1 Introduction

As the Vivaldi antennas have a lot of merits, including high gain, high efficiency, enhanced beamwidth, stable radiation pattern, low sidelobe level, and compact size, it is a good candidate for the operation in the millimeter- (mm) wave band for 5G mobile communications [1]. The ability to achieve high stable gain over a wide bandwidth makes them suitable for several applications. These applications include ultra-wide-band (UWB) communication [2], ground penetrating radar (GPR) [3,4,5], medical applications [6, 7], and 5G devices [8]. Several techniques have been suggested to improve the Vivaldi antenna gain. These techniques include corrugation on the outer edge of antenna flares [9], parasitic element placement between the two antenna flares [10], utilization of dielectric lens [11], metamaterial modeling [12], antenna array arrangement [13], and utilization of substrate integrated waveguide (SIW) [14].

Many researchers introduced Vivaldi antennas with multiple bands. In [15], a triple-band Vivaldi antenna is presented working at 3.8 GHz, 5.2 GHz, and 8 GHz with frequency bandwidths of 1.6 GHz, 1.2 GHz, and 1 GHz, respectively. The final antenna structure consists of a combination of a vertical polarized antipodal Vivaldi antenna and a horizontal polarized spiral antenna. A metamaterial model is exploited to enhance the coupling between four multiple-input multiple-output (MIMO) antenna elements with overall dimensions of 60 × 100 mm2. The antenna achieved maximum gain levels of 13.5 dBi, 9.5 dBi, and 6.75 dBi at the three bands, respectively. The authors of [16] proposed a multi-band antipodal Vivaldi antenna having the bandwidths 14.44–20.98 GHz, 24.34–29 GHz, and 33–40 GHz. An array of eight antenna elements is printed over a substrate with dimensions of \(33.31 \times 54.96 \times 0.787\) mm3. The maximum gains of the 8-element antenna are 10.5 dBi, 11.5 dBi, and 10 dBi at 18 GHz, 28 GHz, and 38 GHz, respectively. In [17], an array of 4-element Vivaldi antennas are arranged on a substrate length of 97.2 mm × 71.2 mm × 0.8 mm to operate at 24.59–24.98 and 27.06–29 GHz bands and gain about 8–12 dBi.

Vivaldi antennas with wide bandwidth have captured the attention of many researchers. A slotted antipodal Vivaldi antenna with dimensions of 70.5 × 37 × 1.5 mm3 was presented in [18]. It has an operating band from 3.29 GHz to more than 45 GHz and a gain of 7.7–11 dBi. The authors of [19] presented a Vivaldi antenna based on the parasitic element concept, with a wide frequency band ranging from 6 to 26.5 GHz and a gain of 9 dBi. This antenna has a large size of \(140\times 66\times 1.5\) mm3. In [20], a Vivaldi antenna with dimensions of \(66\times 110\times 1.575\) mm3 was presented. The authors of [20] adopted a parasitic patch with a trapezoidal shape to improve the antenna gain. The maximum achieved gain is 9 dBi over the operating frequency range of 6 to 26.5 GHz. The authors of [6] presented a Vivaldi antenna with a wide operating bandwidth of 4.2 to 50 GHz. The antenna consists of a conventional Vivaldi structure sandwiched between two dielectric slabs with a fractal shape. The overall antenna size is \(122 \times 66 \times 7.692\) mm3. Its large size makes it unsuitable for 5G mobile applications, which need more compact antennas. In [21], Dixit and Kumar presented a very compact antipodal Vivaldi antenna with dimensions of \(10\times 5\times 0.8\) mm3 and an operating frequency of 20.72 to 45 GHz. Unfortunately, the maximum achieved gain is about 5.22 dBi, which makes this antenna unsuitable for high-loss mm-wave environments. In [22], an antipodal Vivaldi antenna with dimensions of 24 mm × 50 mm × 1 mm and an operating frequency of 24 to 30 GHz was presented. The antenna gain ranges between 10.9 and 13.82 dBi.

