1 Introduction

The 5th generation (5G) of mobile wireless telecommunication systems plays an important role to introduce greater capacity than the existing 4G systems. Therefore, the millimeter wave is considered a good candidate for the next 5G mobile network. The FCC preserved a frequency range from 25 to 70 GHz for 5G communications [1, 2]. These wide frequency bands attract antenna researchers to design suitable antennas with good specifications to meet the 5G requirements and the 28/38 GHz bands are considered the promising choice for 5G cellular communications [3]. The antenna operation at these bands is needed to be used in a single system, also the sub-6 GHz has been used in 5G communications [4]. The millimeter-wave frequencies are facing path-loss attenuation and atmospheric absorption. So, single antenna usage is a challenging task [5]. To undertake this problem, high gain and wide bandwidth antennas are used [6]. As well as, the quality of transmission can be enhanced by using MIMO technology [7].

MIMO is used to increase the channel capacity of a radio link by using multiple transmitting and receiving antennas to avail the multipath effect [8,9,10]. MIMO systems presented highly large data rates and high spectral efficiency [11]. The technology offers benefits that help to meet the challenges of both the weakness in the wireless channel (multi-path fading) as well as the resource constraints [12]. Therefore, the utilization of multiple antennas in both transmitting and receiving stages with low mutual coupling between them has a constructive effect on the overall behavior of wireless telecommunication systems like channel capacity, data rates, coverage, and reliability [13,14,15,16]. MIMO antennas should have high isolation, high gain, low correlations, and high radiation efficiency [3]. In [9], two and four elements of dual-band 28/38 GHz MIMO antennas are discussed with I-shaped slots in the patch. Two elements 28/38 GHz with the tapered radiator in a semicircular shape are investigated in [17]. In [18], two elements monopole MIMO antenna worked at 27/39 GHz is introduced. In [19] wide band from 22.5 GHz, up to 50 GHz using a two-element slots antenna is proposed. A slotted patch with circular polarized two elements 28/38 GHz MIMO antenna is demonstrated in [20]. In [21], two elements for 4G from 5.29 to 6.12 GHz and 4 elements for 5G from 26 to 29.5 GHz are investigated. Four ports MIMO antennas with defected ground structures operated from 25.1 and 37.5 GHz are proposed in [8]. A wide band of eight elements worked from 27.4 to 28.23 GHz is presented in [22]. In [23], a four inverted F elements MIMO antenna operated at 28/37 GHz is discussed. The two elements MIMO antenna with substrate integrated waveguide (SIW) cavity-backed operated at four frequency bands is presented in [24].

In this paper, a 2-port MIMO slot antenna operated at 28/38 GHz for 5G network wireless systems with low mutual coupling is introduced. Furthermore, this work presents the impedance and radiation characteristics, as well as the diverse behavior of the proposed model of a 2 × 2 MIMO antenna, the simulation outcomes, are achieved using CST microwave studio and verified by a higher frequency structure simulator (HFSS). The work is divided into four steps. First, the design of a single crescent monopole element and its analysis of parametric study to obtain the dual-band behavior at the desired frequency bands are investigated. Second, the structure of the 2-port multiple-input multiple-output MIMO arrangement based on the designed single crescent monopole is analyzed. Third, the demonstration and the analysis of the simulation and measurement results are presented. Finally, the MIMO antenna's diverse behavior is demonstrated to investigate the effectiveness of the suggested antenna for MIMO applications.

2 Antenna Configuration and Design Procedures

The 2-D configuration of the single element mm-wave slot antenna is presented in Fig. 1. The suggested antenna is mounted on Rogers (RO4003) substrate with thickness = 0.203 mm, εr = 3.55, and tan δ = 0.0021 as in [25, 26]. The total area of the antenna (W × L) = 15 × 15 mm2. The single-element slot antenna consists of a rectangular slot with WGs = 5.6 mm and LGs = 3.9 mm etched from the back side (ground plane) and is fed by a microstrip transmission line of width WF = 0.8 mm to achieve the desired 50 Ω impedance. The microstrip line on the front side is loaded with a small stub (with Ws = 1.25 mm and Ls = 0.8 mm) and a small Crescent with an outer radius (ro = 1.3 mm) and inner radius (ri = 0.9 mm) to generate the desired dual bands and to improve the impedance matching.

