Introduction

In mobile communication, there’s a massive demand for high data rates, expanded capacity, and reduced latency. Following the COVID-19 pandemic, time has notably amplified the necessity for high-speed communication, given the widespread shift towards remote work1. Moreover, the surge in mobile internet usage, particularly in high-speed Internet of Things (IoT) applications, has underscored the need for practical solutions. Researchers seek an effective and reliable solution to meet these escalating requirements.

5G technology emerges as a promising option for advancing wireless communication systems, with the potential to revolutionize various sectors, including e-health, innovative education systems, intelligent urban infrastructure, medical, industrial internet of things (IIOT), and automation2. Advanced communication systems, such as 5G, demand wideband antennas characterized by high gain, efficiency, and compact form factors. The Federal Communications Commission (FCC) classified the 5G spectrum into two primary categories: the Sub-6 GHz band and the millimetre-wave (mm-Wave) band. Researchers have focused significant attention on the development of patch antennas for 5G in the sub-6 GHz band, Wi-Fi, and other wireless applications due to their compact size and stable radiation patterns in all directions3. Table 1 illustrates the spectrum allocation in the 5G Sub-6 GHz band. In wireless communication systems, antennas are an integral part that plays a pivotal role. While Single microstrip antennas offer a low-profile design, they suffer from limitations such as low gain, restricted spectral efficiency, and insufficient bandwidth. MIMO (Multiple Input Multiple Output) antennas are a good option for 5G applications because they improve performance, particularly in terms of information throughput, data transfer rates, and channel capacity. MIMO antennas facilitate the simultaneous transmission and reception of data across multiple channels, without requiring additional power or bandwidth, thereby enhancing system reliability4. The increasing demand for smart devices highlights the need for efficient connectivity, enabling gadgets to interface with the internet and with each other for seamless operation5. MIMO antennas can enhance communication performance by using spatial multiplexing at the transmitting and receiving ends6.

Table 1 Spectrum allocation of 5G spectrum by FCC.
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Multiple antennas are placed at the transmitter and receiver ends of MIMO systems. The proximity of these numerous antenna elements, however, introduces a challenge known as mutual coupling, which can adversely affect system gain and data transfer rates8,9,10 To mitigate this issue, maintaining low correlation and achieving high isolation between antenna elements is crucial in MIMO systems. Yet, designing a MIMO antenna capable of accommodating a wide bandwidth while ensuring high isolation within the confined space of a mobile terminal remains a challenging endeavour11. Figure 1 depicts the fundamental principle of MIMO systems. A 2-port MIMO antenna with dimensions of 43 × 30 mm² (0.17 λ0 × 0.24 λ0) was introduced for dual-band GSM and WLAN applications in the frequency bands 1.704–1.934 GHz and 5.66–6.25 GHz9.

Fig. 1
figure 1

MIMO antenna system.

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This design showcased isolation levels of <-20 dB and <-28 dB for the respective bands. A 2-port MIMO antenna with dimensions of 43 × 30 mm² (0.17 λ₀ × 0.24 λ₀) was introduced for dual-band GSM and WLAN applications in the frequency bands 1.704–1.934 GHz and 5.66–6.25 GHz9. This design showcased isolation levels of <-20 dB and <-28 dB for the respective bands.

