Introduction

The growing demand for high-speed multimedia data transmission has become increasingly critical in today’s digital landscape1,2. To address the need for rapid data transfer and low latency, numerous countries have deployed fifth-generation (5G) communication systems3,4,5. As a leading future communication technology, 5G is expected to surpass the limitations of existing mobile and local area network technologies6. The Federal Communications Commission (FCC) has allocated specific frequency bands for 5G applications, including 3.5 GHz (sub-6 GHz range) and 24–30 GHz, 37 GHz, 39 GHz, and 64–71 GHz for the mm-wave range7,8. Among these, the 3.5 GHz and 24–30 GHz bands are among the most widely adopted 5G frequencies globally, including in countries like China9. To leverage the broader bandwidth available at higher frequencies, cellular systems are transitioning to mm-wave bands, which enable increased data rates. However, while mm-wave antennas offer faster data transmission compared to sub-6 GHz antennas, they also face significant challenges such as propagation losses10,11,12,13. In contrast, mm-wave technology is anticipated to improve data capacity and connection throughput within short-range coverage areas, despite challenges such as signal attenuation14. While mm-wave bands offer substantial capacity and data speeds exceeding 2 Gbps, the lower frequency bands (sub-6 GHz) ensure robust 5G coverage over wider areas, and the medium band combines aspects of both. Achieving ultra-high data rates necessitates leveraging the 5G mm-wave spectrum15. However, the practical implementation of mm-wave mobile communication requires resolving critical technical hurdles. Notably, mm-waves suffer from atmospheric attenuation, limiting their propagation distance. In comparison, sub-6 GHz frequencies can cover longer distances more efficiently, making them a cost-effective choice for long-range, high-data-rate systems16. Consequently, sub-6 GHz technologies are likely to transition to 5G even before mm-wave solutions mature17. Modern wireless systems demand the integration of multiple applications into a single device. This can be achieved through either an array of dedicated antennas or a single multifunctional antenna18,19,20. However, deploying multiple antennas in a single system is impractical due to spatial constraints, elevated costs, inter-antenna interference, and hardware complexity. A viable alternative lies in reconfigurable antennas21, which are pivotal in contemporary wireless communication for their ability to dynamically adjust polarization22,23,24, steer beams25,26,27, and switch frequencies28,29,30. Reconfiguration can be accomplished through electrical, mechanical, optical, material-based, or structural modifications31. Recent advancements in 5G antenna design have led to the development of several frequency-reconfigurable antennas. For instance32, proposed a pair of dipole antennas integrated with an artificial magnetic conductor (AMC) surface, achieving operation in the 3.3–3.6 GHz and 4.8–5.0 GHz bands for sub-6 GHz 5G applications. However, the design’s bulky structure and inability to support mm-wave frequencies limited its practicality. In33, a microfluidic-based reconfigurable antenna targeting the 3.5 GHz 5G band utilized piezoelectric pumps for broadband tuning, though its complexity hinders integration into portable devices. Similarly34, introduced a differentially fed reconfigurable antenna for WLAN and sub-6 GHz 5G, but its multilayer architecture and reliance on multiple switches made it unsuitable for compact handheld systems. A low-profile slotted T-shaped antenna in35addressed mm-wave bands (26.5 GHz and 40 GHz) using switch-controlled slots, yet its narrow focus excluded sub-6 GHz compatibility. Meanwhile36, demonstrated a varactor diode-based antenna with four reconfigurable states (0.7, 2.4, 3.5, and 5.5 GHz), but its low gain and restriction to sub-6 GHz frequencies rendered it inadequate for robust 5G performance. Collectively, existing designs remain constrained to single-antenna architectures, failing to seamlessly integrate both sub-6 GHz and mm-wave bands, a critical requirement for comprehensive 5G coverage. Recent research has explored frequency-reconfigurable antennas for 5G and ultra-wideband (UWB) applications. For instance37, introduces a CPW-fed sub-6 GHz frequency-reconfigurable antenna using a single PIN diode to switch between 5G and UWB modes. Similarly, a compact CPW-fed design in38 utilizes two PIN diodes to enable dual- and tri-band modes.