Fig. 1
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The millimeter-wave antenna configuration (a) Top view (b) Bottom view

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The design procedure evaluations of the mm-wave slot antenna are investigated in Fig. 2. There are three steps for antenna design (antenna 1, antenna 2, and the proposed mm-wave antenna 3) to achieve the desired requirements. Antenna 1 as shown in Fig. 2a is considered the initial step of the millimeter-wave antenna, which is composed of a slot antenna using a microstrip transmission line feeding method by proximity 50 Ω TL. The simulated S11 results shown in Fig. 3 show that antenna 1 has three resonance modes at 28, 38 GHz with return loss S11 equals around −7 dB (matching not good) and S11 less than −10 dB from 45 GHz up to 50 GHz (good matching). To enhance the matching impedance at 28 and 38 GHz, a small tuning stub as shown in Fig. 2b is added (antenna 2). The antenna 2 has a dual-band with an S11 less than -10 dB from 25 to 30.5 GHz and from 36 to 40 GHz. Finally, a small Crescent is added as shown in Fig. 2c (antenna 3) to enhance the impedance matching. The introduced antenna 3 has return loss S11 less than −10 dB from 25.5 to 30.5 GHz (1st band) and from 35.5 to 40 GHz (2nd band).

Fig. 2
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The design procedures of the mm-wave antenna (a) Antenna 1 (b) Antenna 2 (c) Antenna 3 (d) Bottom view of all antennas

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Fig. 3
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The simulated S11 of the three millimeter-wave antennas

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Several parameters can affect the antenna performance. So, parametric studies to present the effects of these parameters are investigated as depicted in Figs. 4 and 5. As shown in Fig. 4, the stub position “g” and stub length “Ws” can affect the bandwidth and the matching impedance of the proposed antenna. As shown in Fig. 4a when the stub position is changing from 0.1 to 0.3 mm, the matching of the second band can be affected so the best position is optimized to 0.2 mm to cover the desired bands. Moreover, the stub length “Ws” can affect the matching and the bandwidth of both the first and second bands as depicted in Fig. 4b, hence the optimized length equals 1.25 mm.

Fig. 4
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The S11 performance of mm-wave antenna (a) for various stub positions “g” (b) for various stub lengths “ws”

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Fig. 5
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The S11 performance of mm-wave antenna (a) for various inner radii of the crescent “ri” (b) for various ground slot widths “wGs”

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The effects of the inner radius “ri” and slot width “WGs” on the antenna performance are shown in Fig. 5. Figure 5a presents the effect of changing the inner radius “ri” from 0.8 to 1 mm on impedance matching and bandwidth of both first and second bands. The value of the inner radius is optimized to be 0.9 mm. Finally, when the ground slot width “WGs” is changed from 4.6 to 6.6 mm, the S11 performance (bandwidth and impedance matching) is clearly affected as presented in Fig. 5b. The optimized value of the WGs equals 5.6 mm for good performance. After the parametric studies are carried out, the optimized dimensions of the proposed mm-wave antenna are declared in Fig. 2, and to validate its performance, the suggested model is fabricated.

The investigated dual-band antenna (antenna3) is fabricated as illustrated in Fig. 6 and the reflection coefficient S11 is experimented with using Vector Network Analyzer (VNA) (Rohde & Schwarz ZVA 67). The commercial end launch 1.85 mm connector is used in the measurements process. So, two holes are drilled as shown in the fabricated model of Fig. 6. Moreover, Fig. 6 illustrates the simulation and experimental S11 results with an achieved dual-band with an S11 less than −10 dB from 25.5 to 30 GHz and from 35 to 40 GHz. Also, the simulated and the experimental outcomes have good agreements with slight shifts due to the tolerance of the manufacturing process.

Fig. 6
figure 6

The S11 experimental and simulation results and antenna fabricated photo (top and bottom)

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3 The 2-Element MIMO Antenna

3.1 MIMO Antenna Structure

According to the previous discussion of the suggested single antenna (antenna 3), the 2-elements operated at mm-wave are printed together on the two sides of the same substrate as illustrated in Fig. 7. The first antenna is added on the upper layer of the substrate, however, the second antenna is added on the lower layer of the substrate and aligned in the opposite direction of the first one. The size of the innovative model of the MIMO antenna is (30 mm × 15 mm) assuring its compactness. It is worth noting that the dimensions of each one of the two elements are the same as the previously designed single antenna (antenna 3). The decoupling structures aren’t added between the antenna elements to keep the configuration as simple and compact as possible. The top view and bottom view fabricated photos of the mm-wave MIMO antenna are depicted in Fig. 7.