The utilization of the mm-wave frequencies satisfies the high demand for high-speed communications. Among the mm-wave frequencies, the 28-GHz frequency has captured the interest of many researchers to allow a wide bandwidth and a high data rate. Moreover, the 28-GHz frequency band has a low absorption rate compared to that of other bands [23]. Hence, 28 GHz is a good choice of 5G mobile communications. In [24], the authors introduced an antipodal Vivaldi antenna with regular edge slots to operate in the frequency range from 4 to 30 GHz with a maximum gain of about 5 dBi. The antenna dimensions are 50 × 66.4 × 1 mm3. In [25], the authors presented a compact wideband antipodal Vivaldi antenna that operates in the range of 22.5 to 45 GHz with dimensions of 5.5 mm × 12 mm × 0.254 mm. It achieved a gain that is more than 5 dBi.

The MIMO Vivaldi antenna with pattern diversity offers a good merit for the wide angular coverage required for 5G wireless communications. A little work has been presented for achieving pattern diversity with Vivaldi antenna. The authors of [26] presented a Vivaldi antenna with pattern diversity for UWB applications. In [27], the authors presented an all-metal Vivaldi antenna with pattern diversity for mm-wave 5G access points. In [28], the authors presented a MIMO Vivaldi antenna with pattern diversity for mm-wave applications.

In this paper, a new procedure is invented to construct the arms of the Vivaldi antenna. The procedure is based on creating the arm structure from the intersection of two ellipses. The two constructed arms are printed on the two sides of a Rogers substrate and fed through a microstrip line through a waveguide region for impedance matching. Parasitic ring is added to each arm to enhance the gain.

The paper is organized in nine sections. Section 2 describes the multi-band Vivaldi antenna construction and design. Section 3 presents the performance of the multi-band Vivaldi. Section 4 describes modal analysis for the multi-band operation of the proposed Vivaldi antenna. Section 5 presents an optimization for the proposed Vivaldi antenna to operate at 28 GHz with wideband and high gain. Section 6 introduces a MIMO antenna system using the optimized Vivaldi for 28-GHz applications. Section 7 provides the results of the fabrication and measurements. Section 8 presents a comparison of the multi-band Vivaldi and the optimized Vivaldi with other published work. The conclusions of the work are summarized in Section 9.

2 Multi-band Vivaldi Design

It is possible to view the Vivaldi antenna as a radiating slot that has a varying width which increases as getting far from the feeding point. The two conducting arms on both sides of the slot are printed on the top and bottom sides of the dielectric substrate. For practical purposes, the two arms of the Vivaldi antenna are not extended to infinity; they are truncated to finite extent. In this way, the two arms can be considered two side plates of a coplanar structure. A new design criterion is used to construct each antenna arm from two ellipses, one vertical and another horizontal. The horizontal ellipse has a major axis of length \(2{a}_{v}\) which lies on the y-axis and minor axis of length \(2{a}_{h}\) which lies on the x-axis. The vertical ellipse has a major axis of length \(2{b}_{h}\) which lies on the x-axis and minor axis of length \(2{b}_{v}\) which lies on the x-axis. The horizontal ellipse has its long axis which lies on the short axis of the vertical ellipse and lies on the x-axis as shown in Fig. 1. The distance between the two centers of the ellipses is denoted \({X}_{S}\). A line at a distance \({W}_{A}\) from the y-axis truncates the antenna arm. The resulting arm shape is shown shaded in Fig. 1. The other arm is a copy of the resulting shaded shape.

Fig. 1
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Geometrical construction of one Vivaldi arm

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In this way, the two Vivaldi arms are constructed as shown in Fig. 2. One arm is printed on the top of the dielectric substrate and connected to the feeding microstrip line and the other arm is printed on the bottom side and connected to the ground plane as shown in Fig. 2. A twin waveguide region is employed to connect the microstrip feedline to the two antenna arms. This is done to improve the impedance matching. An annular ring is capacitively loaded to each arm of the Vivaldi antenna to enhance the realized gain.