Concurrently, Machine Learning (ML) has emerged as a powerful tool for accelerating antenna design39. Recent work has begun to apply ML to antenna miniaturization and reconfiguration, but with notable limitations. For example, the design in40 achieved ML-driven size reduction. Moreover, the antenna in41was an ML-optimized compact, frequency-reconfigurable design. In the context of LoRa (Long Range) communications42, reported an ML-optimized wearable antenna for LoRa localization. Beyond these specific cases, ML is being applied broadly across antenna engineering. For instance43, used ML to optimize a double-T monopole antenna and achieved a very low prediction error (2.90%) relative to full-wave HFSS simulations. In44 utilize ML together with data augmentation to improve the performance of circularly-polarized base-station antennas. In45, an efficient k-nearest neighbors (KNN) based method was introduced for antenna optimization, yielding significant reductions in computational time. Likewise46, employed ML to optimize a microstrip-line–fed dielectric resonator antenna covering multiple bands (approximately 1.59–2.26 GHz, 3.1–3.87 GHz, and 5.25–6.91 GHz). Several recent review articles47,48 have emphasized the feasibility and advantages of applying ML and deep learning to antenna design, particularly noting reduced computational cost. By utilizing large datasets and advanced ML algorithms, antenna designs can be optimized to meet multiple design criteria, constraints, and performance metrics simultaneously. While previous works have applied ML to antenna design, its application to compact, wearable, dual-band frequency-reconfigurable antennas covering both sub-6 GHz and mm-wave spectra is novel.

Research gap and contribution

As wireless devices increasingly demand support for diverse services and standards, designing antennas that combine high data rates, efficient spectrum use, and multi-standard compatibility remains a challenge. Frequency-reconfigurable antennas offer a promising solution by enabling high throughput and multi-band coverage in a single structure. However, most prior studies overlook critical user safety metrics, such as specific absorption rate (SAR) and power density (PD), particularly at 5G frequencies. This work bridges that gap.

The key contributions of this study are:

  • The development of a compact, flexible, frequency-reconfigurable antenna that uniquely integrates both sub-6 GHz (3.5 GHz) and mm-wave (28 GHz) bands with an 8:1 ratio, a feature rarely achieved in wearable form factors.

  • The implementation of a supervised ML framework to predict and optimize antenna performance, which reduced the computational time for design iteration by 80% compared to traditional parametric sweeps in CST Microwave Studio (MWS).

  • An evaluation, including bending tests, on-body performance analysis, and SAR compliance verification with international safety standards, aspects often overlooked in prior ML-antenna works.

Antenna design

This section outlines the fundamental geometry, design principles, and switching methodologies of the proposed wearable frequency-reconfigurable patch antenna. To enable frequency reconfiguration, the antenna is simulated within the schematic design environment of CST MWS, utilizing lumped elements and Touchstone 2-port S-parameters (s2p files). However, during physical fabrication and experimental measurements, a practical PIN diode is integrated to realize the reconfigurable functionality.

Proposed antenna structure

The design of an antenna capable of resonating at multiple frequencies begins with optimizing a single-frequency structure before applying reconfiguration techniques. Initially, the antenna is parametrically analyzed and optimized to resonate at 28 GHz, though this baseline design exhibits insufficient impedance bandwidth. To address this limitation, two slits are integrated into the circular patch, significantly improving bandwidth. Subsequently, a rectangular patch is connected to the top of the modified circular structure to enable dual-band operation. An H-shaped slot is etched into the rectangular patch, allowing the antenna to resonate at two optimized frequencies: 3.50 GHz and 28 GHz. A defected ground structure (DGS) is then implemented on the partial ground plane to enhance bandwidth, gain, and isolation while minimizing mutual coupling. The proposed wearable frequency-reconfigurable patch antenna, as shown in Fig. 1 which operates at 3.50 GHz (sub-6 GHz band) and 28 GHz (mm-wave band). It features compact dimensions of 14 × 27.8 × 0.508 mm3 and is fabricated on a Rogers RT/duroid 5880 substrate thickness of 0.508 mm, dielectric constant of 2.2, loss tangent of 0.0009. This substrate choice mitigates mm-wave losses and aligns with practical fabrication constraints.

Fig. 1
Fig. 1
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Proposed antenna geometry: (a) Top view (b) Back view. The dimensions of the antennas are Ls = 27.8 mm, Ws = 14 mm, Wp = 6.1 mm, Lp = 6.8 mm, Lg = 5.7 mm, Wb = 1.4 mm, Lb = 1.4 mm, Wf = 2.71 mm, Lf = 4.28 mm, Ra = 0.96 mm Rb = 3.2 mm, Wa = 1 mm, La = 4 mm.