Fig. 7
figure 7

The proposed 2-D arrangement with the fabricated photos of 2-elements dual-band 5G MIMO antenna (a) Front view (b) Back view

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3.2 The S-Parameters and Current Density Distributions

The two elements MIMO mm-wave antenna are fabricated and tested using (Rohde & Schwarz ZVA 67) as introduced in Fig. 8. It can be noticed that the S-parameters (S11 and S21) are measured to assert the simulated results. Additionally, The S11 and S21 are only displayed in Fig. 8 because of the symmetry of the suggested configuration (S11 = S22, S12 = S21). It can be noticed from Fig. 8 that the simulation results have S11 less than −10 dB from 25.5 to 30.5 GHz and from 35.5 to 40 GHz, and the S21 result is less than −31 dB within the desired two bands. Furthermore, the measured results have S11 less than −10 dB at the first band (25.5–30 GHz) and the second band (35–40 GHz), and the S21 result is lower than -31 within the designed two bands. Finally, the simulated results mimic the experimental ones with a few mismatches due to the tolerance in the fabrication procedures.

Fig. 8
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The measured and simulated (S11, S21) of a 2-element dual-band 5G MIMO antenna

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The simulated current density distributions at 28 GHz (center of the first frequency band) and 38 GHz (center of the second frequency band) are shown in Fig. 9. The current is calculated at port 1 when port 2 is terminated with 50 Ω. It is noticed that at 28 GHz, the current is focused around both the radiator, the stub, and the crescent as displayed in Fig. 9a, while the distribution of surface current density is concentrated around the radiator at 38 GHz as depicted in Fig. 9b. Also, there is a weak current coupled to port 2 which confirms the high level of isolation between the two ports.

Fig. 9
figure 9

The current distribution of the MIMO antenna (a) @28 GHz (b) @ 38 GHz

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3.3 Radiation Patterns of the MIMO Antenna

The simulated 3-D radiation patterns of the innovative model of mm-wave MIMO antenna at 28 and 38 GHz are shown in Fig. 10. The antenna at 1st port is excited while the 2nd port is ended with 50 Ω and vice versa. The suggested antenna has a gain of around 7 dBi with bi-directional radiation patterns at both frequencies. It can be noticed from the radiation patterns at each frequency that there is a phase difference of 180° when exciting each of the two orthogonal ports which emphasizes the diverse behaviour of the proposed MIMO antenna. Figure 11 presents the simulated peak gain of the suggested MIMO mm-wave antenna at port 1. The antenna has peak gain that varies from 5.5 dBi to 6 dBi at the first band (25.5–30.5 GHz) and from 6 dBi up to 7.5 from the second band (35.5–40 GHz).

Fig. 10
figure 10

The radiation patterns (3-D simulation) of the MIMO antenna (a) at port 1 (b) at port 2

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Fig. 11
figure 11

The simulated peak gain of the MIMO antenna

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Figures 12 and 13 illustrate the E and H planes co and cross-polarization radiation patterns (simulated) of the innovative MIMO antenna at 28 and 38 GHz. The simulated results only are provided because of the unavailability of measuring mm-wave antennas (from 28 to 40 GHz) in our labs at this time. The 1st port is excited while the second port ended with 50 Ω and vice versa. It is observed that the proposed antenna has almost dipole-like radiation patterns in co-polarized E and H planes at both 28 and 38 GHz. The level of the cross-polarization of the E-plane is high, especially at 28 GHz for both ports. However, it has a low level at 38 GHz as depicted in Figs. 12b and 13b. This is due to the concentration of the current around the stub, which is perpendicular to the basic radiation current direction as illustrated in Fig. 9.

Fig. 12
figure 12

The radiation patterns of MIMO antenna when port 1 is excited (a) @ 28 GHz (b) @ 38 GHz

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Fig. 13
figure 13

The radiation patterns of MIMO antenna when port 1 is excited (a) @ 28 GHz (b) @ 38 GHz

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4 MIMO Performance Results and Discussions

This section introduces the investigation of three important parameters as ECC, DG, and finally, CCL to judge MIMO system performance.