Fig. 2
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a Top side of the dielectric substrate showing the right arm of the Vivaldi antenna connected to the feedline. b Bottom side showing the left arm connected to the ground plane

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The different dimensional parameters of the proposed Vivaldi antenna are shown in Fig. 3 assuming transparent substrate just for illustration. The impedance matching is improved through the twin waveguide region with length \({L}_{T}\) connecting the ground to the arms of the antenna. The best design parameters that result in the best antenna matching and gain are given in Table 1. The used substrate is Rogers RO3003 with \({\epsilon }_{r}=3\) and thickness 0.25 mm. The best design parameters are reached through electromagnetic simulations using the commercial available CST package.

Fig. 3
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The dimensional parameters of the proposed Vivaldi antenna presented with a transparent substrate to illustrate the top and bottom layers

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Table 1 Best design parameters of the proposed Vivaldi antenna
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3 Multi-band Vivaldi Antenna Performance

The proposed Vivaldi antenna has six operating bands within the millimeter-wave range. The antenna reflection coefficient is shown in Fig. 4 showing good impedance matching over the operating bands. It is clear that the proposed antenna design has six operating bands centered at 24.8, 34.7, and 44 and 54.2, 64.8, and 74.5 GHz. The corresponding bandwidths are 5.7, 5.5, and 5.1 and 1.8, 1.27, and 1.25 GHz, respectively, with percent bandwidths of \(23\%\), \(16\%\), \(11.6\%\), \(3.5\%\), 2%, and 1.7%, respectively. The maximum gain over each of the frequency bands is calculated numerically using the CST simulator and plotted in Fig. 5. It can be seen that the antenna achieves high gain that ranges from 6 to 11.5 dBi over all the operating bands.

Fig. 4
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The proposed multi-band Vivaldi antenna reflection coefficient

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Fig. 5
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Maximum gain over each operating frequency band

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The antenna is fabricated on flexible substrate RO3003. The effect of bending the antenna in both the x-direction and y-direction on its reflection coefficient is studied for different bending radii. The results are shown in Fig. 6. It can be seen that bending the structure on the x-axis affects the impedance matching greater than bending it on the y-axis.

Fig. 6
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Effect of bending the substrate for different bending radii in the a x-direction and b y-direction

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4 Modal Analysis of the Multi-band Vivaldi

The multi-band operation of the proposed Vivaldi antenna can be attributed to the formation of higher order modes at the higher frequency bands. This is depicted graphically in Fig. 7 where the surface current distribution over the conducting arms is plotted at different operating frequencies, namely, 25, 35, 45, and 55 GHz. It is clear from Fig. 6 that the formed surface current is first, second, third, and fourth order at 25, 35, 45, and 55 GHz, respectively. The electric field distribution within the tapered slot between the proposed Vivaldi arms is plotted in Fig. 8 showing the same order of modes, first, second, third, and fourth order at 25, 35, 45, and 55 GHz, respectively.

Fig. 7
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Surface current on the conducting arms of the proposed multi-band Vivaldi antenna at a 25, b 35, c 45, and d 55 GHz

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Fig. 8
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Electric field distribution within the slot between the two conducting arms of the proposed Vivaldi antenna at a 25, b 35, c 45, and d 55 GHz

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5 Antenna Optimization at 28-GHz Band

Definitely, the proposed Vivaldi antenna in Fig. 3 will not operate in the six bands at the same time for one application. In a realistic application, only one of the six operating bands is selected for operation. The proposed Vivaldi antenna is optimized to enhance the gain at 28 GHz and to increase the operating bandwidth. This is done by adjusting the dimensional parameters in Fig. 3 and adding two reflectors. The introduced reflectors are placed in front of the radiating tapered slot as shown in Fig. 9. Each reflector is constructed from three adjacent circles with diameter \({d}_{c}\). The antenna is fed through a vertical coaxial cable connected to the microstrip feeding line. The inner probe is soldered to the microstrip line and the outer probe is soldered to the ground plane. These modifications allowed the proposed Vivaldi antenna to achieve a gain of 10 dB at 28 GHz with a wide bandwidth of 6.1 GHz. The resulted reflection coefficient and maximum gain over frequency are shown in Figs. 10 and 11, respectively. The optimum design parameters are listed in Table 2. The directive radiation patterns of the modified Vivaldi antenna at different frequencies within the operating band, namely, 25, 28, and 30 GHz, are presented in Fig. 12 in the two principle planes, \(\theta =90^\circ\) and \(\phi =90^\circ\).

