A Miniaturized Tri-Wideband Sierpinski Hexagonal-Shaped Fractal Antenna for Wireless Communication Applications

Abstract

This paper introduces a new tri-wideband fractal antenna for use in wireless communication applications. The fractal manufactured antenna developed has a Sierpinski hexagonal-shaped radiating element and a partial ground plane loaded with three rectangular stubs and three rectangular slits. The investigated antenna has a small footprint of 0.19λ₀ × 0.24 λ₀ × 0.0128 λ₀ and improved bandwidth and gain. According to the measurements, the designed antenna resonates throughout the frequency ranges of 2.19–4.43 GHz, 4.8–7.76 GHz, and 8.04–11.32 GHz. These frequency ranges are compatible with a variety of wireless technologies, including WLAN, WiMAX, ISM, LTE, RFID, Bluetooth, 5G spectrum band, C-band, and X-band. The investigated antenna exhibited good gain with almost omnidirectional radiation patterns. Utilizing CST MWS, the performance of the suggested Sierpinski hexagonal-shaped fractal antenna was achieved. The findings were then compared to the experimental results, which were found to be in strong agreement.

1. Introduction

In order to address the needs of many applications, rapid advancement in wireless communications has led to an increase in the demand for miniaturized antennas that can operate across numerous frequency ranges. As a result, employing a single integrated antenna configuration that can function over a wide frequency range while minimizing the overall system footprint is important. In light of this, it has become more and more common for antenna designs to integrate the functions of multiple antennas into one construction. Furthermore, they outperform their rivals and serve as the best options for modern wireless communication systems due to their desirable properties, including simplicity of integration, compact size, and low production costs.

For wireless communication applications, a number of multiband antenna designs using rigorous approaches have been published in the literature, including the usage of slots in the radiator or in the ground plane and fractal and metamaterial constructions [1,2,3,4,5,6,7].

B. Mandelbort described fractal geometry for the first time in 1975. He claimed that fractal geometry is a type of geometry that repeats itself at a specific scale; examples of it can be found in nature, including snowflakes, peacock fins, and broccoli [8]. Fractals are employed frequently today due to their self-similarity and space-filling qualities, which enable multiband and wideband characteristics as well as downsizing. The Sierpinski gasket [9], Sierpinski carpet [10], Koch curve [11], and Minkowski [12], Giuseppe Peano [13], and Hilbert curves [14] are examples, among others, of frequently employed fractal geometries.

Kaur et al. [15] investigated a circular fractal antenna with Split Ring Resonator (SRR) stubs for multiband wireless applications. SamadpourHendevari et al. [16] presented an annular ring fractal antenna for wideband operation. Kola et al. [17] designed a fractal antenna for an X-band application; it consisted of a four-fold centrosymmetric radiating element. Gupta et al. [18] reported a hexagon Koch snowflake fractal antenna shielded the broad bandwidth (3.265–8.2 GHz). Puri et al. [19] designed a multiband plus-shaped fractal antenna with dual frequency bands covering the Global System for Mobile (GSM) band, 5G spectrum band, sub-6 GHz band, Long Term Evolution (LTE) band, and Wireless Local Area Network (WLAN) band. Vipul Sharma et al. [20] presented a multiband circular fractal antenna with parasitic SRR, which operates at 3, 5, 6.8, 7.5, and 8.5 GHz. Jaffri et al. [21] introduced a stair-shaped fractal antenna that resonated at 3.65, 4.825, and 6.325 GHz. Choukiker et al. [22] reported a dual wideband modified Sierpinski square fractal antenna. Madhav et al. [23] designed a wheel-like fractal antenna suitable for IMT, GSM, LTE, and WLAN bands.

The authors in [13,24,25,26,27,28,29,30] reported antennas created by combining or superimposing two or more fractal structures.