Various studies12,13,14,15,16 Have investigated MIMO antennas tailored for 5G mid-band applications. Researchers have introduced two-port and four-port MIMO antenna topologies to support various application domains. A CPW-fed 4-port triple-band MIMO antenna was suggested in12 for potential use in upcoming 5G applications in the sub-6 GHz spectrum. This antenna, fabricated on a 60 × 60 mm² FR-4 substrate, exhibited a minimum isolation of more than 30 dB at three different frequencies: 2.4, 5.2, and 8.1 GHz. Another study in reference13 presented a fractal circular antenna including two and eight elements, constructed for the frequency spectrum of 3.4–5.85 GHz. This design, utilizing a 72 × 72 mm² FR-4 substrate, achieved isolation exceeding 15 dB for the two-element antenna by incorporating a T-shaped stub into the ground plane. Although a gain of 2.5 dBi or more was achieved within the antenna’s working region, the resultant gain was relatively modest for a MIMO system. The research examined the integration of UWB (Ultra-Wideband) technology with MIMO (Multiple-Input Multiple-Output) systems, demonstrating its capacity to enhance overall system performance. This resulted in the creation of a 4-port UWB-MIMO antenna14, featuring an electrical length of 0.6 λ0 × 0.6 λ0 × 0.032 λ0, and utilizing a split rectangular loop resonator (SRLR) in the ground plane to attain a minimum isolation of -17 dB. For Wi-Fi and 5G applications, a 4 × 4 MIMO antenna was designed in14. This antenna functions concurrently in two frequency bands: 3.3–3.8 GHz and 4.5–8.4 GHz. A number below 10 signifies inadequate isolation between the antenna elements. A two-port T-shaped monopole antenna functioning within the frequency range of 3.14–5.42 GHz was designed in an independent study16. This antenna was designed to cater to 5G and WLAN services for 5G devices. This antenna had a T-shaped slot that was offset to improve bandwidth and isolate one of the antenna elements. Additionally, the other element had two L-shaped stubs that were incorporated to improve impedance matching. The isolation achieved between the antenna components exceeded 15 dB. To establish triple-band capability, a G-shaped antenna configuration was proposed in17 to support a 4-port MIMO system.

In18 circular and rectangular slot cuts were investigated to accomplish this functionality. These antennas operate in multiple frequency bands, specifically 2.30–2.45 GHz, 3.36–3.65 GHz, 4.53–5.88 GHz, 3.72–3.82 GHz, 4.65–4.76 GHz, and 6.16–6.46 GHz. The dimensions of these antennas are 46 mm × 46 mm² and 32 mm × 32 mm², respectively. To mitigate the impacts of mutual coupling, various methods were utilized, including the introduction of slots and the establishment of stub connections in the ground. Quarter-annular rings and inverted U-shaped strips are the components that make up each antenna element. A rectangular dual-port MIMO antenna for S and C-band applications, operating within the frequency range of 2.61 to 7.64 GHz, was designed in19. A C-shaped metamaterial was positioned between the patches in the ground plane to promote isolation. The substrate dimension is 40 × 49 mm2. Wideband antennas are essential in communication, sensing, and radar systems. In20, a dual-band antenna operating in the sub-6 GHz range, designed for wearable applications, is described, along with a characteristic mode analysis. The antenna is configured with four ports and features an isolation level of 23 decibels. The antenna is capable of operating in the bands of 3.8–4.43 GHz and 5.25–6.3 GHz. The antenna has a total dimension of 62 × 52 mm². The ground plane features a decoupling arrangement designed to improve isolation properties. Multilayer and reconfigurable antennas are recent and promising techniques for wideband antennas; however, these techniques utilize switches, capacitors, and other components, making MIMO antenna technology a more suitable choice21. Other MIMO antennas can be found in22,23. In22, A dual-arm CPW-fed antenna for 5G applications is introduced. A dual-band antenna with Frequency Selective Surface (FSS) is engineered to function at 3.5 and 5.8 GHz in23. The FSS is implemented to enhance gain and diminish SAR levels. The antenna element dimensions are 31.5 mm by 26 mm, and the FSS unit cell measures 38.5 mm by 38.5 mm.

This project aims to create a wideband 2-port MIMO antenna designed for sub-7 GHz frequencies, intended for implementation in 5G networks and various wireless communication applications. The performance of an antenna is assessed by multiple measures, including isolation, correlation coefficient, diversity gain, and channel capacity loss (CCL). The antenna design demonstrates versatility by accommodating many 5G bands designated in various countries, as detailed in Table 1. Thus, the principal characteristics of the proposed antenna are as follows:

  1. i.

    The suggested antenna is electrically small in size, which is 0.27λ × 0.35λ for a single antenna and 0.35λ × 0.74λ at the lowest frequency, 3.7 GHz.

  2. ii.

    The proposed antenna operates broadly, with a bandwidth ranging from 3.70 to 7.60 GHz, suitable for sub-7 GHz 5G applications, eliminating the need for multiple antennas for multiple applications.

  3. iii.

    An elliptical ring structure is placed to enhance the isolation. Additionally, the ground planes of both antenna elements are connected to provide a common reference voltage. The minimum isolation between two antenna elements is 21 dB within the whole operating band, and the maximum isolation exceeds 28 dB.