Reconfigurable antenna design theory

At the early stage of the wearable reconfigurable antenna implementation, a copper bridge with a dimension of 0.5 × 1 mm2 was placed into the patch within the slot, as can be seen in Fig. 2. A copper bridge shall act as an ideal switch to represent ON state of a PIN diode, as shown in Fig. 2a. Conversely, Fig. 2b illustrates the OFF state by removing the copper bridge. A simulation was performed using CST MWS software to investigate the dual-band antenna linear characteristics. Figure 3 shows the simulated reflection coefficient (S11) of the dual-band antenna without and with an ideal switch (a copper bridge) to represent the ON and OFF states. As the copper bridge was connected to represent the ON state, the antenna operates at a dual-band frequency of 3.5 GHz and 28 GHz. At 3.5 GHz, which exceeds the − 10-dB line within the frequency range of 3.019 GHz to 4.089 GHz, and the upper resonant frequency at 28 GHz is between 24.975 GHz and 42.382 GHz. On the other hand, when the copper bridge was removed in the OFF state, the antenna operates at a single frequency of 28 GHz, which exceeded the − 10-dB line within the frequency range of 21.579 GHz to 42.031 GHz. This is consistent with the theory of electrical current length, which determines where each resonant frequency is located. The lower the resonant frequency, the longer the electrical current path takes to complete the loop on an antenna’s radiating structure. The situation is the same when a copper bridge is present on the radiating patch. In contrast, the copper bridge permits the current to pass through it and shortens the electrical current path. The proposed antenna’s simulation results are further summarized in Table 1.

Fig. 2
Fig. 2
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Proposed Dual-band antenna: (a) with a copper bridge to represent the ON state (b) without a copper bridge to represent the OFF state.

Fig. 3
Fig. 3
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Simulated S11 of the dual-band antenna with a copper bridge (ON state) and without a copper bridge (OFF state).

Table 1 Proposed antenna performance.
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PIN diode switching technique

The PIN diode is selected for its superior performance over alternative active switches49. Specifically, the SMP1321 PIN diode from Skyworks Technologies, chosen based on availability, offers a low junction capacitance (0.18 pF). The diode’s behavior in both ON/OFF states, including parasitic package effects is modeled using Touchstone 2-port S-parameters (*.s2p files). Figure 4a,b depict the CST MWS circuit schematic integrating these S-parameter files, which correspond to the commercially available SMP1321 diode. The biasing circuit as shown in Fig. 4c employs an RF choke (30 nH) and a DC-blocking capacitor (1500 pF). The RF choke isolates the DC bias current from the RF signal path, while the capacitor prevents DC interference with RF signals. These components are optimized to match the RF line impedance, ensuring efficient PIN diode operation. The substrate selection and biasing circuit were made with practical wearable use in mind. The Rogers RT/duroid 5880 substrate was chosen for its excellent high-frequency properties, specifically its low loss tangent (0.0009), which is critical for maintaining high radiation efficiency at mm-wave frequencies (28 GHz), combined with its mechanical flexibility for on-body conformity. For the PIN diode biasing, the SMP1321 diode was selected for its low junction capacitance and, importantly, its low DC bias requirement. This low current consumption is compatible with small, lightweight batteries typically used in wearable devices, ensuring practical operational longevity without compromising performance50.

Fig. 4
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Schematic view: (a) PIN diode ON state (b) PIN diode OFF state (c) detailed biasing circuit.

Antenna optimization using machine learning

The rising demands for high-performance and multifunctional capabilities in modern antenna systems have spurred the development of increasingly intricate designs51. To satisfy the specifications of emerging applications such as IoT networks, medical imaging, biomedical telemetry, disaster response systems, and healthcare monitoring, these antennas require precise optimization. This drive toward compact, adaptable designs has yielded architectures capable of multi-band operation, integrated beam steering, and specialized components like impedance transformers, radiation slots, and engineered ground planes52. However, the growing demands of these systems introduce substantial optimization challenges. Conventional design methods often depend on full-wave electromagnetic (EM) simulations to fine-tune geometries, a process that is computationally demanding and time-intensive. As antenna structures evolve into more complex configurations, traditional algorithms struggle to balance performance goals with computational efficiency, often incurring prohibitive resource costs53. The integration of ML into the antenna design process represents a significant advancement over traditional, simulation-heavy methods. While conventional full-wave electromagnetic solvers like CST MWS are accurate, they are computationally expensive and time-consuming for exploring vast design spaces. ML framework, once trained on an initial dataset, enables near-instantaneous performance prediction for new geometric parameters. This approach reduced the optimization time for the final dual-band design by approximately 80% compared to a traditional parametric sweep, allowing for a more efficient and comprehensive exploration of optimal configurations while maintaining a high degree of accuracy, as validated by final simulations. This paradigm shift enhances the precision and speed of adjustments in complex antenna systems, revolutionizing the design workflow54. Within ML-driven antenna optimization, four primary learning frameworks are employed: supervised learning (SL), reinforcement learning (RL), semi-supervised learning (SSL), and unsupervised learning (UL), as shown in Fig. 5. SL remains the most prevalent due to its capacity to predict performance from labeled data, though its dependence on large training datasets presents limitations55. To mitigate computational bottlenecks, regression models, artificial neural networks (ANNs), and support vector machines (SVMs) are widely used to build surrogate models. These tools enable rapid performance forecasting, slashing simulation overhead and expediting the design process. This study focuses on leveraging ML algorithms to predict S11 response curves, a key metric of impedance matching between antennas and transmission lines, directly from geometric parameters. By training ML models to correlate structural features with S11 behavior, the framework bypasses repetitive full-wave EM simulations, achieving fast and accurate performance approximations.

