1 Introduction

Nowadays, both software and hardware parts of wireless communication systems for multiple applications are being enriched rapidly. Wideband and ultra-wide band planar microstrip patch antennas have become extremely popular due to their low profile, compactness, low cost, low weight, and simplicity of integration with any wireless device as compared to traditional wire antennas [1, 2]. A 5G communication system is able to provide several significant benefits, like seamless coverage, higher capacity, a higher rate, and lower latency than other previous generations. One promising 5G band for wireless systems has been projected around 3.5 GHz, jointly acknowledged as a sub-6 GHz band or mid-band (under 6 GHz). The mid-band provides a compelling amount of capacity and area coverage [3, 4]. With the demand for high mobility in the modern era, wireless cellular technology has developed step by step, like 1G, 2G, 3G, 4G, and 5G. Currently, researchers are also working on 6G. With the introduction of 5G technology, many smart services, including the Internet of Things (IoT), ultra-reliable low-latency communications (uRLLC), non-orthogonal multiple access (NOMA), massive machine-type communications (mMTC), and enhanced mobile broadband (eMBB) services, were added [5]. In the USA, 3.1–3.55 GHz and 3.7–4.2 GHz, in Europe, 3.4–3.8 GHz, and in China, 3.3–3.6 GHz and 4.8–4.99 GHz bands are regarded as suitable for 5G applications. Table 1 summarizes the spectrum coverage (the key frequency range) for 5G technology.

Table 1 Spectrum coverage for 5G technology [5]
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The multifunctional advantages provided by a smart phone, smart TV, tablet, or laptop are reducing day by day [6,7,8]. There are a lot of smart and fast services that are possible due to the use of high-speed embedded electronics within the devices [9, 10]. These advantages come from the deployment of compact planar antennas within the handy electronic devices [11, 12]. Some promising antennas are operating within the mid-band 5G, wireless local area network (WLAN) band, or world-wide interoperability for microwave access (WiMAX) applications [13, 14]. The planar antennas are widely deployed in 3G, 4G, 5G, WMAN, wireless fidelity (WiFi), and WiMAX applications for their robustness, light weight, cost effectiveness, dual polarization, support for multiband, and pinpoint management of radiation patterns [15]. Several researchers have proclaimed that an array antenna would be one of the best techniques for improving gain, and it helps to meet the requirement of good impedance matching [16]. In [17], a flexible CPW-fed transparent antenna is developed for sub-6 GHz and WLAN applications by using finite element method (FEM)-based HFSS software. The antenna uses a transparent and flexible PET substrate as well as AgHT-8 conducting material with an electrical size of 0.48λ × 0.64λ. Yerlikaya et al. [18] also designed a compact wideband antenna for sub-6 GHz mobile systems. It has a maximum gain of 2.3 dB, a low bandwidth of 0.8 GHz (3.4–4.2 GHz), and an efficiency of 73%. A FR4 (dielectric constant 4.4)-based 180 × 60 × 1.6 mm3 dual band antenna had been proposed for LTE-R and 5G communications [19]. The antenna possesses narrow bandwidths (0.13 GHz and 0.5 GHz). The authors in [20] have discussed a WiFi/5G antenna that is made by Rogers RT/Duroid substrate and whose dimension is 46 × 46 × 3.175 mm3 (0.37λ × 0.37λ). The bandwidths of the antenna are 0.1 GHz and 0.36 GHz. In [21], a high-volume (0.57λ × 0.57λ) stacked microstrip antenna working from 3.3 to 3.6 GHz has been designed. The reflection coefficient of the antenna is − 18.33 dB at 3.45 GHz. A planar antenna (40 × 30 × 1.6 mm3) with a bandwidth of 0.72 GHz and a maximum gain of 2.5 dB has been designed for 5G applications. The antenna resonates at 3.83 GHz, where the reflection coefficient is − 31.15 dB [22]. Another FR4-based multi-slotted 32.4 × 27.9 × 1.6 mm3 planar antenna is introduced in [23]. It possesses a total bandwidth of 0.019 GHz. It also provides a peak gain of 4.2 dB at 3.5 GHz and a reflection coefficient of − 26.5 dB. A FR-4 based multiband monopole antenna with a low gain (1.5–2 dB) and efficiency (around 80%) has been designed for futuristic wireless communications [24]. A low-profile and directive metamaterial antenna (60 × 40 mm2) for 5G, the Internet of Things (IoT), healthcare systems, and smart homes is composed of Rogers RO4350B, which has a maximum gain of 7.14 dB with good impedance matching and a standard VSWR [25]. Abdulbari et al. designed a Rogers/Duriod 5880 LZ-based T-shaped planar antenna (22 × 24 × 0.25mm3) with a fractional bandwidth of 42.81% at 3.6 GHz for 5G applications [26]. Therefore, from the above discussion, it is obvious that there is some room for further improvement of the antenna system for 5G and WMAN applications.

