate entirely new and multi-frequency antenna structures, as it loses critical boundary cues necessary for maintaining electromagnetic and geometric coherence during training.

The 512 × 512 model inputs progressively down to 4 × 4 feature maps for final classification (

Table 1. The Layers of Discriminator Structure.

Name	Type	Output_Shape	Params	Connected_to
input_2	InputLayer	(None, 4, 4, 3)	0	[]
from_rgb_4 × 4	EqualizeLearningRate	(None, 4, 4, 512)	2049	[‘input_2[0][0]’]
conv2d_up_channel	EqualizeLearningRate	(None, 4, 4, 512)	262,657	[‘from_rgb_4 × 4[0][0]’]
minibatch_stddev	MinibatchSTDDEV	(None, 4, 4, 513)	0	[‘conv2d_up_channel [0][0]’]
d_output_conv2d_1	EqualizeLearningRate	(None, 4, 4, 512)	2,364,417	[‘minibatch_stddev[0][0]’]
leaky_re_lu_2	LeakyReLU	(None, 4, 4, 512)	0	[‘d_output_conv2d_1[0][0]’]
d_output_conv2d_2	EqualizeLearningRate	(None, 1, 1, 512)	4,194,817	[‘leaky_re_lu_2[0][0]’]
leaky_re_lu_3	LeakyReLU	(None, 1, 1, 512)	0	[‘d_output_conv2d_2[0][0]’]
flatten	Flatten	(None, 512)	0	[‘leaky_re_lu_3[0][0]’]
input_alpha	InputLayer	(None, 1)	0	[]
d_output_dense	EqualizeLearningRate	(None, 1)	514	[‘flatten[0][0]’]
Total_params			6,824,454
Trainable_params			6,824,449
Non_trainable_params			5

). It begins with an RGB-to-feature conversion using Equalized Learning Rate (EqLR) layers to stabilize training without batch normalization. Intermediate convolution and LeakyReLU activations extract deep spatial–semantic features, while a Minibatch Standard Deviation layer introduces inter-sample statistics to prevent mode collapse. The final Flatten and Dense layers output a single scalar “realness” score. An α (alpha) blending input enables smooth resolution transitions during progressive growing. Overall, the model integrates EqLR, LeakyReLU, and minibatch statistics to ensure stable, high-resolution adversarial learning and reliable discrimination at the 512 × 512 stage.

The generator begins from a 512-dimensional latent vector and progressively transforms it into 4 × 4 feature maps (

Table 2. The Layers of Generator Structure.

Name	Type	Output_Shape	Params	Connected_to
input_1	InputLayer	(None, 512)	0	[]
g_input_dense	EqualizeLearningRate	(None, 8192)	4,202,497	[‘input_1[0][0]’]
pixel_normalization	PixelNormalization	(None, 8192)	0	[‘g_input_dense[0][0]’]
leaky_re_lu	LeakyReLU	(None, 8192)	0	[‘pixel_normalization[0][0]’]
reshape	Reshape	(None, 4, 4, 512)	0	[‘leaky_re_lu[0][0]’]
g_input_conv2d	EqualizeLearningRate	(None, 4, 4, 512)	2,359,809	[‘reshape[0][0]’]
pixel_normalization_1	PixelNormalization	(None, 4, 4, 512)	0	[‘g_input_conv2d[0][0]’]
leaky_re_lu_1	LeakyReLU	(None, 4, 4, 512)	0	[‘pixel_normalization_1[0][0]’]
input_alpha	InputLayer	(None, 1)	0	[]
to_rgb_4 × 4	EqualizeLearningRate	(None, 4, 4, 3)	1540	[‘leaky_re_lu_1[0][0]’]
Total_params			6,563,846
Trainable_params			6,563,843
Non_trainable_params			3

). A dense layer (g_input_dense) expands the latent space to 8192 dimensions, followed by pixel normalization and LeakyReLU activation to stabilize feature variance. The vector is then reshaped into a 4 × 4 × 512 tensor, forming the initial spatial feature block. Subsequent Equalized Learning Rate (EqLR) convolutions refine spatial representations, while repeated pixel normalization and LeakyReLU layers ensure controlled signal magnitude and stable gradient propagation. The to_rgb_4 × 4 layer converts the feature maps into a 4 × 4 RGB image, serving as the foundation for later progressive upsampling to higher resolutions. Overall, this architecture establishes the base resolution (4 × 4) of the Progressive Growing GAN, ensuring stable synthesis and coherent feature formation before the generator expands to larger spatial scales.

The following is a detailed explanation of Figure 8—Loss Function Analysis.

