1 Introduction

In [1], a compact monopole antenna is designed for UWB frequency. The proposed design with substrate dimensions 25 × 18 × 1.6 mm3 utilizes two kite-shaped elements in coalesced form with the tapered slotted ground. The parametric analysis of the kite-shaped patch and the tapered base is made, an Impedance Bandwidth (IBW) of 14.2 GHz is accomplished, and the gain is in the range of 2.28–5.0 dBi for the entire UWB. In [2], a hexagonal-shaped MIMO antenna is analyzed and studied, covering the S-band, WLAN, UWB, and X-band. The substrate used is FR4 with dimensions 0.18λ0 × 0.37λ0. The distance between the two patches is 0.053λ0. Triangular-shaped-edge-cuttings are made in the design bottom, and DGS is used. Isolation is enhanced by 20 dB with an E-shaped tree arrangement and parasitic elements. Various MIMO parameters like ECC, DG, and Total Active Reflection Co-efficient (TARC) are measured for the operating frequency bands. In [3], a compact Minkowski design for reducing MC in between two elements is analyzed. The proposed MIMO design, which resonates at 2.5, 3.5, 5.2, and 7 GHz frequencies, shows the reduction in MC with 54, 50, 40, and 44 dB at the resonating frequencies. In [4], the miniaturization of the antenna design with gain enhancement is proposed with Modified Minkowski Fractal DGS (M-MFDGS) for three patch antennas with different feeding techniques. The design with strip-line feeding provides 70% patch area reduction with a gain of 1.43 dBi.

The design with proximity-coupled feeding achieves a higher gain and bandwidth (5.11 dBi and 110 MHz). The design with aperture coupled feeding provides a gain of 5.91 dBi. In [5], a compact patch with M-MFDGS for 2.4 GHz WLAN application is proposed. Incorporating capacitive M-MFDGS, without changing the dimensions of the patch, the operating frequency is shifted from 4.16 GHz to 2.4 GHz. The design dimensions are 0.15 λ0 × 0.13 λ0, with IBW of 5.20%, and gain of 1.4 dBi centered at 2.41 GHz. This design is suitable for portable wireless applications.

In [6], a four-port monopole design is analyzed for MIMO applications. To enhance bandwidth, the structure is studied by making an arrow-shaped slot etched on the radiator and stepped ground. In [7, 8], a band-notched miniaturized Printed Log Periodic Dipole Array (PLPDA) with a meander fractal concept is proposed for wide-band applications. This concept is applied to all the elements in the PLPDA. Using the sub-sectional tapered concept, band notch characteristics are obtained in the WLAN band, WiMAX band, and a broad bandwidth with this meander fractal concept. The proposed design, fabricated on a RO3003 substrate, is best applicable for short-range, high-speed wireless communications. In [9], a modified radiating patch with high-gain broadband using a Poly tetra fluoro ethylene (PTFE) substrate is proposed. Dimensions for the design are 0.52λ0 × 0.51λ0. Gain and BW effects are analyzed using a slot and five slits on the proposed antenna element design. In [10], resistor-loaded paired parallel-coupled resonators (PCRs) are used for isolation enhancement in MIMO elements. The spacing between array elements is 0.125λ0, and isolation greater than 25 dB is achieved within the UWB.