Fig. 5
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ML models.

Dataset generation and ML implementation

To train the ML models, a comprehensive dataset was generated using CST MWS. Nine key geometric parameters were identified as input features: Lp, Wp, Ls, Ws, Lg, Wf, Lf, Ra, and Rb. The ranges for these parameters were defined based on initial parametric studies to ensure feasible antenna geometries. The output target was the reflection coefficient across the frequency band of interest. A total of 500 data samples were generated through Latin Hypercube Sampling (LHS) to ensure uniform coverage of the design space. The dataset was subsequently randomized and partitioned, with 90% (450 samples) used for training the models and 10% (50 samples) reserved for testing. The models were implemented in Python using the Scikit-learn library. For the top-performing Decision Tree model, the key hyperparameters were optimized via grid search, resulting in a maximum tree depth of 15 and a minimum sample split of 2. The total time for dataset generation was approximately 75 h, while model training and prediction for thousands of design points took less than 5 min, highlighting the massive speed-up for the optimization phase.

Five established ML regression frameworks were used, each briefly outlined below:

  1. (1)

    Decision Tree Regression: Decision tree regression is a ML method that predicts continuous target variables by recursively partitioning a dataset. The algorithm iteratively splits the data into branches based on feature value thresholds, optimizing these divisions to minimize variance within each resulting subset56.

  2. (2)

    Nonparametric Regression: Nonparametric regression offers a flexible modeling approach that avoids assuming a predetermined functional relationship between variables. By employing data-driven techniques such as kernel smoothing or local polynomial regression, this method estimates patterns directly from the dataset itself. This adaptability enables the capture of complex, nonlinear interactions and trends without relying on predefined structural assumptions, making it particularly valuable for scenarios where theoretical relationships are unknown or inadequately defined57.

  3. (3)

    Random Forest Regression: The Random Forest regression technique employs an ensemble of decision trees, each trained on randomly sampled data subsets, to enhance prediction accuracy and mitigate overfitting by reducing model variance. This method leverages key antenna parameters including gain, efficiency, and return loss at resonance frequencies to predict complex design characteristics such as patch dimensions and substrate properties. By aggregating predictions across multiple trees, Random Forest effectively models nonlinear relationships between input variables and performance metrics, ensuring robust and precise antenna design optimization58.

  4. (4)

    Extreme Gradient Boosting (XGB) Regression: An ML algorithm implementing a scalable, regularized boosting framework that iteratively constructs decision trees in sequence. Each subsequent tree addresses residual errors from prior models through gradient-based optimization, systematically refining predictions while controlling overfitting via regularization constraints59.

  5. (5)

    Bayesian Linear Regression: Bayesian linear regression extends conventional linear regression by incorporating Bayesian inference principles. Unlike traditional approaches that generate fixed parameter estimates (e.g., maximum likelihood values), this method calculates posterior probability distributions for model parameters. By treating parameters as probabilistic variables rather than deterministic values, Bayesian regression quantifies uncertainty and enables probabilistic interpretations of predictions60.

Optimal ML performance hinges on systematic model selection. As depicted in Fig. 6, the workflow for resonance frequency prediction begins with training candidate algorithms on input-output relationships between design parameters and target frequencies. During validation, predictions are benchmarked against ground truth values using the held-out test data, with performance quantified through error metrics (e.g., MAE, RMSE) and accuracy scores. In the evaluation phase, algorithms demonstrating low prediction error and high accuracy advance as top candidates, while underperformers are iteratively replaced with alternative regression methods. This refinement cycle continues until convergence on the most effective model. The finalized algorithm is then deployed for resonance frequency forecasting on new data, leveraging learned patterns to deliver robust, data-driven predictions.

Fig. 6
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Flowchart showing the ML optimization.

Performance measurement metrics

The evaluation, selection, and optimization of ML models depend critically on robust performance metrics. In this context, “error” refers to the quantitative difference between a model’s predicted output and the true observed value. A high-performing model demonstrates generalizability by consistently generating accurate predictions when applied to new, unseen data. Model efficacy improves proportionally as predictions increasingly align with ground truth values, with reduced error magnitudes directly correlating to enhanced predictive capability61. Table 2 summarizes these metrics alongside their corresponding mathematical equations and definitions.