• Step 0–200: Initial Learning Phase (Warm-up Phase)
  • G_loss (red line) fluctuates strongly between positive and negative values, indicating that the generator is still randomly exploring how to produce meaningful samples.
  • D_loss (green line) stays mostly negative or shows large negative swings, meaning the discriminator can easily distinguish real from fake samples.
  • At this point, the adversarial balance has not yet formed—D clearly dominates.
  • Recommendation: To accelerate stabilization, slightly reduce the discriminator’s learning rate or apply label smoothing.
• Step 200–800: Early Stabilization and Oscillation Zone
  • G_loss gradually decreases and begins to oscillate periodically—a typical sign that the generator is starting to approximate the true data distribution and the adversarial game is approaching balance.
  • D_loss rises toward the 0 ~ −2 range, showing that D is no longer winning completely.
  • If both losses fluctuate violently in sync, it suggests “gradient tug-of-war” between G and D; consider gradient clipping or smaller alternating update steps.
• Step 800–1600: Formation of Adversarial Balance Region
  • G_loss and D_loss curves get closer, with smaller amplitudes.
  • Short-term rises in G_loss (for example around step 1200–1400) usually mean the discriminator temporarily learns faster.
  • When both losses oscillate around −2 ~ 2, the model is in an ideal adversarial equilibrium region.
  • In this period, sample diversity typically increases, and the generated quality improves.
• Step 1600–2500: Second Oscillation and Mode-Search Phase
  • D_loss shows prominent peaks and sometimes very high or low values (>3 or <−3), indicating the discriminator is occasionally fooled—a good sign.
  • G_loss temporarily rises and falls again, meaning the generator is exploring new structural or pattern modes.
  • If oscillations become excessive (> ±5), consider:

    ○

    Using mini-batch standard deviation trick,

    ○

    Lowering the generator learning rate or adding gradient penalty.

• Step 2500–4000: Stable Learning and Fine-detail Adjustment
  • G_loss slowly decreases and oscillates near zero; D_loss also converges gradually, suggesting both networks are near a Nash equilibrium.
  • This is the ideal training phase, where sample quality and diversity are usually best.
  • Save model checkpoints in this range for later evaluation or deployment.
• Step 4000–4500 +: Late Phase/Possible Over-fitting
  • If G_loss continues to drop very low (around −1~−3) while D_loss rises, it may indicate that the discriminator is weakening or the generator is entering mode collapse.
  • Examine whether:

    ○

    Generated samples are becoming repetitive,

    ○

    The discriminator’s accuracy is declining.

  • If convergence is confirmed, stop training or switch to fine-tuning (lower LR, freeze parts of D).
• Optimal Training Region for Model Selection

Based on the above analysis of the generator and discriminator learning dynamics, this study identifies the optimal training region around Step 4000 as the most stable and representative phase of adversarial equilibrium. During this interval, both G_loss and D_loss exhibit minimal oscillation and converge toward balanced values, indicating that the generator produces consistent, high-fidelity outputs while the discriminator maintains effective discrimination without overpowering the generator. Therefore, the 512 × 512 generative model adopted in this research is derived from the checkpoint corresponding to this optimal region (around Step 4000), ensuring that the trained model reflects the best compromise between image quality, diversity, and training stability.

Table 3. Training Configuration and Performance of the WAG-PGGAN Model for 512 × 512 Antenna Generation.

Resolution	512 × 512	Total
Data Samples	5016	5016
Approx. Time per Epoch	288 min	-
Epochs	40	40
Total Time (minutes)	11,520	11,520
Total Time (hours)	192	192
Training Parameters and Hardware configure	TensorFlow GPU Version: 2.7.4, Batch Size: 2, Learning Rate: ${1 \times 10}^{-3}$, Optimizer: Nadam, Beta 1: 0, Beta 2: 0.99, Epsilon: ${1 \times 10}^{-8}$, GPU: NVIDIA GeForce RTX 3060 Ti 8 GB, CPU: i5-8400, DDR 32 GB
Time to produce antenna (Using Model)	The trained model generates one antenna every 3 s.

summarizes the training duration, computational setup, and generation performance of the WAG-PGGAN model at a resolution of 512 × 512. The dataset contains 5016 antenna samples, with each training epoch requiring approximately 288 min. The model was trained for 40 epochs, resulting in a total training time of 11,520 min, equivalent to roughly 192 h. Training was implemented using TensorFlow GPU version 2.7.4, with the following key parameters:

• Batch size: 2
• Learning rate: 1 × 10⁻³
• Optimizer: Nadam (β₁ = 0, β₂ = 0.99)
• Epsilon: 1 × 10⁻⁸

The computation was carried out on a custom-built workstation, comprising an NVIDIA GeForce RTX 3060 Ti (8 GB VRAM) GPU, an Intel i5-8400 CPU, and 32 GB of DDR4 RAM. All components were procured locally in Taipei and assembled by the author. After training, the PGGAN achieved highly efficient antenna synthesis, producing one complete antenna design approximately every three seconds. This rapid generation capability highlights the practicality of AI-based antenna design once the model has converged—contrasting the prolonged setup phase with a highly accelerated post-training design process.

Following model convergence, the trained PGGAN demonstrates exceptional generation efficiency, producing one complete antenna design in approximately 3 s. This efficiency underscores the scalability of the generative approach—while initial training is computationally intensive, the inference phase achieves near-real-time generation, far surpassing the throughput of traditional EM simulation workflows.