In [11], to achieve better data rates with enhanced gain for the 5G communications, the antenna design is made with a substrate, Polymethacrylate. This substrate provides a high gain compared to all the other substrates used in the antenna design. A gain of 10.054 dB with a bandwidth of 80 MHz is achieved with this substrate. The patch antenna with this substrate is preferred for 5G cellular base station (BS) antenna for the frequency range of 3.3 GHz–3.7 GHz. These high gain antennas are designed with two simple techniques: Simple shorting pin and chip impedance shorting. The overall geometry of the patch antenna is reduced with a simple shorting pin technique with improved gain, and the narrowband effect can be minimized by implementing the chip impedance shorting method. The design with high gain is best suitable for 5G cellular communications. In [12], a novel design structure, Spiro Meander Line Uniplanar Compact Electromagnetic Band Gap (SMLUC-EBG), is presented. This design is proposed to minimize MC between elements for WLAN applications. The spacing between the elements is 0.14λ0, and isolation of 20.3 dB is achieved with the proposed design. In [13], a circular patch antenna for WLAN application is presented with an eroded ground plane, and it is electromagnetically coupled. The eroded ground plane minimizes the physical area of the circular patch and can be utilized for WLAN services. The miniaturized antenna provides excellent reflection characteristics at a 2.4 GHz frequency. In [14], a circular annular ring patch by embedding an Electromagnetic Band Gap (EBG) structure reduces surface waves. An M-shaped EBG is utilized on the ground with vias at the center of each EBG, and this EBG is inscribed in the 6 × 6 mm2 patch. This proposed design can be utilized for the Mobile Satellite Service (MSS) band, UMTS, and WCDMA. In [15], a dual-band patch for WLAN and WiMAX applications are presented with narrow vertical slots. The proposed antenna with two vertical slots resonates at 3.5 GHz WiMAX and 5.3 GHz WLAN bands. Particle Swarm Optimization (PSO) method is incorporated to optimize the proposed design dimensions. This design provides better radiation properties at the two bands, making it appropriate for dual-band implementation. In [16], threefold stubs are etched to reduce MC between elements. This design consists of two polyhedron annulus patch elements, threefold fork-shaped stubs (TFSS), a conventional dielectric substrate, and a microstrip line feeder. By using this TFSS, the performance parameters are improved. MC was improved by 42 dB when the TFSS and polyhedron annulus patch elements were introduced. In [17, 18], three patch antennas are designed with direct, proximity, and aperture coupled feeding for X-band portable applications by loading the M-MFDGS technique. The overall physical size of the patch with these feeding techniques and M-MFDGS reduces up to 67% and overall volumetric reduction of 84%. The gain of this proposed design is about 6.2 dBi at 10 GHz. In [19], a compact design with the partial ground and parasitic elements and a rectangular slot on the I-shape element is proposed. The FR-4 substrate dimensions of the proposed technique are 15 × 20 × 1.6 mm3. This design provides bandwidth enhancement. Simulated results show that the IBW was achieved at three resonant frequencies. This antenna design is suitable for Wi-Fi, WiMAX, and X band. In [20], a novel periodic defected ground structure of S-shape (PDGS) to reduce MC between elements is proposed with three S-shaped DGS structures placed between the elements, and the spacing is 50 mm. With this arrangement, a 40 dB reduction in MC is achieved. PDGS interrupts the far-field and induces current between the elements, and etched PDGS minimizes the surface current considerably within a restricted substrate area.

In [21], compact EBG integrated MIMO is proposed for WLAN and WiMAX to reduce MC between the elements, and the proposed design operates within the range 2.01–3.92 GHz. The proposed MIMO design has very low ECC, good DG, very low Channel Capacity Loss (CCL). In [22], a DGS used to suppress MC in MIMO design is presented, and this design eliminates the phased array scan blindness. By analyzing, the surface waves will get squashed in the substrate using back-to-back U-shaped DGS. In [23], a compact UWB-MIMO with low MC is introduced and is designed with 50 × 30 mm2. In this design, F-shaped stubs maintain isolation between the elements. This design has S21 <  − 20 dB, better ECC, DG, over the UWB frequency. In [24], in a slot array, a metamaterial is used for steering the surface waves so as to reduce MC. Both Complementary Split Ring Resonator (CSRR) and complimentary fishnet structures are used to minimize MC. An isolation improvement of 14 dB is obtained throughout 2 GHz bandwidth, with a 3.4 mm slot gap. In [25], a novel fractal DGS to minimize MC between coplanar elements is proposed, and the bandgap characteristic of the design is studied. Results show that isolation enhancement of > 35 dB is obtained. In [26], a compact design for UWB is investigated. This design implementation is performed with a patch and parasitic elements at the top, and DGS is etched on the substrate bottom. The proposed design dimensions are 20 × 20 × 1.6 mm3 with an efficiency of 79.8%, respectively. It is best suitable for WiMAX, WLAN. In [27], a MIMO antenna design for reducing MC is proposed. Six parallel metal strips are introduced between two patches to reduce MC between the elements, and \(-\) 42 dB is achieved with metal strips at 5.8 GHz frequency. In [28], an effective technique of utilizing metallic pins at the square element edges to alter the antenna polarization is proposed. The measurements indicate that the isolation enhances from 2.8 dB to 20 dB at 3.5 GHz. In [29], to reduce the MC, an EBG is used as an isolator and is of about 30.5 dB and provides low ECC. In [30], a compact design with improved isolation consists of slot antennas with 22 × 26 mm2. A T-shape slot is etched on the ground to provide better impedance matching and reduce the MC. The design provides MC of < \(-\) 18 dB over the UWB. In [6], dual-band MIMO elements that operate at 3.7 and 4.1 GHz is presented. The MIMO element spacing is about 0.034λ0. The design consists of a decoupling surface and H-shaped DGS. The isolation is greater than 30 dB in both 3.7 and 4.1 GHz bands from the decoupling structure and the DGS.

