Modelling and evolutionary stages of the proposed antenna

The initiation of the proposed antenna begins with a circular patch with a radius (r) of 10 mm, which is considered the initiator in this work, as seen in Fig. 1(a). The equations (1–4) adapted from reference [Reference Yimdjopoffelie, Soh, Yan and Vandenbosch15] are used to calculate the r to achieve a lower edge frequency (LEF) of around 3 GHz. The maple leaf, resembling an open hand with serrated edges (Fig. 1(b)), has a maximum edge length from its center of 10 mm. The initiator’s area, calculated using equation (2) for the area of a circle, is 314.2 mm². However, through measurements with the high-frequency structure simulator (HFSS), the resultant maple leaf shape is found to have an area of 239.9 mm², indicating a 14% reduction compared to the initiator. This reduction influences the LEF; an expected LEF of 3.2 GHz is calculated with the resultant area equations (3) and (4).

(1)\begin{equation}{f_{\,lower}} = \frac{{0.24 \times 300}}{{\left( {D + G + \left( {\frac{D}{{2\pi }}} \right)} \right) \times K}}\left( {GHz} \right)\end{equation}

(2)\begin{equation}A = \pi {r^2}\end{equation}

(3)\begin{equation}{f_{\,r}}\left( {GHz} \right) = \frac{{300}}{{\varphi \sqrt {{\varepsilon _{eff}}} }}\end{equation}

(4)\begin{equation}{\varepsilon _{eff}} \approx \frac{{{\varepsilon _r} + 1}}{2}\end{equation}

Figure 1. (a) Circular patch with radius “R” =10 mm (b) maple leaf patch with maximum edge length “r” of 10 mm from its center.

The symbol “D” corresponds to the millimeter measurement of the circle’s diameter, the gap, expressed in millimeters, between the ground plane and the radiating patch is denoted by the letter “G.” “A” is the area of a circle. φ represents the patch’s perimeter, while ε_r stands for the substrate’s dielectric constant, f _r expresses the resonant frequency, and the variable k considers the influence of the substrate’s dielectric permittivity, with its value specified as 1.15 [Reference Yimdjopoffelie, Soh, Yan and Vandenbosch15].

In stage 1, the patch is modified to the maple leaf structure, which resembles an open hand with serrated edges and has a maximum edge length from its center of 10 mm, which enables multiple resonating modes and results in multiple frequency bands and a total impedance bandwidth of 3.85 GHz. In stage 2, a rectangular stub is perpendicularly added to the feed line, which increases the electrical length of the antenna and results in a bandwidth of 5.21 GHz. A rectangular slot is etched in the center of the patch in stage 3, and the antenna resonates with an increased bandwidth of 6.06 GHz. Further, to tune the frequency of operation and improve the return loss (<−10 dB) for the entire UWB band, the edges of the maple leaf structure are chamfered [Reference Roy, Biswas, Nandi and Basu24]. A change in resonating modes occurred, and the increment in bandwidth was due to the chamfering of the corners, which resulted in an impedance bandwidth of 7.32 GHz. An optimization process was pursued in Ansys HFSS version 2022 to fix the dimensions and position of the slot, stub, and chamfering length. The evolution of the modified maple leaf full ground (MFG) antenna and its reflection characteristics are shown in Fig. 2. Table 1 details the frequency range, number of bands, and impedance bandwidth obtained at each evolutionary stage.

Figure 2. Evolutionary stages and their return loss characteristics.