Comparative Analysis of Generative AI Antenna Design and Traditional Electromagnetic (EM) Wave Simulation is shown in

Table 4. Time and Cost Summary Details.

Aspect	Generative AI Antenna Design	Conventional EM Wave Simulation
Preparation / Setup Duration	Requires an extended training phase of about 192 h before the model is fully optimized.	Quick initialization—approximately 1 h to configure and begin simulation.
Computational Resources	Requires on powerful CPUs and multi-core CPUs for deep learning training and inference.	Operates on a high-end workstation optimized for numerical EM solvers.
Design Generation Speed (per sample)	Once trained, a new design can be produced in about 3 s.	Each simulation typically takes 30 min to 2 h, depending on complexity
Large-Scale Design Generation (10,000 samples)	Can complete in roughly 8.3 h, allowing for largescale exploration.	Practically impossible to achieve within a reasonable timeframe due to computational cost.
Iteration and Optimization Cycles	Extremely fast refinement once the Al model is established—ideal for rapid iteration.	Time-intensive, often requiring 5—100 h for multiple trial-and-error runs.

presents a detailed comparison of Generative AI–driven antenna design and conventional EM wave simulation, focusing on time efficiency, computational demand, and iterative flexibility. Generative AI methods require an extensive training phase of approximately 192 h before deployment, whereas traditional simulation systems can be initialized within about one hour. However, once trained, the AI model can produce new antenna designs in only three seconds, while each traditional EM simulation typically takes 30 min to 2 h depending on model complexity and mesh density. From a scalability perspective, the AI framework can generate 10,000 distinct designs in roughly 8.3 h, enabling broad design-space exploration. In contrast, achieving a similar scale using traditional solvers is computationally impractical. Although AI-based approaches demand high-performance GPUs and multi-core CPUs during training, traditional methods only rely on a single high-end workstation.

When it comes to iterative refinement and optimization, the AI model exhibits exceptionally short iteration times once the base model is established, allowing designers to test and adjust parameters almost instantly. Traditional EM simulation, however, remains time-intensive, with each iteration potentially requiring 5 to 100 h depending on the antenna’s complexity and boundary conditions. Overall, despite the higher initial setup cost and computational investment, Generative AI antenna design offers superior throughput, scalability, and agility for large-scale parametric exploration—making it particularly advantageous in early-stage design optimization compared to conventional EM simulation workflows.

In summary, the proposed pipeline (Figure 1) first augments a small number of HFSS-validated wideband seeds, then extracts Hough-transform-based edge features as auxiliary labels, and finally fine-tunes only the 512 × 512 stage of a pretrained dual-band WAG-PGGAN. This enables the generator to inherit the original 2.45/5.2-GHz behavior while learning additional 3.5-GHz wideband characteristics from a limited number of new samples.

2.5. Model Output and Simulation Validation Workflow

After training the WAG-PGGAN model, a set of promising antenna designs was randomly sampled from the generator. The generated images, each with a resolution of 512 × 512 RGB pixels (PNG format), were mapped to the actual physical antenna dimensions in a 1:1 scale. These images were then post-processed and converted into vector drawings compatible with HFSS, where each design was re-modeled to verify its S₁₁ performance and frequency band alignment.

As shown in Figure 9, representative multiband antenna structures were selected along with their corresponding HFSS simulations and experimental measurements. The simulated and measured S₁₁ curves confirm that the generated designs meet the target frequency response and bandwidth specifications, demonstrating the model’s capability to produce realistic, physically valid, and application-ready multiband antenna geometries.

To enhance the structural representation prior to adversarial training, all antenna patterns were transformed using the Hough Transform, which converts the image data into feature points in the parameter space. This transformation strengthens the correlation between the antenna’s radiation frequency and its apparent structural length, effectively encoding geometric–frequency relationships within the training data. The resulting feature points act as guidance labels, directing the model toward generating antenna structures that satisfy specified physical characteristics. This process closely resembles conditional or label-guided learning, in which the model is trained under explicit constraints that steer its output distribution toward physically meaningful targets.

During model optimization, the WGAN-GP (Wasserstein GAN with Gradient Penalty) framework played a crucial role in ensuring training stability and maintaining the physical realism of the learned geometries. In conventional GANs, the discriminator (or critic) often suffers from unstable gradients, leading to mode collapse or gradient explosion/vanishing, which prevents the generator from learning continuous and valid structural relationships. The gradient penalty term in WGAN-GP introduces a smoothness constraint on the discriminator’s gradients, enforcing their norms to remain close to unity. This regularization maintains a well-defined and stable Wasserstein distance throughout the optimization process.

In practice, this approach enables balanced adversarial training, allowing the generator to produce designs that are both electromagnetically consistent and geometrically coherent. The inclusion of the gradient penalty effectively prevents gradient collapse, stabilizes learning dynamics, and empowers the model to discover valid multi-frequency conductive patterns, which are essential for achieving high-performance, real-world antenna implementations.