4.1 ECC of the MIMO Antenna

The ECC calculates the linkage between the MIMO antenna elements. The ECC can be calculated and extracted from S-parameters by permitting a uniform multipath environment as [27, 28]:

$$ECC = \rho_{e} = \left| {\rho_{ij} } \right| = \frac{{\left| {{\text{S}}_{{{\text{ii}}}}^{ * } {\text{S}}_{{{\text{ij}}}} + {\text{S}}_{{{\text{ji}}}}^{ * } {\text{S}}_{{{\text{jj}}}} } \right|^{{2}} }}{{\left( {{1} - \left( {\left| {{\text{S}}_{{{\text{ii}}}} } \right|^{{2}} + \left| {{\text{S}}_{{{\text{ji}}}} } \right|^{{2}} } \right)} \right)\left( {{1} - \left( {\left| {{\text{S}}_{{{\text{jj}}}} } \right|^{{2}} + \left| {{\text{S}}_{{{\text{ij}}}} } \right|^{{2}} } \right)} \right)}}$$
(1)

The acceptable edge of the ECC is lower than 0.5 according to Ref [28]. Figure 14 shows the ECC performance results (measured and simulated) extracted from Eq. (1). The ECC has a value less than 0.0002 within the first and the second bands respectively. The ECC simulated result has a good agreement with the measured result and has low values which means good MIMO antenna performance.

Fig. 14
figure 14

The ECC simulation and measurement of 2-elements dual-band mm-wave MIMO antenna

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4.2 DG of the MIMO Antenna

The DG is related to the ECC by applying Eq. (2) [29].

$$DG=10*\sqrt{1-\left|ECC\right|}$$
(2)

The DG performance results are calculated and shown in Fig. 15. The DG approximately equals about 10 dB within the dual bands (25.5–30.5 GHz and 35.5–40 GHz).

Fig. 15
figure 15

The DG measured and simulated of 2-elements dual-band mm-wave MIMO antenna

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4.3 CCL of the MIMO Antenna

Finally, the CCL(Bit/S/Hz) is the 3rd parameter to evaluate the MIMO antenna behavior. It can be defined as the rate of transmitted data through the communication channel [29]. The matrix of the correlation coefficient can be used to evaluate the CCL as in Eqs. (3), and (4). The acceptable range of the CCL is less than 0.4 Bit/S/Hz [30].

$$C\left( {Loss} \right) = - \log_{2} \det (\psi^{R} )$$
(3)
$$\psi^{R} = \left[ {\begin{array}{*{20}c} {\rho 11} & {\rho 12} \\ {\rho 21} & {\rho 22} \\ \end{array} } \right],\rho_{ii} = 1 - \left( {\left| {S_{ii} } \right|^{2} + \left| {S_{ij} } \right|^{2} } \right)\;{\text{and}}\;\rho_{ij} = - \left( {S_{ii}^{*} S_{ij} + S_{ji}^{*} S_{ij} } \right),\;for\;i,\;j = 1\;or\;2$$
(4)

Figure 16 illustrates the CCL performance results (simulated and measured) extracted from Eqs. (3), and (4). A value less than 0.4 bit/s/Hz is achieved within the operated two bands.

Fig. 16
figure 16

The CCL simulation and experimental results of the dual-band mm-wave MIMO antenna

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Table 1 is constructed to compare our work with the cases of other works to evaluate the performance of our MIMO antenna. It is evident that our presented model MIMO antenna system has a compact size, low mutual coupling, and high MIMO behavior which permits the antenna to be appropriate for 5G networks.

Table 1 The suggested mm-wave MIMO antenna in comparison with other reported designs
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5 Conclusion

The two slot antenna elements built-in highly isolated MIMO antenna with dual-band in mm-wave frequency range have been suggested in this work for 5G wireless application. The proposed model of the MIMO antenna has a consolidated size of 30 × 15 mm2 and can be simply manufactured. The simulation and measured outcomes have been conducted to assure the desired behavior. The MIMO antenna has experimental return loss S11 less than −10 dB at the first band (25.5–30 GHz) and the second band (35–40 GHz), and the isolation coefficient S21 result is lower than -31 within the designed two bands. Also, it achieved a reasonable gain that reaches (5.7, and 6.9 dBi) in the 28/38 GHz bands, respectively. As well as, the ECC, DG, and CCL achieved about 10–4, 10 dB, and less than 0.3bit/s/Hz, respectively over the two achieved frequency bands. Finally, the aforementioned results confirm the possibility of adopting the suggested innovated MIMO antenna for operation in 5G wireless systems at 28/38 GHz.