The prime aim of this work is to enhance bandwidth, gain, and efficiency with a compact volume. Two branches of hexagonal elements and three parasitic elements are introduced in the design to achieve the goal. At first, the design and optimization steps have been accomplished by using the CST-MWS suite, and then fabrication and measurement have been done in microwave laboratory. The information flow of the article is presented as follows: The design structure, fabricated prototype, and equivalent circuit of the hexagonal array antenna are described in Sect. 2. Then, the corresponding results, different parametric studies and analyses, as well as compatibility with some relevant works, are incorporated in Sect. 3. Finally, key findings and concluding remarks from the studies are presented in Sect. 4.

2 Design structure and evolution process

This section describes the designed structure and evolution steps of the proposed low-profile 10-hexagonal element array antenna with three parasitic elements and a DGS-based partial ground plane for 5G/WMAN applications. Among the three parasitic elements, two are placed on both sides of the main feeder, and one is placed at the top of the partial ground plane. A H-shaped slot is introduced in the partial ground plane. Figure 1a–c show the evolution process of the designed antenna, amplified hexagonal element, and fabricated prototype, respectively. Initially, two hexagonal elements are used and the performance is analyzed. Then, two elements have been added at every step for further improvement of the antenna's performance. Finally, the proposed antenna has 10 elements in total, which provides the best performance for the intended applications. A comparably lower-lossy dielectric material, Rogers RT5880 (2.2, 0.0009) with a thickness of 0.79 mm, is used for the design. The ground plane is made of copper (annealed) with a thickness of 0.035 mm. Initially, the dimensions of the design are estimated by the following formulas with equation numbers (1–4), then optimized to a suitable value [27]. The patch width (W) of the proposed antenna is determined by:

Fig. 1
figure 1

Proposed low-profile proposed 10-elements array antenna

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Patch width,

$$W_p = \frac{c}{2f_r }\sqrt {{\frac{2}{\varepsilon_r + 1}}}$$
(1)

where c = Velocity of light, fr = Resonance frequency and εr = Dielectric constant length,

$$L = 0.412h\frac{{\left( {\varepsilon_{reff} + 0.3} \right)\left( {\frac{W_P }{h}}+ 0.264 \right)}}{{\left( {\varepsilon_{reff} - 0.258} \right)\left( {\frac{W_P }{h} + 0.8} \right)}}$$
(2)

Antenna is prone to the fringing effect, which makes the antenna's patch appear electrically larger than its actual size. It is important to note that an increase in substrate height speeds up fringing and causes the feedline and resonance frequency to be farther apart.

Effective length,

$$L_{eff} = \frac{c}{{2f_r \sqrt {{\varepsilon_{reff} }} }}$$
(3)

and Patch length,

$$L_p = L_{eff} - 2\Delta L$$
(4)

Finally, the optimized volume of the low-profile hexagonal element array antenna is 35 mm × 25 mm × 0.79 mm. The antenna model contains 10 hexagonal patch elements, which are connected to two parallel branches. The length (G) and width (H) of the connecting strip of two branches are 16.2 mm and 1 mm, respectively. The feeder length (Lf) is 18.5 mm, and the feeder width (Wf) is 2.4 mm. The lengths of the four arms of trapezoid parasitic elements are 17 mm, 18.03 mm, 4 mm, and 10 mm, which are denoted as V1, V2, V3, and V4, respectively. A 50 Ω microstrip feedline technique is used to energize the proposed hexagonal element partial grounded array antenna.

From the amplified view of the hexagonal element as shown in Fig. 1b, the patch of 10-element array antenna is an irregular hexagon having six arms: A = 2 mm, B = 1.41 mm, C = 1.41 mm, D = 2 mm, E = 1.41 mm, and F = 1.41 mm. The length of the connecting strip of two successive hexagonal elements (I) is 1 mm, while the width of the connecting strip of two successive hexagonal elements (K) is 0.2 mm. The list of optimized parameters for the low-profile MPA is summarized in Table 2. The area of the ground plane is 18.5 × 25 mm2. In this research work, waveguide port excitation k = 8.55 is used during port creation, and the line impedance is adjusted to 50 Ώ. The estimated range of the excitation coefficient (k) is 4.64–8.68. The DGS-based ground plane is not only used to widen bandwidth but also to reduce antenna volume. Figure 2 shows an equivalent circuit diagram of the proposed antenna. A parallel combination of R1, C1, and L1 is replicated by the antenna's main feeder. Two trapezoid parasitic elements produce R2, C2, L2 and R3, C3, L3. The gaps between main feeder and trapezoid parasitic elements are represented by C4 and C5, respectively. Each hexagonal patch element of the proposed antenna is represented individually by a resistor (R4–R13), an inductor (L5–L14) and a capacitor (C8–C17). The gaps between sub-feeder and trapezoid parasitic elements are C6 and C7.