3. Results

Measurements were performed using an Albatross (Germany) platform combined with the fully automated R&S TS8991 test system (Figure 10). S₁₁ was measured with an R&S ZND vector network analyzer. The results show excellent agreement with the simulations.

Although S-parameters were measured for eight generated antennas to demonstrate model effectiveness—and all samples met the expected 2D radiation patterns and efficiency—only the first three antennas were selected for detailed comparison of simulated and measured 2D patterns and efficiency. Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18 and Figure 19 present the gain data and 2D radiation patterns of representative generated antennas, together with brief descriptions and the measured antenna efficiencies.

The simulated and measured low-band (Lo-band) radiation patterns of the multiband PIFA-like antenna (Antenna 1) are summarized below.

Figure 11 presents the Lo-band patterns at 2.68 GHz for three principal cuts—ϕ = 0°, ϕ = 90°, and θ = 90°—comparing simulations with measurements.

• ϕ = 0° Plane:

The pattern is nearly omnidirectional. The measured curve (orange) is smoother than the simulated one, maintaining a gain of approximately −5 to −7 dB across all azimuths. The simulation shows slightly stronger lobes near 60° and 240°, indicating marginally higher directivity. Both results confirm broad coverage with stable gain variation.

• ϕ = 90° Plane:

The measured pattern exhibits moderate variation, with peaks near −4 dB and minima around −15 to −20 dB. The simulated pattern is more directive, with lobes peaking near 45° and 225°. This suggests some mismatch in side-lobe behavior, though the main lobes are reasonably aligned.

• θ = 90° Plane:

This horizontal cut shows a distinctly directional pattern. The measured gain peaks near 45° and 225°, with a null around 135°. The simulation follows the same trend with slightly higher peak levels. Overall, the measured pattern confirms strong directivity in the θ = 90° plane.

These patterns indicate omnidirectional behavior in some planes and directional gain in others, making the antenna suitable for mixed-coverage applications. The measured patterns exhibit a consistent directional gain distribution. The measured radiation efficiency at 2.68 GHz is 73.62%, confirming satisfactory Lo-band performance.

The simulated and measured Mid-band radiation patterns of the multiband PIFA-like antenna (Antenna 1) are summarized below.

Figure 12 shows the mid-band patterns of the PIFA-like antenna (Antenna 1) at 3.56 GHz for three principal cuts—ϕ = 0°, ϕ = 90°, and θ = 90°—with simulations and measurements overlaid.

• ϕ = 0° Plane:

The measured pattern (orange, solid) is smooth and largely omnidirectional, with gains between 0 and −7 dB. The simulated pattern (blue, dashed) has a similar shape but slightly higher levels in some directions, notably near 60° and 240°. The measured result shows a consistent directional-gain distribution.

• ϕ = 90° Plane:

The measured gain varies moderately, with a main lobe around 0–30° and reduced levels toward 180–240°. The simulation shows a broader lobe but follows the same trend, indicating reasonable coverage in both vertical and inclined directions.

• θ = 90° Plane:

The measured pattern exhibits clear directivity with nulls near 135° and strong lobes at 0° and 225°. The simulated pattern aligns well in shape, confirming the directional characteristics and good symmetry in this plane.

These patterns show that Antenna 1 provides near-omnidirectional coverage in some planes and directional behavior in others. Because it reflects practical implementation, the measured pattern is used for performance evaluation. The measured radiation efficiency at 3.56 GHz is 66.68%, confirming satisfactory mid-band performance.

The simulated and measured high-band (Hi-band) radiation patterns of the multiband PIFA-like antenna (Antenna 1) are summarized below.

Figure 13 shows the high-band patterns of the PIFA-like antenna (Antenna 1) at 5.83 GHz for three principal cuts—ϕ = 0°, ϕ = 90°, and θ = 90°—with simulations and measurements overlaid.

• ϕ = 0° Plane:

The measured pattern (orange) exhibits clear bidirectional behavior, with nulls near 270° and strong lobes toward 60° and 240°. The simulated pattern (blue, dashed) is similar but slightly underestimates backward radiation. Both confirm strong directional gain in the X–Z plane.

• ϕ = 90° Plane:

The measured pattern is quasi-omnidirectional, with gains between 0 and −15 dB. The simulation shows slightly deeper nulls at certain angles, but the overall trend is consistent, indicating adequate vertical coverage.

• θ = 90° Plane:

The horizontal cut shows directional gain, with lobes near 60° and 240° and a null around 150°. The simulation follows a similar lobe structure with some magnitude differences. The measured pattern demonstrates reliable horizontal-plane directivity.

These patterns confirm that Antenna 1 provides directive coverage at high frequencies, especially in the horizontal and diagonal planes; the measured pattern is used as the primary basis for evaluation. The measured radiation efficiency at 5.83 GHz is 69.02%, indicating satisfactory high-band performance.

The simulated and measured low-band (Lo-band) radiation patterns of the multiband PIFA-like antenna (Antenna 2) are summarized below.