Khan. et al. [31] presented a slotted conical antenna for WLAN and 5G applications. In [32], Kulkarni et al. reported a maze-shaped antenna for multiband applications. Elkorany et al. [33] introduced an F-shaped tri-band antenna for Wireless sensor Networks (WSNs) applications. Kulkarni et al. [34] presented an L-shaped antenna with a crescent-shaped substrate and DGS for WLAN and V2X applications. Abdulkawi et al. [35] designed a wideband slotted square for IoT applications. In [36], Naik et al. presented a miniaturized T-shaped antenna with a single band at 10.98 GHz.

However, several antenna configurations described in the literature have large dimensions. Considering all of these factors, fractal antennas ought to perform better, offering multiple wide bands to meet wireless communication applications’ requirements while maintaining a small size and good radiation pattern.

The aim of this study was to design and investigate a tri-wideband Sierpinski hexagonal-shaped fractal antenna for wireless communication applications. The tri-wideband characteristic was achieved by employing the second iteration of a Sierpinski hexagonal structure and by introducing three rectangular slots and three rectangular stubs in the partial ground plane. The first band with a frequency range of 2.19–4.43 GHz resonated at 2.4 GHz. The second frequency range was 4.8–7.76 GHz with a 6.66 GHz resonant frequency. The third frequency range (8.04–11.32 GHz) was centered at 9.8 GHz. At the resonant frequencies, the developed antenna operated well in terms of radiation proprieties. As a result, the investigated antenna is appropriate for LTE 2300, LTE 2500, RFID, Bluetooth, 5G spectrum band, WLAN, Industrial, Scientific and Medical (ISM), Worldwide Interoperability for Microwave Access WiMAX, C-band, and X-band. The sections that come are as follows. The Section 1 explains the construction procedure for the suggested Sierpinski hexagonal-shaped fractal antenna. A parametric study of the investigated antenna’s parameters is provided in the Section 2. The Section 3 analyzes the simulation and experiment’s findings. The conclusion of the study is revealed in the Section 6.

2. Antenna Design Conception

2.1. Design of Sierpinski Hexagonal-Shaped Fractal Antenna

Figure 1 depicts the geometry for the designed Sierpinski hexagonal-shaped fractal antenna. The proposed antenna consisted of a Sierpinski hexagonal-shaped fractal radiating element with a modified partial ground plane. A microstrip transmission line of W_f × L_f supplied power to the proposed antenna’s structure in order to provide the 50 Ω port impedance. The developed antenna was manufactured from a 24 mm × 30 mm, low-cost FR-4 substrate (height h = 1.6 mm; ε_r = 4.4).

It was obvious that the proposed fractal antenna was stated to have optimal dimensions for incorporation into small size devices. A parametric investigation and the suggested antenna’s evolution process were used to identify the antenna’s optimal parameters in order to examine the outcomes of the designed antenna structure and acquire a multiband characteristic. The optimal parameters of the designed antenna are shown in

Table 1. Optimal dimensions of developed antenna.

Parameters	Dimensions (mm)	Parameters	Dimensions (mm)
L	30	L2	3.25
W	24	W2	1
h	1.6	L3	6.5
h1	0.035	W3	1
Lf	12	L4	3.25
Wf	1	W4	1
S	1	L5	6.5
Lg	11.4	W5	1
L1	18.6	L6	3
W1	1	W6	1

. Using the CST MWS software 2018, the performance of the suggested Sierpinski hex-agonal-shaped fractal antenna was examined.

2.2. Design of Sierpinski Hexagonal-Shaped Fractal Antenna Evolution Mechanism

Figure 2 illustrates the design evolution steps of the antenna from the beginning structure (basic hexagonal antenna) to the final structure (proposed antenna) for a better understanding of how the antenna evolved. Figure 3 presents the simulation results of the reflection coefficient S₁₁ of the various stages of the proposed antenna’s design evolution.

Figure 2a depicts the first step of the developed antenna’s design. A basic hexagonal patch with a partial ground plane served as the starting point for the antenna evolution process.