Table 1. Details of the evolutionary stages and reflection characteristics

Optimization of the proposed antenna through ML

The final structure and optimal dimensions of the MFG antenna are obtained after the optimization of the antenna dimensions using ML algorithms. Figure 3 illustrates the proposed antenna’s ML flow chart. The proposed UWB antenna is designed using HFSS software. A large amount of data is required to apply the ML algorithms for the proposed antenna [Reference Cao29–Reference Rai, Ranjan, Chowdhury and Jamaluddin38]. The dataset is prepared by varying the various parameters of the UWB antenna. In total, there are 4,50,451 datasets created. The whole dataset is distributed into training and testing datasets. Eighty percent of the dataset is used to train the ML algorithms, and the remaining 20% is used for testing the trained ML models. In this work, five ML algorithms, extreme gradient boosting (XGB), artificial neural network (ANN), decision tree (DT), K-nearest neighbour (KNN), and random forest (RF), are used [Reference Ranjan, Krishnan, Dwivedi, Singh and Sharma34–Reference Rai, Anuragi, Mishra, Chowdhury, Kumar and Ranjan42]. Table 2 represents the ML algorithms’ mean square error (MSE), mean absolute error (MAE), and R ² Score. Actual and predicted values of S parameters are shown in Fig. 4. R ² Score represents the accuracy of our ML algorithms. Training time, testing time, and accuracy of various ML algorithms are represented in Figs. 5–7. respectively. From Table 2 and Fig. 7. it is seen that KNN ML algorithms achieved the highest accuracy compared to other ML algorithms. It accurately predicts the S₁₁ of the proposed UWB antenna. The comparison of KNN ML with HFSS is shown in Fig. 8.

Figure 3. Flow chart of Mmachine learning in the proposed UWB antenna.

Figure 4. Actual and predicted values of ML algorithms.

Figure 5. Training time of ML algorithms.

Figure 6. Testing time of ML algorithms.

Figure 7. Accuracy of ML algorithms.

Figure 8. Comparison of KNN ML with HFSS.

Table 2. MSE, MAE, and R ² score of ML algorithms

Geometry and prototyping of the proposed antenna

The proposed antenna is initially designed based on a bio-inspired maple leaf structure and further modified for desired performance characteristics, as shown in Fig. 9(a) and (b). Bioinspired structures, such as fractal structures, are known for their compactness and increased electrical length [Reference Zarrabi, Shire, Rahimi and Gandji43–Reference Poorgholam-Khanjari, Hatami and Zarrabi45]. The antenna has overall optimized dimensions of 35.5 × 30.5 × 1 mm³, and the detailed dimensions are given under the caption for Fig. 9. The entire ground plane has been maintained on the bottom side, and the modified maple leaf-shaped patch is positioned above a substrate with a relative permittivity of 2.77. Conductive textile is used for radiating components because of its high conductivity with the combination of nickel + copper-plated and silver-coated nylon [46]. Several methods for bandwidth enhancement have been used to achieve an ultra-wide bandwidth, including the adoption of bioinspired radiating structures, etching slots, truncating edges, and introducing stubs in the feeds, as covered in paper [Reference Alomainy, Sani, Rahman, Santas and Hao12]. Figures 10 and 11 illustrate the prototype of the fabricated antenna from various perspectives, including Fig. 10(a) front view, 10(b) rear view, Fig. 11(a) X-bent, and 11(b) Y-bent, respectively. Surface current distribution diagrams at 3.1 GHz, 5.5 GHz, and 9.5 GHz frequencies covering lower, middle, and higher frequencies of the UWB band are shown in Fig. 12. From the surface current distribution, it is observed that the maximum current is at the feeding point and around the slot.

Figure 9. Dimension (in mm) (a =35.56, b =13.79, c =4.06, d =5.59, e =7.9, f =3.9, g =3, h =8.5, i =5.1, j =3, k =5.9, l =3.9, m =2.2, n =2.7).

Figure 10. Prototype of the UWB antenna (a) front view and (b) rear view.

Figure 11. Flexibility of the UWB antenna (a) bent in the Y (b) X-axis.

Figure 12. Surface current distribution at 3.1, 5.5, and 9.5 GHz.

Free space measurements

The simulated and measured return loss in free space under flat and bent scenarios are compared in Figs. 14 and 15, respectively. The simulated return loss is identical to the measured in flat and bent conditions. It is noticeable that the measured results exhibited a wider bandwidth of 8.8 GHz, i.e., from 3.212 GHz. The E and H plane radiation patterns are measured in an anechoic chamber at different frequencies, such as 4.8 GHz, 6.2 GHz, 8.6 GHz, 9.2 GHz, and 10.2 GHz. Overall, as seen in Figs. 16–17, respectively, there is a noticeable agreement between the simulated and measurements at the E and H planes. As expected, the antenna mostly radiates in its boresight direction because of the complete ground plane. Consequently, this reduces the coupling between the antenna and the body, minimizing energy dissipation within the body and loading of the antenna.