Figure 14 shows the Lo-band patterns of the PIFA-like antenna (Antenna 2) at 3.22 GHz for three principal cuts—ϕ = 0°, ϕ = 90°, and θ = 90°—with simulations and measurements overlaid.

• ϕ = 0° Plane:

The measured pattern (orange) exhibits a figure-8 bidirectional distribution with main lobes near 60° and 240° and a null near 180°. The simulated pattern (blue, dashed) broadly matches the shape but shows slightly shallower nulls. Both indicate directivity in the X–Z plane.

• ϕ = 90° Plane:

The measured pattern shows irregular lobes and nulls with gains from 0 to −30 dB. The simulation is smoother with fewer fluctuations, though the overall form is similar, suggesting asymmetric behavior in the vertical plane.

• θ = 90° Plane:

In the horizontal plane, the measured pattern shows an elliptical directional distribution with gains from 0 to −20 dB. The simulation agrees in shape but exhibits a slightly narrower beamwidth. The measurements confirm a directional yet stable pattern in this plane.

At 3.22 GHz, Antenna 2 shows directional and quasi-omnidirectional behavior across different planes. The measured pattern is used as the reference for performance evaluation. The measured radiation efficiency is 70.15%, indicating satisfactory low-band performance.

The simulated and measured mid-band radiation patterns of the multiband PIFA-like antenna (Antenna 2) are summarized below.

Figure 15 shows the radiation patterns of the Mid-band PIFA-like antenna (Antenna 2) at 4.35 GHz, including three principal cuts: ϕ = 0°, ϕ = 90°, and θ = 90°, comparing both simulated and measured results.

• ϕ = 0° Plane:

The measured radiation pattern (orange line) shows a symmetric bidirectional distribution, with strong main lobes at approximately 60° and 240°, and a deep null at 180°. The simulated pattern (blue dashed line) exhibits similar shape but slightly smoother transitions. The measured pattern confirms clear directional gain in the X–Z plane.

• ϕ = 90° Plane:

The measured pattern is quasi-omnidirectional, with gain ranging from 0 dB to –20 dB across angles. The simulated result maintains a similar overall trend but with less angular fluctuation. This indicates good vertical plane coverage at this frequency.

• θ = 90° Plane:

In the horizontal plane, the measured pattern shows directional characteristics, with peaks at 60° and 240°, and a clear null at 150°. The simulated shape aligns well, with slightly narrower lobes. The measured pattern indicates effective horizontal directionality.

The radiation patterns at 4.35 GHz confirm that Antenna 2 exhibits stable directional and omnidirectional features across different planes. The measured radiation pattern is taken as the final performance reference. The measured radiation efficiency at 4.35 GHz is 69.66%, confirming satisfactory radiation performance.

The simulated and measured radiation patterns of the Hi-band for the multi-band PIFA-like antenna (Antenna 2) in Figure 16 are detailed as follows:

Figure 16 shows the radiation patterns of the Hi-band PIFA-like antenna (Antenna 2) at 5.56 GHz, including three principal cuts: ϕ = 0°, ϕ = 90°, and θ = 90°, comparing both simulated and measured results.

• ϕ = 0° Plane:

The measured radiation pattern (orange line) exhibits a narrow, directional beam with two main lobes near 45° and 225°, and a deep null around 180°. The simulated pattern (blue dashed line) follows a similar directional trend but with smoother transitions. This indicates directional radiation characteristics in the X–Z plane.

• ϕ = 90° Plane:

The measured pattern reveals asymmetrical gain variation across the Y–Z plane, with We have checked and revised all.

Multiple lobes and notches. The simulated pattern is relatively smooth, lacking the finer variations captured in measurement. Despite the difference, the directional trend remains comparable.

• θ = 90° Plane:

In the horizontal plane, the measured pattern exhibits a complex lobe structure with peak gain around 30° and 210°, and nulls at multiple locations. The simulated result provides a simplified version of this behavior, missing some side-lobe details. The measured pattern better reflects the antenna’s actual directional characteristics.

The radiation patterns at 5.56 GHz confirm that Antenna 2 maintains complex directional behavior with angular variation across all principal planes. The measured radiation pattern is adopted as the primary reference for evaluation. The measured radiation efficiency at 5.56 GHz is 86.9%, confirming satisfactory radiation performance.

The simulated and measured radiation patterns of the Lo-band for the multi-band PIFA-like antenna (Antenna 3) in Figure 17 are detailed as follows:

Figure 17 presents the simulated and measured radiation patterns of the Lo-band PIFA-like antenna (Antenna 3) at 1.86 GHz, including three principal planes: ϕ = 0°, ϕ = 90°, and θ = 90°.

• ϕ = 0° Plane:

The radiation pattern exhibits a generally omnidirectional shape. The measured pattern (orange solid line) shows moderate ripples, with gain values fluctuating between –5 dB and –20 dB. The simulated curve (blue dashed line) is smoother with slightly higher gains overall, especially in the 45–135° and 225–315° directions. Both patterns indicate reasonable radiation coverage.