  4. iv.

    The proposed antenna offers a maximum gain of 5.42 dBi within the operating frequency range and can be a perfect choice for various wireless services.

  5. v.

    Conducted analysis of different diversity performance parameters, including ECC, DG, CCL, and MEG, showing excellent performance parameters for 5G applications.

This work is structured as follows: Sect. “Antenna geometry and design methodology” elucidates the antenna’s geometric configuration and design technique, and provides both simulated and measured results for a single antenna element. Section ”Proposed 2-Port MIMO antenna configurations” delineates the configuration of the proposed 2-port MIMO antenna, encompassing simulations, empirical results, and diversity metrics. To confirm the effectiveness of the proposed antenna, its performance is compared with that of recent publications. Section ”Comparative analysis” offers a definitive summary of the work.

Antenna geometry and design methodology

Single antenna geometry and evolution

The first phase in developing a 2-port MIMO antenna involves designing a single antenna element, depicted in Fig. 2. The patch design features three interconnected circular structures positioned at varying centres. The antenna is printed on a low-cost FR-4 substrate with a dielectric constant of 4.4 and a dielectric loss tangent of 0.02.

Fig. 2
figure 2

Geometry of proposed single antenna element (a) Top view (b) Bottom view (c) Placement of different circular parts of the Patch in HFSS.

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In Fig. 2c, the antenna assembly comprises distinct circular components, denoted as C1-C6, that are interconnected to form a unified structure.

Table 2 Centre position (x, y) of C1-C6 in HFSS.
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A rectangular stub is attached to the leftmost portion of the partial ground plane to optimize impedance matching and achieve small bandwidth increments. The specific placements of the circular components (C1-C6) are detailed in Table 2.

The process for obtaining the proposed antenna structure consists of four sequential steps, as depicted in Fig. 3. Initially, a circular patch with a radius of 5.5 mm with a full ground plane is selected. The equation to determine the frequency of a circular patch is given by24:

$$\:f=\frac{{\xi\:}_{mn}\times\:c}{2\pi\:{a}_{eff}\sqrt{{\mu\:}_{0}{\epsilon\:}_{0}{\epsilon\:}_{r}}}$$
(1)

\(\:{\xi\:}_{mn}\)= 1.841 for first dominant mode (TM11).

aeff is the effective radius of the patch, which can be found using the equation25:

$$\:{a}_{eff}=a.{\left[1+\frac{2h}{{\pi\:a\epsilon\:}_{r}}\left(ln\left(\frac{\pi\:a}{2h}\right)+1.7726\right)\right]}^{1/2}$$
(2)
$$\:{a}_{eff}=5.5\sqrt{1+\:\frac{2\times\:0.8}{\pi\:\times\:5.5\times\:4.4}\left(ln\left(\frac{\pi\:\times\:5.5}{2\times\:0.8}\right)+1.7726\right)}$$

\(\:{a}_{eff}\) is the fringing field corrected radius, which is \(\:{a}_{eff}\:=5.74\:\text{mm}\).

The expected resonant frequency with an effective radius of 5.74 mm is given as

$$\:{f}_{r}=\frac{5.523\times\:{10}^{8}}{2\pi\:\times\:5.74\sqrt{4.4}}=7.3\:\text{GHz}$$

With this configuration, the antenna fails to resonate effectively at the desired frequency, resulting in poor matching with an S11 value of -3.89 dB. Subsequent modifications involve reducing the ground size to 8.3 mm to improve the bandwidth. This transition from whole ground to partial ground was modelled with the given Eq. (3)

$$\:{f}_{pg}=\:{f}_{fg}\left(1-\alpha\:(1-{{r}_{g})}^{\beta\:}\right)$$
(3)

Where:

rg is the ground ratio, α and β are the fitted constants, fpg is the resonance frequency with partial ground, and ffg is the resonance frequency with whole ground.