In [31], a UWB-MIMO design that provides good dual-band suppression with port isolation is presented. This design utilizes a fractal-shaped patch, parasitic neutralization stubs, ground, and notches to achieve band notches at WiMAX and X-band. In [32], a four-port monopole is presented using arrow-shaped slot etching and step etching to enhance isolation and bandwidth. The ECC obtained was less than 0.001 and the efficiency was greater than 85.70%. In [33], a slit embedded mushroom EBG and periodical CSRRs are implemented to reduce surface waves between elements. An H-shape DGS is introduced to reinforce the decoupling effect, and a12 dB MC reduction is realized. In [34], a two-element miniaturized MIMO antenna with reduced MC is presented. MIMO antenna is simulated with four T-shaped slots on the patch with 50 × 25 mm2 on FR-4 epoxy. A T-shape ground stub and a slot reduce the MC of the proposed method. This provides multi-band characteristics for the applications like WiMAX, WLAN, X-band SATCOM and Radar, Mobile phones, and WLAN.In [35], applications like WLAN, Wi-MAX are studied. In [36], a miniaturized slot-shaped EBG design structure with cell dimensions, 6.3 × 6.3 mm2 is proposed. This proposed design analyses the surface wave effects in the antenna array resonating at 5.8 GHz frequency. The slot-shaped design will modify the S-parameters with S11< \(-\) 10 dB and S12 < \(-\) 51 dB and changes the surface current distribution to avoid surface waves. This miniaturized structure is best suitable for the WLAN application.

The remainder of the paper is organised as follows: The antenna analysis with different parameters is described in Sect. 2. Section 3 deals with the results of the design proposed. The conclusion is presented in Sect. 4

2 Antenna Design and Analysis

Figure 1 represents a MIMO design with slits on all four sides of the patch. The proposed structure simulation is performed on FR-4 substrate with Ws × Ls (36 × 50 mm2), tan δ = 0.002, εr = 4.4. The height of the substrate is 1.6 mm. An M-shaped DGS between two radiators for isolation enhancement is shown in Fig. 1. This design uses Lp × Wp (Lp = Wp) patch element, four slits on all the sides with L length and N width. The proposed structure is excited with strip-line feed, and inter-element spacing is approximately 11 mm, between the two MIMO elements.

Fig. 1
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A Proposed MIMO structure

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The upper patch and the ground structure of the proposed design is shown in Fig. 2.

Fig. 2
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Upper patch and ground plane of the proposed design

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As it is a square patch, length and width are identical. Figure 1 depicts a MIMO antenna fed with strip-line, uses four cross-shaped slots on four sides of the antenna element, with two different sizes, length L and width N. The upper patch and ground plane is represented in Fig. 2.

The antenna design is simulated using HFSS 15.0 and fabricated on FR-4 substrate with a thickness (height) of 1.6 mm, length and width, Ws × Ls. An M-shaped DGS between two cross-shaped elements is indicated in Fig. 1. The design implements a patch with different sizes of cross-shaped slots are etched on the four directions of the patch with length L (where L = M) and width N. The edge-to-edge distance between the elements is 11 mm. Multiple slits are introduced for the MIMO element, and the design operates for the UWB with specific applications at WiMAX, WLAN, X-band SATCOM, and commercial WLAN. The simulated S11 and S12 plots for the proposed technique are shown in Fig. 3. The optimized parameters are listed in Table 1. As the notations provided in the Table 1, Ls and Ws indicates the substrate length and width. Lp and Wp denotes the patch length and width. A, B, C, E, F, and G denotes the slotted ground dimensions. D indicates the diameter of the circle. L, M, and N provides the slit length and width. I, J, and K denotes the M-shaped DGS length and width. d denotes the edge-to-edge spacing between the patch elements and Wf denotes the width of the feed line. H denotes the feedline height.

Fig. 3
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Proposed S11 and S12 of the design

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Table 1 Proposed design Parameters
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Finally, the proposed design with |S11|< − 10 dB, resonating from 2.5 GHz to 12 GHz, is plotted in Fig. 4(h). Isolation of <  − 20 dB is observed. The simulation is performed for all the evolution design steps of the proposed design, and S11 for the iterations is shown in Fig. 5

Fig. 4
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Formation steps of the design

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Fig. 5
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S11 Iterations

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From iteration 0 to the proposed method, S11 is plotted and is represented in Fig. 5. For iteration 0 S11 is approximately at -12 dB. As the iterations are increased from iteration 0 to the proposed design the return loss achieves better performance and the peaks occurs at four different resonant frequencies.