In order to determine the resonant frequency for a hexagonal patch antenna, the equation for a circular strip patch antenna, stated in Equation (1), was utilized by comparing the areas [37].

$$f_r=\frac{Y_{mn}c}{5.714R_e\sqrt{{\epsilon }_{reff}}}$$

(1)

where c is the speed of light in free space and is the effective dielectric constant. For the mode TM11, Y_mn = Y₁₁ = 1.8412. Additionally, R_e is the circular patch antenna’s effective radius and is computed by Equation (2):

$$R_e=R_c\sqrt{1+\frac{2h}{R_c\pi {\epsilon }_r}\left(\ln \left(\frac{\pi R_c}{2h}\right)+1.7726\right)}$$

(2)

where R_c is the circular patch antenna’s radius.

By equating the areas of circular and hexagonal patch antennas, one may use the resonant frequency to design a hexagonal patch antenna.

$$\pi ·R_e^2=\frac{3}{2}\sqrt{3}·S^2$$

(3)

where S is the hexagonal patch antenna’s side length.

The basic hexagonal patch used to create the proposed antenna’s first design operated at 4.43 GHz. The typical hexagonal patch antenna’s side S was computed to be 9 mm from Equations (1) through (3).

The reflection coefficient S₁₁ of the basic hexagonal patch (Iteration 0) was up to −22 dB; it had two resonant frequency modes. The first resonant frequency was close to 3.44 GHz and with an impedance bandwidth of 3.12–3.89 GHz. The second impedance bandwidth was 7.65–8.77 GHz centered at 8.89 GHz.

In the second step of the evolution design mechanism (Figure 2b), Iteration 1 of the Sierpinski hexagonal-shaped structure was applied. The construction of this structure was achieved by introducing a hexagonal slot in the middle; six triangular shapes were cut in the corners of the hexagonal radiating element in order to obtain a shape composed of six similar hexagons [38], as illustrated in Figure 4 with:

$$S_i=\frac{S_{i-1}}{3}$$

(4)

Equation (5) indicates the Sierpinski hexagonal-shaped fractal’s Hausdorff dimension:

$$d=\frac{\log \left(6\right)}{\log \left(3\right)}=1.6309$$

(5)

It can be claimed that, in this step (Iteration 1), the antenna was suitable to operate over a 2.99–8.77 GHz band. As a result, the antenna’s bandwidth was extended without changing its size.

Similar to the first iteration, the second iteration’s structure, illustrated in Figure 2c, was obtained by repeating the same process represented above for the six sub-hexagons. According to Figure 3, the antenna presented in Figure 2c covered two bandwidths, 2.89–8.99 GHz and 10.52–11.147 GHz, having 3.6 and 10.8 GHz as its resonant frequencies.

In the last step of the evolution mechanism of the developed Sierpinski hexagonal-shaped fractal antenna (Figure 2d), the ground plane was adjusted to cover additional lower frequencies and to increase the antenna’s impedance bandwidth. More current tracks were achieved by employing slits and slots in the partial ground plane, modifying the capacitance and inductance of the antenna system. As a result, a wider impedance bandwidth and more frequency bands were displayed. The developed antenna provided three broadbands: 2.26–4.3, 4.9–7.3, and 9.27–11.147 GHz. For better comprehension,

Table 2. Comparison of results for the various stages of the developed antenna’s design evolution.

	Resonant Frequency	Reflection Coefficient	Operating Band
Iteration 0	fr1 =3.44 GHz fr2= 8.89 GHz	S11 = −11.12 dB S11 = −22.17 dB	3.12–3.89 GHz 7.65–9.89 GHz
Iteration 1	fr1= 3.6 GHz fr2= 6.77 GHz	S11 = −15.64 dB S11 = −22.08 dB	2.99–8.77 GHz
Iteration 2	fr1 = 3.6 GHz fr2 = 10.8 GHz	S11 = −19.73 dB S11 = −12.40 dB	2.89–8.09 GHz 10.52–11.147 GHz
Developed antenna	fr1 = 2.4 GHz fr2 = 3.1 GHz fr3 = 3.9 GHz fr4 = 5.5 GHz fr5 = 6.66 GHz fr6 = 9.98 GHz fr7 = 10.57 GHz	S11 = −25.37 dB S11 = −32.98 dB S11 = −21.01 dB S11 = −14.2 dB S11 = −45.7 dB S11 = −21.02 dB S11 = −21.42 dB	2.26–4.3 GHz 4.9–7.3 GHz 9.27–11.147 GHz

compares the various parameters of the designed antennas (Iteration 0 to developed antenna).