The ground ratio, rg is given by

$$\:{r}_{g}=\:\frac{{L}_{g}}{{L}_{s}}$$
(4)
$$\:{r}_{g}=\:\frac{{L}_{g}}{{L}_{s}}=\:\frac{8.3}{28}=0.296$$

The resonance frequency predicted in step 2 using Eq. (3) for α = 0.663 and β = 1.75 is

$$\:{f}_{pg}=7.3(1-0.663(1-0.296{)}^{1.75})$$
$$\:{f}_{pg}=4.70\:\text{GHz}$$

This predicted a shift in frequency from 7.3 to 4.70 GHz, which is approximately equal to the simulated result of 4.80 GHz with a reflection coefficient of -17.02 dB, as plotted in Fig. 4. To obtain a wideband response, it is necessary to create a multi-resonant structure. This can be achieved by increasing the radiating area and creating multiple current paths. In the third step, modifications were made to the antenna designed in the second step by connecting three circular patches of radii 5.5 and 6 mm with varying centers, denoted as C1, C2, and C3 in Fig. 2c. The total effective area was calculated using Eq. (5)

$$\:{A}_{eff}=\:{A}_{1}+{A}_{2}+{A}_{3}-\left({A}_{12}+{A}_{13}+{A}_{23}\right)$$
(5)

A1, A2, and A3 are the actual areas of circular patches C1, C2, and C3 respectively.

A12 is the overlapping area of C1 and C2, A13 is the overlapping area of C1 and C3, A23 is the overlapping area of C2 and C3.

A1 = A2 = π× (5.5)2 = 95.03 mm2.

A3 = π× (6)2 = 113.10 mm2.

ATotal = A1 + A2 + A3 = 95.03 + 95.03 + 113.10 mm2 = 303.16 mm2.

The overlapping area between two circles can be found by the formula26

$$\:\:{A}_{Overlapping}=\:{R}_{1}^{2}{cos}^{-1}\left(\frac{{d}^{2}+{R}_{1}^{2}-{R}_{2}^{2}}{2d{R}_{1}}\right)+{R}_{2}^{2}{cos}^{-1}\left(\frac{{d}^{2}+{R}_{2}^{2}-{R}_{1}^{2}}{2d{R}_{2}}\right)$$
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:-\frac{1}{2}\sqrt{(-d+{R}_{1}+{R}_{2})(d+{R}_{1}-{R}_{2})(d-{R}_{1}+{R}_{2})(d+{R}_{1}+{R}_{2})}$$
(6)

d is the centre-to-centre distance between circular patches.

With the above formula, the overlapping areas A12, A13, and A23 are.

A12 = 32.5 mm2.

A13 = 23.9 mm2.

A23 = 23.9 mm2.

So, the total effective area is:

Aeff = 303.16 mm2- (32.5 + 23.9 + 23.9) mm2 = 222.86 mm2.

With this effective area, the equivalent radius of the patch is

$$\:{a}_{eff}=\sqrt{\frac{{A}_{eff}}{\pi\:}\:}=\:\sqrt{\frac{222.86}{3.14}}\text{mm}=8.42\:\text{mm}$$

Now, using Eq. (1), the new calculated resonant frequency is

$$\:f=\:\frac{1.841\times\:3\times\:{10}^{8}}{2\pi\:\times\:8.43\times\:{10}^{-3}\sqrt{4.4}}\:\approx\:4.49\:\text{GHz}$$

This estimated frequency is close to the computed resonant frequency of 4.30 GHz from the HFSS. Additionally, the bandwidth has been improved from 3.76 to 7.65 GHz. Still, the matching is poor. In the final step, two smaller circles, C5 and C6, are combined with the structure obtained in step 3. Along with this, an elliptical slot is etched in the upper part of the patch, and a rectangular stub is connected on the left side of the ground plane. These modifications in the shape significantly altered the effective inductive-capacitive behaviour of the antenna27 and enhances the antenna’s performance by increasing the effective radiating area, enabling support for multiple resonances, which also improves the impedance matching and provides a broader bandwidth. The antenna exhibits an exceptional bandwidth of 3.88 GHz (3.72–7.60 GHz) and a maximum S11 value of -37.45 dB at 6.66 GHz. Figure 4 illustrates the reflection coefficient parameters for all design steps, and Table 3 lists the design parameters of the single-element antenna.

Fig. 3
figure 3

Design evolution of proposed antenna.

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Fig. 4
figure 4

Reflection coefficients of design steps.