Figure 14. Comparison of the measured and simulated return loss in free space.

Figure 15. Comparison of measured and simulated return loss free space in X and Y axis bending.

Figure 16. Simulated and measured E plane at various frequencies (a) 4.8 GHz, (b) 6.2 GHz, (c) 8.6 GHz, (d) 9.2 GHz and (e) 10.2 GHz.

Figure 17. Simulated and measured H plane radiation pattern at (a) 4.8 GHz, (b) 6.2 GHz, (c) 8.6 GHz, (d) 9.2 GHz and (e) 10.2 GHz.

Assessing the group delay of UWB antennas is crucial for verifying the undistorted nature of their structure. A consistent group delay signifies that the antenna is nonresonant, leading to effective radiation [Reference Wiesbeck, Adamiuk and Sturm48]. It is essential to minimize the group delay, with a maximum acceptable value of Dt = 1/2 fs, and for short pulse transmission, it should be 3.8 ns [Reference Biswas and Poddar49, Reference Narbudowicz, John, Sipal, Bao and Ammann50]. Two identical antennas are positioned facing each other and in side-by-side orientations with far-field distance (Ds) of 221 mm calculating at 3 GHz frequency as shown in Fig. 18. The group plots are presented in Fig. 19, revealing that the variations are under 2.5 ns and exhibit an almost linear pattern across the entire UWB frequency range.

Figure 18. Antenna setup for group delay analysis (a) side by side (b) face to face.

Figure 19. Group delay plot of the proposed MFG antenna.

On-body measurements

It is essential to examine how the antenna affects the human body and vice versa to ensure the stability of the antenna’s operation and the safety of human tissues. Using Ansys HFSS, a four-layered flat human body model and the cylindrical dispersive HTM are created, incorporating skin, fat, and muscle and bone as shown in Fig. 20. On-body bending analysis is performed both in X and Y orientations on a 30 mm radius cylindrical dispersive HTM. The corresponding return loss characteristics are compared and plotted in Fig. 21. From the plot is evident that the antenna bent on the body in the X and Y axis agrees well maintaining the resonating bandwidth with negligible frequency shift. MFG antenna placed on the flat HTM (90 × 90 mm²) with 0 mm gap and comparison of return loss is plotted in Fig. 22. It is observed that the proposed antenna exhibited S₁₁ < −10 dB for 7.32 GHz bandwidth (3.1–10.42 GHz) over the human body for simulated results and bandwidth of 9.8 GHz (2.2–12 GHz) for measured results. The nonuniformity of the substrate is the reason for the discrepancies between the measured and simulated findings. The manufacturing fault that occurred during the soldering of the connection is another element that contributes to the mismatch. Mismatches have also been seen in the free space measurement facility since the proposed antenna input parameters were determined using a Vector Network Analyzer (VNA)in an open environment. Safety assessment involves measuring SAR, while antenna performance is evaluated through return loss measurements. As per the FCC standards, the maximum SAR limit is 1.6 W/kg for 1 g of tissue. The simulated SAR values for different frequencies with an input power of 25 mW are 0.66 W/kg, 0.53 W/kg, and 0.90 W/kg at 3.8 GHz, 7.5 GHz, and 10 GHz, respectively, as demonstrated in Fig. 23. It is observed that the obtained SAR values are significantly lower than the FCC standards. The proposed antenna is compared with the state of artwork in Table 4. The comparison shows that the proposed antenna is a compact, single-layered structure with smaller dimensions covering the entire UWB.

Figure 20. Human tissue layer model (a) flat (b) cylindrical.

Figure 21. On body bending in X and Y orientations.

Figure 22. Return loss comparison of the simulated and measured return loss at 0 mm on flat human body model.

Figure 23. SAR values at (a) 3.8 GHz (b) 7.5 GHz and (c) 10 GHz.

Table 4. Comparison with state-of-art works