Table 2 Performance metrics for regression analysis.
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ML-based prediction results

To determine the optimal predictive model, multiple regression algorithms were evaluated, including Decision Tree, Random Forest, XGBoost Regression, Bayesian Linear Regression, and nonparametric regression techniques. These algorithms were chosen for their capacity to capture nonlinear relationships, manage high-dimensional input data, and resist overfitting, essential characteristics for reliable S11 parameter prediction in antenna design. Figure 7 assesses the predictive accuracy of these algorithms using key error metrics MAE, MSE, MSLE, RMSLE and RMSE for resonant frequency estimation. Figure 8 supplements this evaluation with R2 scores, which quantify the goodness-of-fit for each model.

Fig. 7
Fig. 7
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Comparison of various ML algorithms and their corresponding errors in predicting S11.

Fig. 8
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Accuracy plots showing the R2 values of various ML algorithms in predicting S11 performance.

Figure 9 further illustrates the alignment between CST MWS simulation results for the proposed antenna’s resonant frequency and the predictions generated by the regression models. The Decision Tree algorithm emerged as the top performer, delivering the lowest error rates (MAE: 0.72, MSE: 0.28, MSLE: 0.56, RMSLE: 0.81, RMSE: 0.66) and achieving the highest R2 accuracy score of 97.80%. The superior performance of the Decision Tree model can be attributed to its ability to effectively capture the non-linear relationships between the geometric parameters and the resonant frequency without overfitting on our dataset of 500 samples. Furthermore, its interpretability and computational efficiency make it a practical and robust choice for antenna optimization tasks.

Fig. 9
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Comparative analysis of the ML-based predictions.

Results and analysis

The proposed antenna design was transitioned from simulation to physical realization through a fabrication process to experimentally validate its performance against theoretical predictions, as illustrated in Fig. 10a. To establish a reliable feed mechanism, a commercially available 50-Ω SMA edge-mounted connector was integrated, chosen for its impedance-matching capability and minimal signal loss at the operating frequency band. The connector was soldered using lead-free solder to maintain mechanical stability and electrical continuity, critical for preserving the antenna’s radiation characteristics. Antenna performance metrics, including S11, radiation patterns, and gain, were characterized using a Keysight PNA-L Vector Network Analyzer (VNA) with a frequency range of 10 MHz – 43.5 GHz, as depicted in Fig. 10b at the UKRI National microwave/mmWave facility at the University of Sheffield, Portobello Centre, Pitt Street, Sheffield, United Kingdom. Prior to measurements, the VNA was calibrated using a Short-Open-Load-Thru (SOLT) calibration kit to eliminate systematic errors and ensure measurement fidelity. To mitigate environmental interference and multipath reflections, all radiation patterns and efficiency measurements were conducted in a fully calibrated anechoic chamber as seen in Fig. 10c, equipped with pyramidal absorbers to emulate free-space conditions.

Fig. 10
Fig. 10
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Photographs: (a) fabricated prototype (b) S11 measurement setup (c) far-field measurement setup.

Reflection coefficient

The reflection coefficient of the proposed antenna was measured using a VNA. Figure 11 presents a comparison between the measured and simulated S11 of the antenna in both the ON and OFF states of the SMP1321 PIN diode. In the ON state, the antenna operates in a dual-band mode at 3.5 GHz and 28 GHz. The lower resonant frequency at 3.5 GHz exhibits a measured − 10 dB bandwidth of 25.4%, corresponding to a frequency range from 3.081 GHz to 3.971 GHz. The upper resonant frequency at 28 GHz demonstrates a measured bandwidth of 70.2%, spanning from 22.661 GHz to 42.330 GHz. In the OFF state, the antenna operates in a single-band mode at 28 GHz with a measured bandwidth of 73.2%, covering the range from 21.622 GHz to 42.118 GHz. Despite its compact size, the antenna effectively covers two distinct frequency bands, with an 8:1 frequency ratio between the mm-wave and sub-6 GHz ranges.

Fig. 11
Fig. 11
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Comparison of S11 in the ON state and OFF state.

Surface current distribution

The current distribution of the proposed antenna is illustrated in Fig. 12. In the ON state, the maximum current is observed to concentrate around the edges of the H-shaped slot etched into the rectangular patch at 3.5 GHz, as depicted in Fig. 12a. Conversely, at 28 GHz, the maximum current becomes more prominent around the circular patch, as shown in Fig. 12b. Conversely, in Fig. 12c, it is evident that, in the OFF state, a minimal amount of current flows around the edges of the H-shaped slot, contributing to the lower resonant frequency at 3.5 GHz. Meanwhile, at the upper resonant frequency of 28 GHz, depicted in Fig. 12d, the maximum current is notably concentrated around the center of the circular patch. The finding is in line with the theoretical justification given in the literature62, which states that the length of the current path on the radiating patch does affect the resonant frequency. The lower the resonant frequency, the longer the current path travels across the radiating patch or vice versa.