Figure 5 shows the evolutionary steps for the construction of the redesigned ground plane, from step 1 until step 6, avoiding changing the radiating patch. The first stage involved joining stub1 (L₁ × W₁) to the left corner of the partial ground plane, as shown in Figure 5a. In the second and third steps, stub2 (L₂ × W₂) and stub3 (L₃ × W₃), respectively, were additionally incorporated and appear in Figure 5b,c. Additionally, in the fourth step, the geometry produced in the previous step was used to etch the slit1 (L₄ × W₄), as illustrated in Figure 5d. The second and third slits, designated slit2 (L₅ × W₅) and slit3 (L₆ × W₆), were also carved to produce the redesigned ground plane’s final structure, as shown in Figure 5e,f. In Figure 6, the frequency responses at each step of the evolution of the ground plane are contrasted and depicted in terms of the reflection coefficient. Figure 6 demonstrates that, by using stub1, stub2, and stub3 in that order from steps 1 to 3, the antenna displayed the first band at 3.6 GHz. The progression of the improved ground plane was also reported to increase the reflection coefficient and impedance bandwidth of other frequency bands. Moreover, slit1 was also implemented in the fourth stage, shifting the initial frequency spectrum from 3.8 GHz to 3.2 GHz. The final process (step 5 and step 6) involved etching slit2 and slit3 from the ground plane structure created in step 4 and shifting the first frequency band from 3.2 GHz to 2.4 GHz with an improved impedance bandwidth of 2040 MHz in the frequency range from 2.26 to 4.3 GHz. The adjustment to the partial ground plane of the proposed antenna, coupled with improvements to the reflection coefficient and impedance bandwidth, played an essential role in obtaining the downsized form of the antenna.

3. Parametric Study

To achieve the best results with a wide bandwidth and to improve impedance matching, a parametric study of the essential parameters (L_g, L_f, W_f, L₁, L₂, L₃, L₄, L₅, and L₆) was conducted.

The effect of the ground plane length L_g on the impedance bandwidth and resonant frequencies was examined in the first parametric study, as depicted in Figure 7a. By varying L_g from 10.6 to 11.8 mm, the impedance bandwidth of the two bands was increased. However, the third frequency range was affected and the impedance bandwidth was decreased. It was proven that L_g = 11.4 mm delivered a greater S₁₁ result.

We investigated how the length and width of the microstrip feed line affected the performance of the constructed antenna by adjusting L_f from 11 to 13 mm and W_f from 1 to 2.4 mm. Figure 7b presents the variation of the reflection coefficient S₁₁ for various values of L_f and W_f. The simulations demonstrated that the optimal feed line length and width were L_f = 12 mm and W_f = 1 mm in order to obtain adequate tri-wideband bandwidth and acceptable impedance matching.

The length of the first stub L₁′s impact on the reflection coefficient S₁₁ is seen in Figure 7c. The figure shows how the value of L₁ had a substantial impact on the impedance bandwidths and resonant frequencies. The first and third bands’ impedance bandwidths were extended from 2040 MHz (2.26–4.3 GHz) and 1877 MHz (9.27–11.147 GHz) to 1840 MHz (2.46–4.3 GHz) and 2140 MHz (9.27–11.41 GHz), respectively, by increasing L₁ from 15.6 mm to 18.6 mm. Additionally, the designed antenna’s second frequency range was unaffected by the variation of L₁; however, the second resonant frequency in this band was shifted from 7.04 GHz to 6.65 GHz. It was shown that the optimum value of L₁ was 18.6 mm.