Table 2 Geometrical parameters
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Fig. 2
figure 2

Equivalent circuit of the antenna

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3 Results and analysis

Firstly, the design and optimization of the 10-hexagonal element array antenna have been accomplished by using a licensed CST-MWS suite. Thereafter, it is fabricated and measured in our microwave laboratory. The simulated and measured reflection coefficient curve of the low-profile 10-element array antenna is depicted in Fig. 3. It shows that the center frequency is 3.225 GHz and its working frequency range is 2.75–4.94 GHz. The 10-element array antenna has a good reflection coefficient of − 36 dB at 3.225 GHz and a wide bandwidth of 2.19 GHz. The designed low-profile array antenna covers the lower 5G (3.33–4.2 GHz), WWAN n48 CBRS (US) (3.55–3.7 GHz), WiMAX rel 2 (3.4–3.6 GHz), n77 (3.3–4.2 GHz, most European and Asian countries), n78 (3.3–3.8 GHz, USA), and n79 (4.4–5.0 GHz, China, Hong Kong, Japan, and Russia) bands. The S11 measurement setup at the microwave laboratory is presented in Fig. 4.

Fig. 3
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Reflection coefficient of the 10-elements array antenna

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Fig. 4
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|S11| measurement setup at microwave laboratory

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The equivalent circuit of the proposed antenna has been designed, optimized, and simulated by advanced design system (ADS) software. The reflection coefficient of the low-profile proposed 10-element array antenna and the response of its equivalent circuit have been compared in Fig. 5. From the comparison, it is obvious that both responses agree with each other. All the resistors, capacitors, and inductors have been adjusted to suitable values to get a similar response. The reflection coefficient and gain responses of the antenna during all five steps of the evolution process are recorded and presented in Figs. 6 and 7, respectively. By increasing the number of hexagonal elements in the array, the return loss reduces and the gain increases. In the case of 10-hexagonal elements, the resonant frequency is shifted to the left side, and it shows enhanced gain compared to the 8-element array antenna, which makes the antenna more suitable for our aforementioned intended wireless applications. The proposed 10-element antenna shows the best gain profile of all other evolution steps.

Fig. 5
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Reflection coefficient of the antenna and equivalent circuit of the antenna

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Fig. 6
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Impact of number of elements on reflection coefficient

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Fig. 7
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Impact of number of elements on gain

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The impact of the largest parallel arms, A and D, on the reflection coefficient of the proposed low-profile 10-element array antenna is illustrated in Fig. 8. It is clear to see that the operating frequency band is most suitable for the length of A = D = 2 mm. With an increase in the weights of A and D, the bandwidth becomes narrower, and at the same time, it increases the return loss. The antenna bandwidth increases, but the resonant frequency shifts to the higher frequency, and return loss increases with increasing both the width of the connecting strip of two successive hexagonal elements (K) and the length of the connecting strip of two branches (G), as presented in Fig. 9. Therefore, K = 0.2 mm and G = 16.2 mm are the best combination for our target applications. Similarly, feedline length and length of the 1st arm of the trapezoid parasitic element have also been studied in Fig. 10. The optimized values are Lf = 18.5 mm and V1 = 17 mm. It also ensures good impedance matching with a reflection coefficient of − 36 dB at 3.225 GHz. A slotted partial ground has been implemented in the proposed 10-element hexagonal patch array antenna, where the area of the partial ground layer is 25 mm × 18 mm. Lg = 18 mm is the best optimized value as presented in Fig. 11. The optimized DGS-based ground plane not only increases the bandwidth but also reduces reflection loss.

Fig. 8
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Impact of A and D on reflection coefficient

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Fig. 9
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Impact of K and G on reflection coefficient

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Fig. 10
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Impact of Lf and V1 on reflection coefficient

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Fig. 11
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Impact of Lg on reflection coefficient