Fig. 9
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Optimized Vivaldi antenna for 28-GHz applications

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Fig. 10
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Frequency dependence of the reflection coefficient of the modified Vivaldi antenna

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Fig. 11
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Maximum gain versus frequency over the operating band of the modified Vivaldi antenna

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Table 2 Optimized Vivaldi antenna parameters for 28-GHz operation
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Fig. 12
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Radiation pattern of the modified Vivaldi antenna at 28 GHz in the planes a \(\theta =90^\circ\) and b \(\phi =90^\circ\)

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6 MIMO Antenna System with Pattern Diversity for 5G Mobile Applications

A MIMO antenna system is created with the proposed modified Vivaldi antenna to operate at 28 GHz for 5G mobile applications. The MIMO antenna is composed of four orthogonal antennas placed in cyclic form to provide the required pattern diversity. The proposed MIMO has square form with side length \({L}_{M}=4.5 {\text{cm}}\) as shown in Fig. 13. Good isolation between elements \(< - 30 {\text{dB}}\) is achieved due to the spatial orthogonality. The design is simple and compact-size and can be easily fabricated in a mobile phone board. The total MIMO size is 4.5 × 4.5 cm2. The proposed MIMO system shows good performance regarding the self-coupling where the reflection coefficients over the operating band of the modified Vivaldi antenna have not been affected from constructing the four-port MIMO. Also, the coupling coefficients between the different antennas is <  − 30 dB over the whole operating band. The different scattering parameters for the proposed MIMO are plotted in Fig. 14.

Fig. 13
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Proposed MIMO antenna system for pattern diversity at 28 GHz

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Fig. 14
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Scattering parameters for the proposed MIMO antenna system

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The placement of the antennas in the proposed MIMO has been selected to provide pattern diversity as shown from the radiation patterns at 28 GHz in Fig. 15 when each port of the MIMO is excited separately. It is clear that each antenna covers a sector of 90° from the \(360^\circ\) space. The MIMO performance regarding the envelope correlation coefficient (ECC) and the diversity gain (DG) is assessed numerically and illustrated in Fig. 16. It is clear in the figure that the antenna is very well behaved over the operating frequency band where the ECC < 0.001 and the DG is almost 10.

Fig. 15
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a Radiation pattern of the proposed MIMO system at \(\theta =90^\circ\) when each port is excited, (a) port 1, (b) port 2, (c) port3, and (d) port 4. b Radiation pattern of the proposed MIMO system at \(\phi =90^\circ\) when each port is excited, (a) port 1, (b) port 2, (c) port3, and (d) port 4

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Fig. 16
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a Envelope correlation coefficient. b Diversity gain of the proposed MIMO system

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It is worth noting that the ECC can be calculated from the radiated field as

$${\text{ECC}}=\frac{{\left|\underset{4\pi }{\overset{}{\iint }}\left[{\overline{F} }_{1}(\theta ,\phi )\bullet {\overline{F} }_{2}(\theta ,\phi )\right]\mathrm{d\Omega }\right|}^{2}}{\underset{4\pi }{\overset{}{\iint }}{\left|{\overline{F} }_{1}(\theta ,\phi )\right|}^{2}\mathrm{d\Omega } \underset{4\pi }{\overset{}{\iint }}{\left|{\overline{F} }_{2}(\theta ,\phi )\right|}^{2}\mathrm{d\Omega }}$$

where \({\overline{F} }_{1}\) and \({\overline{F} }_{2}\) are the radiated field patterns for antenna 1 and antenna 2, respectively, when only one antenna is excited.