2.1 Effect of Slits on Patch Element

The concept of DGS used in MIMO is proposed in ref. [11, 13, 14, 17] and in [21]. Defected Ground Structure (DGS) acts as a band stop filter that blocks the surface currents flowing in the desired frequency from one radiator to another. From the design analysis, the proposed DGS provides good MC reduction. The S-parameters with and without Slotted ground and M-shaped DGS are compared in Figs. 6,7. From Fig. 6, using an M-shaped DGS and the slits on the patch, the peaks at which the antenna resonates are 3.51 GHz, 7.95 GHz, and 9.45 GHz. S12 >\(-\) 15 dB is achieved over the UWB range.

Fig. 6
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Simulated S11 with and without M-shaped DGS and slotted ground

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Fig. 7
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S12 of the proposed design with and without slotted ground and M-shape DGS

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2.2 Slotted Ground and DGS Effects on the Proposed Design

Figures 6, 7 shows S11 and S12 parameters with and without M-shape DGS and slotted ground.

A slotted ground is used to enhance isolation. From the S11 plot, the peaks at which the antenna resonates are 3.51 GHz, 7.95 GHz, and 9.45 GHz using a slotted ground. Etching slots on the ground edges enhance S12 with the slotted ground structure. MC is reduced at the resonating peaks that make S12 >  − 15 dB.

2.3 Parametric Analysis of the Design Proposed

Isolation improvement of the design is analyzed based on the parametric analysis by performing the slit length variation on the patch element and varying the distance between the patch radiators. The scattering parameters |S11| & |S12| for different distances are analyzed in Fig. 8. In this design, parametric analysis has been done by varying one parameter, and all other parameters remain unchanged to evaluate S-parameters.

Fig. 8
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S11 for distance variation of the MIMO design

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2.3.1 Effect On Distance Variation

The distance variation affects S11 with d = 7.5 mm to d = 11 mm, and the S11 variation to the distance between the patches is shown in Figs. 8, 9. From Fig. 8, distance, d = 11 mm, will resonate the antenna at 3.5 GHz, 5.9 GHz, 7.9 GHz and 9.3 GHz and S11 at these resonating frequencies are \(-\) 42.62 dB, \(-\) 45.84 dB, \(-\) 40.23 dB and \(-\) 34.56 dB and S12 at these frequencies are \(-\) 45.26 dB, \(-\) 44.83 dB, \(-\) 41.25 dB and – 42.31 dB and are depicted in Fig. 9. The spacing between the elements, d = 11 mm, S11 & S12, is >\(-\) 40 dB, demonstrating a strong MC reduction between the radiating elements.

Fig. 9
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S12 with different distances for the proposed antenna

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When the distance between the patches varies from d = 7 mm to d = 11 mm, S11 and S12 are greater than \(-\) 20 dB, and the optimized distance is d = 11 mm, which reduces the MC at the resonating frequencies.

2.3.2 Effect on Varying Slit Lengths L, M, and N

Slit lengths L, M, and width N variations on the patch will significantly change the antenna analysis parameters like S11, S12, gain, and directivity. Figure 10 shows that S11 increases by 15 dB, with L, M, and width N variation.

Fig. 10
figure 10

S11 for different slit lengths and widths of the MIMO design

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3 Results and Discussion

This section presents the simulated and measured results for the design proposed. The proposed design analyses the envelope correlation co-efficient, diversity gain, and radiation efficiency.

3.1 Scattering Parameters and Radiation Analysis of The Design

The design is validated by fabricating the antenna, and the results measured are attained with Keysight (9916A) VNA. Figure 11 shows the measured and simulated S-parameters. The proposed design IBW is 7.6 GHz, with S12 below − 35 dB.

Fig. 11
figure 11

S11 and S12 of the proposed MIMO design (Simulated and Measured)

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Figure 12 shows the measurement setup for measurements of the proposed design. The measurements are taken by considering the Horn antenna as a transmitter and the proposed structure as a receiver. The distance between the two antennas is maintained at 2D2/λ, where D is the substrate width, and λ is the wavelength of the smallest resonating frequency of the UWB range. After simulating the equivalent circuit, R = 1 KΩ, L = 5.5 nH, and C = 10 pF. The figure reveals that the UWB band is a parallel combination of R, L, and C for the entire 2.5–12 GHz. The two parallel LC circuits in parallel represent the M-shape DGS structure.