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The maximum surface current is 107.931 A/m at 3.225 GHz, as presented in Fig. 12. The higher-current conducting regions are the lower part of the main feeder, connecting the strip line of two branches and connecting strips of two successive hexagonal elements. The impedance profile of the proposed 10-element hexagonal patch array antenna is depicted in Fig. 13. The impedance of the antenna is (49.80-j1.72) Ω at 3.225 GHz, which tends to have a pure resistive port impedance of 50 Ω. The gain and directivity of the 10-element array antenna are 2.5 dB and 3.2 dBi at 3.225 GHz, as presented in Fig. 14. The ranges of gain and directivity are 2.3–4.3 dB and 3.1–4.75 dBi, respectively, within the operating frequency of 2.75–4.94 GHz. From the E-field radiation pattern presented in Fig. 15 of the hexagonal patch elements array antenna, the main lobe magnitude is 7.39 V/m for ϕ = 0° and 7.31 V/m for ϕ = 90°, while the main lobe direction is 172° for ϕ = 0° and 178° for ϕ = 90° at 3.225 GHz. On the other hand, from the H-field pattern presented in Fig. 16 of the low profile array antenna, the main magnitude is 0.0196A/m for ϕ = 0º and 0.0194A/m for ϕ = 90º, whereas the main lobe direction is 172° for ϕ = 0º and 178° for ϕ = 90º. By applying the DGS-based partial ground technique and parasitic elements simultaneously, the side lobe levels are reduced. The 3 dB angular beam width is 84.7° and the side lobe level is − 1.1 dB at ϕ = 0° and 3.225 GHz for both fields.

Fig. 12
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Current distribution

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Fig. 13
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Impedance of the 10-elements array antenna

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Fig. 14
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Gain and directivity of the 10-elements array antenna

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Fig. 15
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E-field of the 10-elements array antenna

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Fig. 16
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H fields of the 10-elements array antenna

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The radiation efficiency is the ratio of gain to directivity (G/D), i.e., ηrad = G(dB)–D(dB). Antenna efficiency represents the standard of having the ability to radiate power into free space. Figure 17 depicts the radiation efficiency of the proposed low-profile 10-element hexagonal patch array antenna. The efficiency never drops below 86.23%. It varies from 86.79 to 92.14% (simulated) and from 86.23 to 91.48% (measured), and it is 89.48% (simulated) and 90.59% (measured) at 3.225 GHz. The maximum radiation efficiency of the prototype low-profile MPA is 92.14%. The value of the voltage standing wave ratio (VSWR) of a low-profile array antenna is 1.036 at 3.225 GHz, which is close to unity, and 1 < VSWR < 2 within the whole operating band of 2.75–4.94 GHz, as presented in Fig. 18. Therefore, it clarifies good impedance matching because an antenna’s impedance matching is essential to transferring maximum power.

Fig. 17
figure 17

Efficiency of the 10-elements array antenna

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Fig. 18
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VSWR of the 10-elements array antenna

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A comparison between some relevant recently published works and our presented work is depicted in Table 3. Due to the use of the low-loss dielectric material Rogers RT 5880, which has a thickness of 0.79 mm, the antenna possesses a higher efficiency of 92.14% with great gain stability within the whole operating frequency range of 2.75–4.94 GHz. The main contribution of this work is the bandwidth and efficiency enhancement of the antenna and keeping the antenna size compact. Though the area of the antenna in [28] is comparatively smaller, its bandwidth and efficiency are too small compared to our proposed 10-element array antenna. The proposed compact 10-element hexagonal patch array antenna provides the highest bandwidth of 2.19 GHz as well as the highest efficiency of 92.14% of all the papers mentioned in the comparison table. It also ensures compactness (0.32λ × 0.23λ) and a maximum gain of 4.3 dB with a very low VSWR of 1.036. Therefore, the designed low-profile array antenna is more suitable for the intended 5G/WMAN.

Table 3 Comparison table
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4 Conclusion

In this article, a 10-element hexagonal patch compact array antenna (691.25 mm3) with a H-shaped slotted partial ground plane is designed and tested practically. The obtained outcomes demonstrate the potential of the prototype antenna to comply with 5G/WMAN applications allocated by the Federal Communications Commission (FCC). The − 10 dB bandwidth of the prototype antenna is 2.19 GHz, with a good reflection coefficient of − 36 dB at 3.225 GHz. The VSWR over 2.75–4.94 GHz satisfies 1 < VSWR < 2. The introduction of parasitic elements and the increment of the number of hexagonal patch elements in the array enhance the gain and directivity of the antenna. Other different parametric studies, such as the impact of the length of the largest parallel arms of hexagonal elements, the length of the partial ground, the length of the main feeder, the width of the connecting strip of two successive hexagonal elements, the length of the connecting strip of two branches, the height of trapezoidal parasites, etc., have been studied in detail. Due to the properties of huge bandwidth, simplicity, compactness, high gain, massive efficiency, very good extensive parametric studies, and the agreement between simulation and experimental results of the fabricated 10-element antenna prototype, it could be deployed as a good competitor for high-speed 5G/WMAN applications.