• ϕ = 90° Plane:

In this plane, the measured gain pattern reveals a more irregular shape with notches around 120° and 270°, while the simulated result retains a more symmetrical profile. Although local deviations exist, the overall shapes follow a similar trend, with both demonstrating consistent coverage across azimuthal angles.

• θ = 90° Plane:

The horizontal cut displays distinct lobes and nulls in the measured result, with peaks around 45° and 270° and a deep notch near 135°. The simulated curve, while smoother, captures the general directional tendency. This suggests that the antenna maintains a directional pattern with some measured irregularities in this plane.

The radiation patterns at 1.86 GHz confirm that Antenna 3 maintains complex directional behavior with angular variation across all principal planes. The measured radiation pattern is adopted as the primary reference for evaluation. The measured radiation efficiency at 1.86 GHz is 58.48%, confirming satisfactory radiation performance.

The simulated and measured radiation patterns of the Mid-band for the multi-band PIFA-like antenna (Antenna 3) in Figure 18 are detailed as follows:

Figure 18 presents the simulated and measured radiation patterns of the Mid-band PIFA-like antenna (Antenna 3) at 3.51 GHz, including three principal planes: ϕ = 0°, ϕ = 90°, and θ = 90°

• ϕ = 0° Plane:

The measured and simulated patterns both exhibit an omnidirectional shape with a consistent gain distribution. The measured pattern (orange solid line) closely follows the simulated one (blue dashed line), with gain values ranging between –5 dB and –20 dB. The smooth and symmetrical pattern indicates good azimuthal coverage and stable performance in this plane.

• ϕ = 90° Plane:

In this plane, the radiation pattern shows mild asymmetry in the measured result, particularly around 120–150°, where a small notch appears. Nonetheless, the overall shape remains stable and correlates well with the simulated result. This confirms adequate directional consistency across azimuthal angles.

• θ = 90° Plane:

The horizontal plane reveals a more directional behavior with broader lobes and consistent gain roll-off in both the measured and simulated curves. Minor deviations are observed around 150° and 300°, yet the directional trend is preserved.

The radiation patterns at 3.51 GHz confirm that Antenna 3 maintains complex directional behavior with angular variation across all principal planes. The measured radiation pattern is adopted as the primary reference for evaluation. The measured radiation efficiency at 3.51 GHz is 69.18%, confirming satisfactory radiation performance.

The simulated and measured radiation patterns of the Hi-band for the multi-band PIFA-like antenna (Antenna 3) in Figure 19 are detailed as follows:

Figure 19 presents the simulated and measured radiation patterns of the Hi-band PIFA-like antenna (Antenna 3) at 4.26 GHz, including three principal planes: ϕ = 0°, ϕ = 90°, and θ = 90°.

• ϕ = 0° Plane:

The measured pattern (orange solid line) shows a mostly omnidirectional shape, with some notches appearing around 60° and 270°. The simulated curve (blue dashed line) is slightly more directional, especially near 60° and 150°. Overall, both patterns reflect adequate symmetry and broad angular coverage in this vertical plane.

• ϕ = 90° Plane:

In this plane, the measured pattern exhibits good circularity with moderate ripples. The simulated result remains smooth and symmetrical, with slightly higher gains across all directions. The overall agreement is strong, indicating robust radiation consistency along the YZ plane.

• θ = 90° Plane:

This horizontal cut reveals more pronounced lobes in the measured pattern, with peaks near 60° and 240° and nulls around 120° and 270°. The simulated curve shares the same general trends but appears smoother and less fluctuating. Both results confirm that the antenna maintains directional characteristics in this plane.

The radiation patterns at 4.26 GHz confirm that Antenna 3 maintains complex directional behavior with angular variation across all principal planes. The measured radiation pattern is adopted as the primary reference for evaluation. The measured radiation efficiency at 4.26 GHz is 52.24%, confirming satisfactory radiation performance.

The model architecture was developed upon a hybrid foundation combining 2.45 GHz and 5.2 GHz narrowband PIFA-like antennas with a 3.5 GHz-centered wideband structure, forming a balanced spectral representation across both low and high frequency regimes. Each training sample in this dataset inherently contained high-quality S-parameter responses and radiation efficiency profiles verified through HFSS full-wave simulations, ensuring that the learning process was guided by physically valid electromagnetic behaviors rather than purely synthetic data. During preprocessing, these simulated antenna images were transformed into vectorized feature matrices, enabling the generator–discriminator (G/D) pair to learn spatial–spectral correspondences through adversarial optimization.

Within this representation, the frequency–dimension relationship and geometric scaling factors were encoded as implicit weight constraints, ensuring that the model developed sensitivity to both frequency-dependent geometry and size-normalized radiation patterns. As a result, the trained WAG-PGGAN encapsulates a latent prior over frequency, geometry, and efficiency, allowing it to generate entirely new antenna designs that naturally exhibit resonant behavior within the 2.45 GHz, 3.5 GHz, and 5.2 GHz bands.