Figure 7d depicts the simulation outcomes of the reflection coefficient S₁₁ based on several values of the second stub length L₂ (3, 3.25, 3.5, and 3.75). It can be noticed from the figure that the decrement in the value of L₂ improved the second band’s impedance bandwidth from 2400 MHz (4.9–7.3 GHz) to 2610 MHz (4.69–7.3 GHz). Contrastingly, by decreasing the value of L₂, the impedance bandwidth of the first band increased from 1760 MHz (2.28–4.04 GHz) to 2040 MHz (2.26–4.3 GHz). Additionally, the length of L₂ had no influence on the third frequency range. The optimum value of L₂ was 3.25 mm.

Figure 8a illustrates the impact of the third stub length L₃ on the S₁₁. This length’s range was between 6.5 mm and 8 mm. The plot reveals that the value of L₃ did not affect the impedance bandwidth of the three acquired bands. Nonetheless, it did shift where the resonant frequencies of the third band were located. Additionally, it was discovered that the impedance matching at the resonant frequencies was excellent at L₃ = 6.5 mm.

The impact of changing the first slit L₄ on the designed antenna’s reflection coefficient S₁₁ is seen in Figure 8b. When L₄ was stepped up by 0.5 mm from 1.75 mm to 3.25 mm, the resonant frequency in the second band was shifted from 6.96 GHz to 6.65 GHz but the impedance bandwidth of the suggested antenna was unmodified. Further, the figure shows that the value L₄ = 3.25 mm offered good impedance matching at operating frequencies.

The variation of the reflection coefficient S₁₁ is displayed in Figure 8c for several values of the second slit’s length L₅ (5, 5.5, 6, and 6.5 mm). The increase in the value of L₅ shifted the operating bands to lower frequencies. Moreover, the bandwidths of the second and third bands broadened from 1920 MHz (5.38–7.3 GHz) and 1687 MHz (9.46–11.147 GHz) to 2400 MHz (4.9–7.3 GHz) and 1877 MHz (9.27–11.147 GHz), respectively. As a result, it was clearly seen that L₅ = 6.5 mm was the optimal value for the second slit’s length.

A simple parametric study of the third slit length L₆ gave us the results displayed in Figure 8d. By varying L₆ from 1.75 mm to 3.25 mm, it was keenly noticed that the bandwidth of the third band was improved and shifted to a lower frequency from 1130 MHz (10.77–11.9 GHz) to 1877 MHz (9.27–11.147 GHz). Additionally, the second band impedance matching was improved while the first band was still unchanged when L₆ was varied. The third slit’s optimum length was 3.25 mm.

Thus, we deduced that the designed antenna’s resonant modes were more sensitive to changes in the parameters L_g, L_f, W_f, L₁, L₂, L₃, L₄, L₅, and L₆. As a result, the suggested antenna was simple to construct and required few structural components to satisfy the specifications for LTE, RFID, Bluetooth, WLAN, WiMAX, 5G spectrum band, C-band, and X-band wireless communication applications.

4. Current Distribution

Figure 9 illustrates and clarifies the surface current distributions of the designed antenna at several resonant frequencies. From Figure 9a–c, it can be seen that the most current was concentrated in the Sierpinski hexagonal-shaped fractal radiating patch along with the modified ground plane and the feed line, which caused the first band from 2.26 to 4.3 GHz. Similarly, the current was mostly focused on the Sierpinski hexagonal-shaped fractal radiator, feed line, and ground plane at the second frequency band of 6.6 GHz, as depicted in Figure 9d. The current was also heavily concentrated on the radiating patch, the ground plane, the stubs, and the slits in the bottom side in the other frequency bands of 9.8 and 10.57 GHz, which contributed to the improvement of the impedance bandwidth from 627 to 1877 MHz, as shown in Figure 9e,f.

5. Experimental Results and Discussions

To highlight how well the suggested antenna design performed, simulation and measurement results are displayed in this section. Figure 10 displays the constructed prototype of the designed Sierpinski hexagonal-shaped fractal antenna’s front and back views. The comparison of the experimental and simulated reflection coefficient responses and the projection of an excellent agreement between them are illustrated in Figure 11. The measurement was performed using a VNA. There was a disparity between the measured and simulated results because of the environmental conditions, influences of SMA soldering, substrate quality, and inaccuracies in the fabrication.