Fig. 12
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Measurement setup for the measurements of the proposed design

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Radiation plots at the resonant frequency are depicted in Fig. 13. A gain of 4.55 dBi is achieved for the prototype fabricated, and the simulated gain is 5.50 dBi, as shown in Figs. 14, 15 demonstrates the co-polarization and cross-polarization plots in E-plane and H-plane which indicates the desired orthogonal polarization of the proposed design radiation pattern. Figure 16 shows the fabricated model of the proposed design. The equivalent circuit is proposed in Fig. 17. A comparison of different techniques with the proposed design is shown in Table 2. Table 2 indicates the comparison of the proposed design with the existing works. As seen from Table 2, the proposed design resonates at four different frequencies over the UWB range compared to other related works. As seen from the Table 2, the proposed design provides multiple applications as the proposed design resonates at four different resonating frequencies.

Fig. 13
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2-Dimensional radiation plots at the design's resonating frequencies in E-and H-Planes (red color & blue color: simulated and measured in E-Plane, pink color, and green color: simulated and measured in H-Plane)

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Fig. 14
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Simulated and measured gain of the proposed MIMO design

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Fig. 15
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a Co- and cross-polarization at 3.45 GHz in H-Plane b Co and cross-polarization at 3.45 GHz in E-Plane

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Fig. 16
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Fabricated Design, a front view, b back view

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Fig. 17
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Equivalent circuit of the proposed design

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Table 2 Comparative analysis of the proposed work with related research works
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3.2 MIMO Parameters for the Proposed Structure

The validation of the design is done by analyzing Envelope Correlation Co-efficient (ECC) and Diversity Gain (DG). The simulation and measured parameters are compared. ECC analysis is performed using S-parameters as mentioned [29]; ECC is < 0.05 and is shown in Fig. 18. DG with 9.9 dB is shown in Fig. 19. The ECC based on S12 is given in Eq. (1) in terms of field-based equation and specifies the radiation patterns of two radiating elements correlation.

$$\rho_{e} = \frac{{\left| {\int_{0}^{2\pi } {\int_{0}^{2\pi } {\left( {XPR \cdot E_{\theta 1} \cdot E_{\theta 2}^{*} \cdot P_{\theta } + E_{\varphi 1} \cdot E_{\varphi 2}^{*} \cdot P_{\varphi } } \right){\text{d}}\Omega } } } \right|^{2} }}{{\int_{0}^{2\pi } {\int_{0}^{\pi } {\left( {XPR \cdot E_{\theta 1} E_{\theta 2}^{*} \cdot P_{\theta } + E_{\phi 2} \cdot E_{\varphi 2}^{*} \cdot P_{\varphi } } \right) \times \int_{0}^{2\pi } {\int_{0}^{2\pi } {\left( {XPR \cdot E_{\theta 1} \cdot E_{\theta 2}^{*} \cdot P_{\theta } + E_{\varphi 1} \cdot E_{\varphi 2}^{*} \cdot P_{\varphi } } \right){\text{d}}\Omega } } } } }}$$
(1)
Fig. 18
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Simulated ECC

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Fig. 19
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Simulated and measured DG

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The formula gives DG based on the ECC.

$${\text{DG}} = 10\sqrt {1 - {\text{ECC}}}$$
(2)

Irrespective of the antennas used, DG depends on BER, and the radiation efficiency is shown in Fig. 20 and reveals that the RE > 95%. The efficiency is calculated using a formula.

$${\text{Effciency}} = \left( {1 - \left| {{\text{TACR}}} \right|^{2} } \right)*{\text{Radiation}}\;{\text{effciency}}$$
(3)
Fig. 20
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Radiation efficiency (RE) (%) of the proposed design

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4 Conclusion

A slotted MIMO with M-shape DGS and slotted ground with 36 × 50 mm2 is analyzed. Two slotted MIMO antenna elements operate for the UWB band. To validate the design, fabrication of a two-element structure is done and tested. The edge-to-edge gap is 0.215λo. An M-shaped DGS and slotted ground improve isolation at 3.45, 5.89, 7.95, and 9.30 GHz with S12 >  − 15 dB. Isolation enhancement is improved by etching an M-shape DGS on the slotted ground, and the gain is 4.95 dBi, DG > 9.9 dB, and ECC < 0.05, for the entire UWB.