Fig. 12
Fig. 12
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Current distribution: (a) 3.5 GHz (Switch ON), (b) 28 GHz (Switch ON), (c) 3.5 GHz (Switch OFF), (d) 28 GHz (Switch OFF).

Radiation characteristics and gain

The antenna’s radiation patterns, gain, and efficiency in both ON and OFF states were measured in an anechoic chamber and compared with simulated results. Figure 13 illustrates the simulated versus measured radiation patterns in the ON state. At 3.5 GHz as depicted in Fig. 13a, the measured patterns exhibit a bidirectional profile in the E-plane and an omnidirectional profile in the H-plane, aligning closely with simulations. Similarly, at 28 GHz as depicted in Fig. 13b, the measured E-plane remains bidirectional, while the H-plane retains its omnidirectional behavior. In the OFF state at 28 GHz as depicted in Fig. 13c, the measured radiation patterns also show bidirectional E-plane and omnidirectional H-plane characteristics, though minor discrepancies with simulations are observed, likely attributable to cable effects at 28 GHz and measurement uncertainties.

Fig. 13
Fig. 13
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Radiation patterns in the E-plane and H-plane: (a) 3.5 GHz (Switch ON) (b) 28 GHz (Switch ON) (c) 28 GHz (Switch OFF).

Figure 14 compares the simulated and measured gain and radiation efficiency in the ON state. At 3.5 GHz, the measured gain is 3.63 dBi with 90.5% efficiency as depicted in Fig. 14a, while at 28 GHz, the gain increases to 5.25 dBi with 88% efficiency as depicted in Fig. 14b. In the OFF state at 28 GHz as depicted in Fig. 14c, the measured gain is 6.2 dBi, corresponding to a radiation efficiency of 89%. These results demonstrate strong consistency between simulations and measurements across both operating states.

Fig. 14
Fig. 14
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Gain and radiation efficiency at: (a) 3.5 GHz (Switch ON) (b) 28 GHz (Switch ON) (c) 28 GHz (Switch OFF).

Bending investigation

Bending is a critical factor in the design of wearable antennas, as they are frequently subjected to deformation during real-world use. To evaluate this aspect, the antenna’s performance under various bending scenarios was analyzed. Both simulations and experimental measurements were carried out to analyze the antenna’s performance under bending conditions along the x- and y-axes. The bending was replicated using Styrofoam cylinders with curvature diameters of 60 mm, 90 mm, and 120 mm, dimensions representative of a typical human arm and leg, as shown in Figs. 15 and 16. Figure 17a,b show the simulated and measured S11 parameters of the antenna in the ON state under x- and y-axis bending. The simulated S11 results for both axes exhibit similar trends. However, a slight shift in the S11 at the 28 GHz band is observed for the y-axis when the bending diameter is reduced to 60 mm, likely due to the increased curvature. In contrast, the measured S11 shows minor deviations across all Styrofoam diameters, which could be attributed to factors such as the material properties of Styrofoam, fabrication inaccuracies, and cable losses. Despite these discrepancies, the antenna maintains acceptable performance, with the 3.5 GHz and 28 GHz bands staying above the − 10 dB threshold.

Fig. 15
Fig. 15
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Proposed antenna bending (simulation) (a) x-axis (b) y-axis.

Fig. 16
Fig. 16
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Proposed antenna bending (measurement) (a) x-axis (b) y-axis.

Fig. 17
Fig. 17
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S11 under bending investigation Switch ON (a) x-axis (b) y-axis.

Figure 18a,b present the simulated and measured S11 parameters in the OFF state under similar bending conditions. The results show a close match for both bending axes, with only slight variations. These minor differences do not significantly affect antenna performance, as the 28 GHz band continues to meet the − 10 dB requirement.

Fig. 18
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S11 under bending investigation Switch OFF (a) x-axis (b) y-axis.

Moreover, the radiation patterns under bending conditions were measured in an anechoic chamber, but only for the 120 mm diameter due to limitations in resources and available laboratory equipment. These measurements were compared with simulation results for both the ON and OFF states of the PIN diode. As shown in Figs. 19 and 20, the radiation patterns retain their consistent bidirectional characteristics under bending. However, a slight increase in back radiation is observed compared to the unbent state, which is likely due to substrate deformation caused by bending.

Fig. 19
Fig. 19
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Radiation patterns of the antenna under bending conditions Switch ON (a) 3.5 GHz (x-axis) (b) 3.5 GHz (y-axis) (c) 28 GHz (x-axis) (d) 28 GHz (y-axis).