7 Fabrication and Measurements

The designed Vivaldi antenna at 28 GHz is fabricated on Rogers RO3003 with thickness 0.25 mm for the experimental verification of the antenna behavior. The antenna in Fig. 5 is fabricated with the dimensions listed in Table 2. The fabricated prototype is then connected to the vector network analyzer (VNA) model N5244B from Keysight to measure the antenna reflection coefficient. The antenna is connected to the VNA through a soldered coaxial connector. The inner probe is soldered to the top Vivaldi arm and the outer clad is soldered to the ground plane and the bottom arm. The connection setup is shown in Fig. 17. The measured reflection coefficient is shown in Fig. 18, and in the same figure, the simulation results are plotted for comparison showing good agreement. It is clear from the figure that the measured operating band is between 24.7 and 31.6 GHz. The radiation pattern is also measured experimentally at 28 GHz using the setup in Fig. 19. A reference antenna LB-180400 with gain 15 dB is used as the receiving antenna and connected to the signal analyzer N9010A from Keysight. The antenna under test (AUT) is placed on a rotator and connected to the signal generator E8267D. The AUT is excited using the signal generator with a continuous wave at 28 GHz, 20 dBm power. The AUT is rotated by 10° and each new position the received signal at the signal analyzer is recorded. After complete rotation of 360°, the radiation pattern is plotted as shown in Fig. 20.

Fig. 17
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Connection of the fabricated Vivaldi to the VNA N5244B to measure the reflection coefficient

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Fig. 18
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Measured and simulated reflection coefficient of the proposed Vivaldi antenna for the 28-GHz applications

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Fig. 19
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Experimental setup for measuring the far-field pattern of the proposed Vivaldi antenna for the 28-GHz applications

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Fig. 20
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Measured and simulated far-field pattern at 28 GHz of the proposed Vivaldi antenna of Fig. 5 in the two principle planes a \(\theta =90^\circ\) and b \(\phi =90^\circ\)

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A prototype for the MIMO antenna system is fabricated and subjected to practical verifications. The fabricated prototype is shown in Fig. 21 with top and bottom views. The reflection coefficient for each antenna is measured and plotted in Fig. 22. It can be seen in the figure that the four antennas are matched over the operating frequency band. The coupling coefficient between each two antenna pair is also measured and illustrated in Fig. 23. It is obvious from the figure that the coupling is very weak <  − 30 dB.

Fig. 21
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Fabricated prototype of the proposed MIMO antenna system

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Fig. 22
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Reflection coefficient of each antenna in the proposed MIMO system

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Fig. 23
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Coupling coefficients between the Vivaldi antennas of the MIMO system

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8 Comparison with Published Work

In this section, the proposed multi-band Vivaldi is compared to other multi-band antennas from the point of view of the number of operating bands, bandwidths, gain, dimensions, and radiation efficiency. These comparisons are listed in Table 3. The modified optimized Vivaldi antenna for the 28-GHz operation is also compared to other published antennas operating in the same band regarding the bandwidth, the size, gain, and radiation efficiency. The comparisons are depicted in Tables 4 and 5.

Table 3 Comparison of the proposed multi-band Vivaldi and other multi-band antennas in recent publications
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Table 4 Comparison of the proposed wideband Vivaldi at 28 GHz with other published antennas around 28 GHz
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Table 5 Comparison of the proposed MIMO antenna system at 28 GHz with other published MIMO antennas
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9 Conclusion

A new design for Vivaldi antenna is introduced and investigated to operate in more than one frequency band in the millimeter-wave spectrum range with high gain. A parasitic annular ring is added to each arm of the Vivaldi antenna to adjust the impedance matching and maximize the gain at certain frequency bands. The dimensions of the antenna are optimized using the CST microwave simulator to obtain the best impedance matching bandwidths and highest gain in a compact size antenna. The 28-GHz band is selected due to its importance in future generation of mobile communications to enhance the gain and improve the operating bandwidth for the 5G applications. A gain of 10 dBi and bandwidth of 6.1 GHz are obtained at 28 GHz. A MIMO antenna system is designed for pattern diversity. The performance of the MIMO system is evaluated regarding the envelope correlation coefficient and the diversity gain showing good results. The optimized antenna is fabricated and its return loss and radiation patterns are measured showing good consent between the simulations and practical work. The MIMO antenna system is also fabricated and its performance is measured regarding the reflection and coupling coefficients showing good consent between the measurements and simulations.