Figure 11 shows that the designed antenna’s measurements will show three frequency bands with impedance bandwidths of 2240 MHz (2.19–4.43 GHz), 2960 MHz (4.8–7.76 GHz), and 3320 MHz (8.04–11.32 GHz), which make it easy to cover the required band: LTE 2300 (2.3–2.4 GHz), LTE 2500 (2.5–2.69 GHz), RFID (2.4 and 5.4 GHz), Bluetooth (2.4 GHz), 5G spectrum band (5.9–6.4 GHz), WLAN (2.4–2.485, 5.15–5.35, and 5.72–5.85 GHz), WiMAX (5.25–5.85 GHz), ISM (5.725–5.875 GHz), C-band (4–8 GHz), and X-band (8–12 GHz).

A radiation pattern explains how an antenna’s radio frequency signal power is dependent on the direction. It is a schematic illustration of how the radiated energy is distributed spatially in the desired direction. The radiation properties are measured in an anechoic chamber, as depicted in Figure 12. Figure 13a–c depicts a comparison between the simulated and measured 2D normalized radiation patterns at 2.4, 6.6, and 9.8 GHz in both the E- and H-planes. The investigated antenna displayed nearly omnidirectional patterns across the whole range of operative bands, thus identifying it as a viable option for multiband applications.

Figure 14 depicts the simulated and measured co-polar and cross-polar 2D radiation patterns in both the E-plane and H-plane. The cross-polarization decreased in the E-plane, from lowest to greatest resonances, and increased in the H-plane due to the presence of cross-field constituents in the lower part of the patch and feed line. It was demonstrated that when the frequency rose, the fractal antenna lost its omnidirectional pattern and produced a greater cross-polarization component in the H-plane as a result of the emergence of higher-order modes.

An antenna’s capacity to focus RF waves in a certain direction is defined by its gain. The gain is calculated based to the following equation:

$$G_{dB}=10\log \left(\frac{4\pi \eta A}{{\lambda }^2}\right)$$

(6)

where η, A, and λ are the efficiency, the physical aperture area, and the wavelength of the signal, respectively.

Figure 15 compares the outputs of the gain from the designed antenna’s simulation and measurement. Additionally, it should be mentioned that the antenna’s gains for 2.5, 6.6, and 9.8 GHz were 1.074, 4.19, and 4.01 dBi, correspondingly, whereas 1.71, 4.61, and 4.46 dBi were the simulated gains.

Figure 16 displays the radiation efficiency of the designed Sierpinski hexagonal-shaped fractal antenna as simulated and measured. It was observable that the three acquired bands’ average radiation efficiencies were 68.35, 64.15, and 62.7%, respectively.

Numerous elements, such as connector losses or the positioning of the antenna in the anechoic chamber, contribute to the discrepancy between simulation and measurement results.

Table 3. Summary of simulation and experimental results for the designed Sierpinski hexagonal-shaped fractal antenna.

	Simulated (CST)	Measured
fr	2.4 GHz 6.66 GHz 9.8 GHz	2.41 GHz 6.59 GHz 9.8 GHz
Operating band	2.26–4.3 GHz 4.9–7.3 GHz 9.27–11.147 GHz	2.19–4.43 GHz 4.8–7.76 GHz 8.04–11.32 GHz
Gain	1.71 dBi 4.61 dBi 4.46 dBi	1.074 dBi 4.19 dBi 4.01 dBi
Efficiency	75% 78% 68%	68.35% 64.15% 62.7%

gathers and summarizes the experimental findings as well as the simulation findings from the CST MWS simulator. From the table, it can be seen that the simulation and measurement findings were extremely similar. The significant difference between simulation and experimental findings’ impedance can be attributed to a number of factors, such as manufacturing tolerances, SMA connector losses, or the location of the antenna in an anechoic chamber.

Table 4. Comparison with previously released research studies.