Fig. 20
Fig. 20
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Radiation patterns of the antenna under bending conditions Switch OFF (a) 28 GHz (x-axis) (b) 28 GHz (y-axis).

In the ON state the simulated and measured gain under bending conditions are depicted in Fig. 21. At 3.5 GHz, the simulated and measured gain ranged from 4.1 dBi to 5.7 dBi on the x-axis and y-axis as shown in Fig. 21a. Conversely, at 28 GHz, the simulated and measured gain under bending conditions ranged from 4.1 dBi to 5.5 dBi on the x-axis and y-axis as can be seen in Fig. 21b. In the OFF state, at 28 GHz, the simulated and measured gain under bending conditions ranged from 4.2 dBi to 5.6 dBi on the x-axis and y-axis as shown in Fig. 21c. Therefore, the antenna’s performance under bending conditions was not affected with respect to the simulated and measured gain.

Fig. 21
Fig. 21
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Simulated and measured gain for different bending conditions along the x-axis and y-axis: (a) 3.5 GHz (Switch ON) (b) 28 GHz (Switch ON) (c) 28 GHz (Switch OFF).

Antenna’s performance on human body

The antenna’s performance was tested in on-body configurations (lap, arm and chest) to evaluate its reliability in real-world biomedical applications. All on-body measurements conducted in this study were entirely non-invasive and posed no risk of harm to participants. The study protocol received approval from the Human Research Ethics Committee of the University of Bradford, United Kingdom. Informed consent was obtained from all participants prior to their involvement. All procedures strictly adhered to relevant institutional guidelines and national regulations governing research involving human subjects. S11 simulations and measurements were also performed with the antenna positioned on three key body regions relevant to biomedical applications: lap (for mobility-related sensing), the arm (for integration with wearable devices) and the chest (for heart rate monitoring), as shown in Fig. 22. These locations were chosen to reflect typical deployment sites for health-monitoring systems, offering a balance between anatomical significance and practical functionality.

Fig. 22
Fig. 22
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Proposed antenna on various parts of human body: (a) lap (b) arm (c) chest.

The simulated and measured S11 of the antenna in ON and OFF states of the PIN diode, positioned on the lap, arm, and chest are shown in Fig. 23. The dual-band operation at 3.5 GHz and 28 GHz exhibited only minor frequency shifts, which do not substantially affect performance, as both bands remain above the − 10 dB threshold as seen in Fig. 23a. The measured S11 can be viewed in Fig. 23b in ON and OFF states. From both figures, the results from simulations and measurements are all in satisfactory agreement.

Fig. 23
Fig. 23
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S11 for the antenna for various body settings: Lap, arm and chest (a) simulated (b) measured.

Moreover, the radiation patterns in the E-plane were also simulated in ON and OFF states with the antenna placed on different body parts, including the lap, arm and chest to observe the antenna performance as shown in Fig. 24. The radiation patterns retained their consistent bidirectional characteristics as can be viewed in Fig. 24a–c. However, there is a minor increase in back radiation which might be caused by the substrate materials used.

Fig. 24
Fig. 24
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Radiation patterns on various parts of human body at: (a) 3.5 GHz (Switch ON) (b) 28 GHz (Switch ON) (c) 28 GHz (Switch OFF).

The gain of the antenna in ON and OFF states with the antenna placed on different body parts, including the lap, arm and chest as shown in Fig. 25. In the ON state, at 3.5 GHz, the simulated gain ranged from 4.7 dBi to 5.5 dBi as shown in Fig. 25a. Conversely, at 28 GHz, the simulated gain ranged from 4.5 dBi to 5.45 dBi as shown in Fig. 25b. On the other hand, in the OFF state, at 28 GHz as seen in Fig. 25c, the simulated gain ranged from 4.5 dBi to 5.5 dBi. Thus, the gain of the antenna when it is placed on a human body was not affected.

Fig. 25
Fig. 25
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Gain on various parts of human body at: (a) 3.5 GHz (Switch ON) (b) 28 GHz (Switch ON) (c) 28 GHz (Switch OFF).

SAR analysis

Increasing concerns about the potential health effects of electromagnetic radiation, along with global regulatory standards, have prompted researchers to assess the power absorbed by the human body during prolonged exposure. For wearable antennas operating in close proximity to the body, evaluating the SAR which quantifies the power absorbed per unit mass of biological tissue is critical for ensuring user safety. Following the IEEE C95.1 guidelines, SAR simulations were conducted using CST MWS. The material properties of the human body tissue layers used in the simulation are detailed in Table 3. The SAR performance was evaluated with the antenna positioned on body regions relevant to biomedical applications, such as the lap for mobility-related sensing. The on-body setup is shown in Fig. 26a. Figure 26b illustrates the simplified multi-layered human phantom model of the lap, which comprises skin, fat, muscle, and bone layers to replicate realistic tissue interactions for SAR evaluation. This modeling approach enables accurate analysis of electromagnetic energy absorption for SAR evaluation in wearable antenna applications.