This demonstrates that the network not only memorizes existing forms but also generalizes the learned electromagnetic relationships, producing physically consistent multiband antennas guided by embedded frequency-domain knowledge.

4. Discussion

The proposed WAG-PGGAN fine-tuning approach for multiband antenna design advances AI-driven antenna synthesis. The results confirm that the model generates high-fidelity multiband structures while preserving previously learned dual-band performance. The following summarizes key findings, discusses their implications, and outlines directions for future research.

4.1. Interpretation of Results

Integrating three 3.5-GHz wideband antennas into the dual-band dataset—together with Hough-based edge enhancement—extended the model to multiband and wideband design. The generated antennas exhibited consistent S₁₁ agreement between simulation and measurement, with resonances closely aligned to the target bands (2.45, 3.5, and 5.2 GHz). Radiation patterns further confirmed the ability to produce both directional and quasi-omnidirectional designs suitable for diverse wireless applications.

The Hough-derived, edge-aware regularization was critical for preserving structural fidelity and electromagnetic performance. Consistent with prior work on the importance of geometry, this result advances the field by embedding geometric cues within an adversarial framework, showing that auxiliary structural guidance enhances the physical interpretability of AI-generated designs.

4.2. Comparison with Previous Studies

Traditional antenna design depends on iterative simulations and expert heuristics—processes that are time-consuming and limit design-space exploration. Earlier GAN-based methods showed promise but often suffered from instability and limited high-resolution fidelity. The WAG-PGGAN framework addresses these issues by combining progressive growth, a Wasserstein objective, and edge-aware regularization, yielding superior performance for multiband applications. Building on PGGAN (Karras et al. [8]), it incorporates enhancements tailored to electromagnetic structures.

Compared with other AI-driven approaches, the proposed method improves generalization by fine-tuning a pretrained model with a small set of new samples—an advantage when data acquisition is costly or slow, as in high-frequency antenna design.

4.3. Broader Implications

These results position fine-tuning-based adversarial learning as a scalable, efficient paradigm for intelligent antenna design. Leveraging pretrained models with targeted data enables rapid adaptation to new frequency requirements or constraints and extends naturally to EM structures such as filters and metamaterials, where geometry governs performance.

The effectiveness of edge-aware regularization also motivates embedding additional physics-based constraints (e.g., current distribution, near-field effects) into generative models, further closing the gap between AI-generated designs and real-world behavior.

4.4. Differences Between Simulated and Measured Data

After validating both simulations and measurements, the main discrepancy sources are:

(1)

Geometric/material imperfections. Manual fabrication introduces copper-foil deformation, wrinkles, and edge roughness that perturb current paths. Small variations in trace width/shape alter effective inductance and capacitance, shifting resonances. Surface oxidation or thickness nonuniformity increases ohmic loss, slightly degrading the measured return loss relative to the ideal HFSS model.

(2)

Lack of a controlled substrate. The antennas use copper foil on paper/tape without a defined dielectric (e.g., FR-4), making the effective permittivity uncertain. Humidity or pressure changes can vary the air gap or adhesive layer, causing frequency shifts and bandwidth changes not captured in simulation.

(3)

Feed and solder effects. Minor feed-point misalignment (0.5–1 mm) produces noticeable impedance variation at GHz frequencies. Solder joints add parasitic inductance and contact resistance; the solder-blob thickness perturbs local current distribution near the feed.

(4)

Simplified HFSS modeling. Simulations assume perfect conductors, uniform thickness, and fixed air–dielectric properties. In practice, copper surface conditions, glue layers, and paper backing introduce additional losses and boundary irregularities, altering the actual EM response.

In summary, divergences between HFSS and measured S11 primarily arise from fabrication tolerances, feed-connection nonuniformity, and environmental coupling. Despite these factors, the resonance trends agree, confirming that WAG-PGGAN-generated antennas are physically realizable and exhibit reliable multiband behavior in practice.

4.5. Limitations and Future Directions

While the results are promising, several limitations and future directions merit attention:

(1)

Dataset diversity—The model is trained on a limited set of base antennas. Expanding coverage to more geometries and bands would improve generalization.

(2)

Physical constraints—Embedding additional EM constraints (e.g., impedance matching, radiation efficiency) into the loss could enhance practical viability.

(3)

Real-time adaptation—Enabling on-the-fly fine-tuning for new specifications would accelerate rapid prototyping.

(4)

Multi-objective optimization—Extending the framework to jointly optimize bandwidth, gain, size, etc., would better reflect real-world trade-offs.

(5)

Experimental validation—Beyond lab measurements, system-level tests (e.g., integration into mobile devices) are needed to confirm robustness in deployment.

In conclusion, fine-tuning with edge-aware regularization proves effective for AI-driven antenna design, enabling more adaptive and efficient methodologies for future wireless systems. Further work should broaden the model’s capabilities and address current limitations to realize its full potential.