Ref.	Substrate	Size (mm3)	Resonant Frequency (GHz)	Operating Band (GHz)	Gain (dBi)	Antenna Design
[2]	FR-4	50 × 50 × 1.6	3.6; 5.3	(2.48–6.7)	2.78; 5.32	Octagonal antenna with Vicsek fractal slots
[5]	FR-4	20 × 35 × 1.6	2.4; 3.8; 5.5	(2.36–2.45); (3.2–6.29)	1.5; 1.8; 3.38	CPW rectangular antenna with elliptical slot
[9]	FR-4	61 × 87.5 × 1.6	2.5; 3.8; 5.3	(1.8–2.9); (3.4–4.6); (5–5.6)	3.33; 0.38; 0.57	Sierpinski gasket fractal antenna
[10]	FR-4	40 × 40 × 1.6	3.8; 5.66; 8.3	(3.86–3.94); (5.96–7.38); (8.2–8.9)	0.1–0.2 1.9–2.8 0.1–2.8	Sierpinski carpet fractal antenna
[16]	FR-4	32 × 40 × 1.6	2.4; 3.1; 4.5; 6	(2.34–2.52); (3.07–3.59); (4.17–6.26)	1.6; 2.15; 2.75; 3.8	Annular ring-shaped fractal antenna
[18]	FR-4	32 × 32 × 1.6	3.5; 5.8; 7.4	(3.265–8.2)	-	Hexagonal Koch fractal antenna
[29]	FR-4	59 × 51 × 1.575	3.68; 4.72	(3.43–4.85)	6.3; 8.3	Bow-shaped fractal with SRR antenna
[30]	FR-4	34 × 34 × 1.6	2.4201; 5.802	(2.35–2.5); (5.74–5.85)	2.19; 5.74	Giuseppe Peano and Cantor Set fractal-shaped antenna
[31]	Rogers RT5880	30 × 30 × 0.508	2.4; 5.8; 27.5	(2.46–2.49); (5.0–6.3); (23–28)	3.55; 4.72; 5.85	Slotted conical antenna
[32]	FR-4	6 × 4 × 1.6	2.4; 5	(2.37–2.53); (4.9–5.9)	3.05; 6.4	Maze-shaped monopole antenna
[33]	FR-4	60 × 50 × 1.6	1.8; 3.5; 5.4	(1.73–1.86); (3.4–3.54); (5.2–5.45)	2.22; 5.18; 1.38	Two F-shaped monopole antennas
[34]	FR-4	30 × 30 × 0.8	5.5	(4.8–5.9)	2.5	L-shaped monopole and J-shaped DGS
[35]	FR-4	36.4 × 36.4 × 1.6	2.4	(2.33–2.54)	3.45	Slotted square antenna
This work	FR-4	24 × 30 × 1.6	2.41; 6.59; 9.8	(2.19–4.43); (4.8–7.76); (8.04–11.32)	1.074; 4.19; 4.01	Sierpinski hexagonal-shaped antenna

compares the operational properties, including size, resonant frequency, operating band, and gain, of the designed Sierpinski hexagonal-shaped fractal antenna with those of previous antennas published in the literature. The comparison table makes it abundantly clear that, when compared to other reported antennas, the created antenna occupied the least amount of space. Thus, in terms of compactness and bandwidth, the developed antenna performed better than certain prior reported antennas.

6. Conclusions

A tri-wideband Sierpinski hexagonal-shaped fractal antenna with the modified ground plane for wireless communication applications was proposed in this study. The investigated antenna operated in the frequency bands of 2.19–4.43 GHz, 4.8–7.76 GHz, and 8.04–11.32 GHz. Furthermore, the gains and radiation efficiencies were 1.074, 4.19, and 4.01 dBi and 68.35%, 64.15%, and 62.7%, respectively, at the resonance frequencies. The designed Sierpinski hexagonal-shaped fractal antenna also exhibited nearly omnidirectional radiation patterns in the E- and H-planes.

The developed Sierpinski hexagonal-shaped fractal antenna is the perfect solution for WLAN, WiMAX, ISM, LTE, RFID, Bluetooth, 5G spectrum band, C-band, and X-band applications because of its many advantages, which include its compactness, simple structure, and excellent resonance and radiation proprieties.