Table 3 Characteristics of human body tissue63.
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Fig. 26
Fig. 26
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(a) SAR simulation on-body setup (b) simplified multi-layered human phantom model of the lap.

Figure 27 presents the simulated SAR values placed on the Lap at 5 mm distance for 1 g and 10 g tissue masses at the antenna’s operational frequencies. At 3.5 GHz, as shown in Fig. 27a,b, SAR values are 0.438 W/kg (1 g) and 0.0147 W/kg (10 g) under an input power of 100 mW. At 28 GHz, as depicted in Fig. 27c,d, SAR values are 0.801 W/kg (1 g) and 1.09 W/kg (10 g). These results fall well within the safety limits set by the FCC and ICNIRP 1.6 W/kg for 1 g and 2.0 W/kg for 10 g, confirming the antenna’s compliance with international safety standards for wearable biomedical devices.

Fig. 27
Fig. 27
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SAR values (with an input power of 100 mW) (a) 1 g at 3.5 GHz (b) 10 g at 3.5 GHz (c) 1 g at 28 GHz (d) 10 g at 28 GHz.

Table 4 compares the antenna proposed in this work with previously published designs, highlighting key parameters including ML model, operating frequency, substrate material, safety compliance, efficiency, bandwidth, frequency reconfiguration capability, and gain. Model performance was evaluated using MAE, MSE, RMSLE, RMSE, MSLE, and R2 metrics. The decision tree regression model outperformed others, achieving the lowest errors (MAE: 0.72, MSE: 0.28, RMSLE: 0.81, RMSE: 0.66, MSLE: 0.56) and the highest accuracy (R2: 97.8%). Furthermore, it reduced computational time by 80% compared to conventional CST MWS simulations a significant efficiency improvement not reported in prior work. Notably, the antennas presented in references9,32,33,34,58,64,65,66 exhibit larger dimensions than the proposed design. Crucially, the proposed antenna underwent dual validation for SAR compliance with FCC/ICNIRP standards, a critical safety step omitted in most prior works, with9 being the exception.

Table 4 Performance comparison with existing literature.
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Conclusion

The integration of sub-6-GHz and mm-wave bands has become an important issue for future fifth-generation (5G) wireless communications owing to their large frequency ratios. This paper proposes a machine learning-optimized compact wearable frequency reconfigurable antenna for Sub-6 GHz/mm-Wave 5G integration. The proposed antenna is fabricated on a flexible Rogers Duroid with a dimension of 27.8 × 14 × 0.508 mm3. During the initial design stage, the antenna resonates at 28 GHz using a circular structure. For dual-band operation, an H-shaped slot is etched into the rectangular patch, thereby creating another band at 3.5 GHz. A PIN diode is employed to reconfigure the proposed antenna in the ON and OFF states. In the ON state, the antenna operates at 3.5 GHz and 28 GHz, achieving measured bandwidths of 25.4% and 73.2%, gains of 3.63 dBi and 5.25 dBi, and radiation efficiencies of 90.5% and 88%, respectively. In the OFF state, the antenna operates at 28 GHz, achieving a measured bandwidth of 72.9%, a gain of 6.2 dBi, and a radiation efficiency of 89%. Bidirectional E-plane and omnidirectional H-plane radiation patterns are maintained across both bands. At 3.5 GHz, the SAR value for 1 g and 10 g of human tissue is 0.438 W/kg and 0.0147 W/kg, while at 28 GHz, the SAR value is 0.801 W/kg and 1.09 W/kg, which comply with the FCC and ICNIRP standards. Bending tests on the lap, chest, and arm confirmed stable performance under realistic on-body conditions. The antenna’s S11 was predicted using a supervised ML regression framework. Among tested algorithms, the decision tree achieved state-of-the-art accuracy (R2: 97.80%) with minimal errors (MAE: 0.72, MSE: 0.28, MSLE: 0.56, RMSLE: 0.81, RMSE: 0.66). The proposed antenna system is suitable for future 5G mobile devices. While this study demonstrates a successful ML-optimized design, it is not without limitations. The long-term mechanical reliability of the flexible substrate and soldered components under repeated bending cycles was not tested. Furthermore, the practical integration of a compact, battery-efficient biasing circuit for the PIN diode in a garment remains to be implemented. Future work will focus on addressing these aspects, investigating the antenna’s power handling capacity, and extending the ML framework to optimize conformal MIMO arrays for enhanced channel capacity.