4.6. Contributions

This study provides several key contributions to the field of intelligent multiband antenna design:

(1)

Data-efficient multiband transfer learning. With only 836 newly added

3.5-GHz wideband samples (≈17% of the full dataset), the proposed fine-tuning strategy successfully extends a pretrained dual-band generator to synthesize physically consistent multiband antennas, without retraining the model from scratch.

(2)

Physics-aware edge regularization for 512 × 512 geometric fidelity.

A Hough-transform-driven edge-alignment loss is introduced to preserve conductor boundaries, path continuity, and geometry–frequency coupling. This mechanism stabilizes high-resolution training and suppresses tearing or jagged edge artifacts in the generated structures.

(3)

Wasserstein Auxiliary-Guided PGGAN for high-dimensional EM structure learning. By combining progressive growing, WGAN-GP optimization, and edge-aware supervision, the proposed WAG-PGGAN achieves enhanced fidelity, training stability, and electromagnetic consistency.

(4)

Fabrication-level experimental validation.

Eight fabricated prototypes covering 1.86–5.83 GHz all achieve $\mid S_{11}\mid <-10 \mathrm{dB}$, with measured efficiencies ranging from 52.2% to 86.9% and radiation patterns matching HFSS simulations. These results confirm that the generated antenna designs are physically realizable and functional.

(5)

High throughput and practical scalability.

After a one-time training cost (~192 h), the model generates a complete 512 × 512 multiband antenna design in approximately 3 s on an RTX 3060 Ti, demonstrating significantly improved design throughput over traditional EM-only workflows.

(6)

A generalizable framework for EM component synthesis.

The proposed pipeline—data-efficient fine-tuning, physics-guided regularization, and progressive high-resolution generation—can be extended to filters, metasurfaces, and other EM structures, providing a scalable methodology for physics-aware generative design.

5. Conclusions

This paper presents a comprehensive framework for intelligent multiband antenna design that integrates advanced deep learning with electromagnetic engineering principles. The proposed WAG-PGGAN (Wasserstein Auxiliary-Guided Progressive Growing GAN), combined with a targeted fine-tuning strategy and geometric feature enhancement, advances AI-driven antenna synthesis. Key contributions and findings span several critical dimensions.

First, the study establishes an efficient method for extending pretrained antenna generators. By adding only 836 wideband samples centered at 3.5 GHz (a 1:5 ratio relative to the original dataset), the model learns to produce structures that retain strong dual-band performance while acquiring new wideband characteristics. This demonstrates that high-quality multiband designs can be achieved without massive new datasets, substantially reducing computational and time costs. The fine-tuning process preserves prior knowledge at 2.45 and 5.2 GHz while effectively incorporating the 3.5 GHz band, highlighting the adaptability of the framework.

A central innovation of this work is integrating Hough-transform edge enhancement into the high-resolution generation stage. This geometric feature-extraction step supplies crucial structural guidance to the generator, improving its ability to capture relationships between physical antenna geometries and their electromagnetic responses. The edge-aware loss proved effective during fine-tuning, preserving structural fidelity so that generated designs retain physically meaningful conductive paths and resonant features. In doing so, the method addresses a core challenge in AI-driven antenna design: balancing creative exploration with physical realizability.

Experimental validation across multiple metrics is compelling. All tested prototypes achieved excellent impedance matching (|S₁₁| < −10 dB) at their target frequencies, with measurements closely tracking simulations. Radiation patterns exhibited consistent directional characteristics across bands, and measured efficiencies ranged approximately from 52% to 87%. These results validate the WAG-PGGAN framework and show that AI-generated designs, when fine-tuned, can meet or exceed the performance of traditionally engineered antennas. The close simulation–measurement agreement across eight prototypes provides strong evidence of the approach’s reliability and robustness.

From a broader perspective, this work contributes several advances to AI-assisted electromagnetic design. The success of fine-tuning indicates that pretrained models can serve as adaptable foundations for new specifications. The edge-enhancement strategy provides a template for embedding domain-specific physics into generative models and is applicable beyond antennas to other EM components. Moreover, demonstrating functional multiband antennas from image-based synthesis marks a step toward fully automated RF component design.

Looking ahead, the framework can be extended by integrating additional performance constraints—e.g., gain, bandwidth, and pattern control—directly into generation. Real-time optimization, in which the model adapts dynamically to new specifications, is another promising direction. Broadening the training corpus to include more antenna types and frequency ranges should further improve generalization. Finally, applying similar methods to filters, metamaterials, and other EM components could open new avenues in RF engineering.

In conclusion, this work bridges machine learning and practical antenna design through the integration of progressive GANs, geometric feature enhancement, and targeted fine-tuning. The results show that AI-driven methods can match—and potentially surpass—traditional approaches in both efficiency and performance. As wireless systems evolve toward more complex multiband and wideband requirements, methodologies such as ours will become increasingly valuable to engineers. This study lays essential groundwork for intelligent electromagnetic design, where AI and human expertise jointly advance RF technology. The fusion of computational creativity with physical insight points to a new paradigm in high-frequency component design—more adaptive, efficient, and capable of meeting the growing demands of modern wireless systems.