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Table 3 Parameters of single antenna element.
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The use of FR-4 may contribute to increased dielectric losses, generally at higher frequencies. To further enhance gain, efficiency, and other performance parameters, low-loss substrate materials such as Rogers RO4003, with a dielectric constant (εr) of 3.55 and loss tangent of 0.0027, and Rogers RO3003, with εr = 3 and loss tangent of 0.0013, could be used to implement the antenna. The substrate material with a higher εr is beneficial to minimize the size of the antenna, but it also results in degrading the performance parameters, such as radiation efficiency. The use of FR-4 also affects the resonance stability of the antenna, as the dielectric constant varies with temperature. Low-loss materials (Rogers RO4003 and 3003) improve the Q-factor, which is suitable for filter and sensing applications.

Parametric analysis of the proposed antenna

To achieve the desired response of the single antenna element, a parametric analysis is performed in terms of the reflection coefficient (S11), as shown in Fig. 5a–d. Variation of S11 is observed by varying the radius R1 (Radius of circular patches C1 and C2) and R2 (Radius of circular patch C3), ground length (Lg), and stub length (L1).

From the figure, it is clear that for R1 = 5.5 mm, the best result was obtained. Similarly, for R2 = 6 mm, the antenna yields the desired results. To achieve the minimum reflection coefficient and sufficient bandwidth, the height of the ground plane is optimized, yielding the best result at a ground height of 8.3 mm.

Also, a rectangular stub is attached to the ground. For a stub length of 3.7 mm, desired results were obtained in terms of reflection coefficient and bandwidth. The effect of all four parameters, i.e., R1, R2, Lg, and L1, is analyzed, and values are optimized for effective and desired results.

Fig. 5
figure 5

Variation of S11 with (a) Radius R1, (b) Radius R2, (c) Ground Height Lg, (d) Stub Length L1.

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Equivalent circuit of the antenna

The equivalent circuit (EC) of the designed single antenna was simulated using Advanced Design System (ADS), which is shown in Fig. 6a. It is simulated as three parallel RLC circuits and a series LC circuit connected in series to produce a wideband operation. The resistance in a parallel RLC circuit represents radiation resistance, and L and C are responsible for resonance. Three RLC circuits broaden the bandwidth, and an LC circuit in series further adds resonances, producing a wideband response. Values of R, L, and C are selected with a tolerance of ± 20% and calculated for the given range of frequencies using the basic parallel and series RLC resonance circuits28,29, and Eqs. (7) and (8) are used to calculate the capacitors and inductances for the circuit30.

$$\:L=\frac{img\left({Z}_{11}\right)}{2\pi\:f}$$
(7)
$$\:C=\:{\left[{\left(2\pi\:f\right)}^{2}L\right]}^{-1}$$
(8)
Fig. 6
figure 6

(a) Equivalent circuit of the antenna (b) Reflection coefficients (HFSS and Circuit).

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The reflection coefficients simulated for the single antenna using HFSS and computed from ADS are illustrated in Fig. 6b.

The lower resonance obtained from HFSS is 4.30 GHz, whereas the equivalent circuit simulated in ADS yields 4.20 GHz. The frequency range obtained from HFSS is 3.7 to 7.6 GHz, whereas it is 3.63 to 7.57 GHz using circuit simulation. This difference in the results using HFSS and ADS is because the simulation approaches used by HFSS and ADS are different31. The optimized values of R, L, and C of the equivalent circuit are summarized in Table 4.

Table 4 Optimized values of R, L, and C (Units are in Ω, nF, and pF).
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Surface current distribution

The surface current distribution of the proposed antenna is examined to understand its operational principle better. Figure 7a depicts the surface current at 4.5 GHz. The current is concentrated on feed. Additionally, a small amount of current is distributed around the edges on the left side. Additionally, at 5.5 GHz, the current is distributed on the lower side of the patch, feed, and around the upper left edges of the ground, as can be observed in Fig. 7b. The current distribution displayed in Fig. 7c indicates that the surface current at 6.5 GHz is concentrated along the feed line and the lower edges of the patch, with the most significant current. The current is also focused around the upper edges of the ground and the rectangular stub connected to the ground.

Fig. 7
figure 7

Surface current distribution (A/m): (a) at 4.5 GHz and (b) at 5.5 GHz, (c) at 6.5 GHz.

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Simulation and measured results of single antenna element

A simulation and analysis of the individual antenna element were performed with Ansys Electronics Desktop HFSS software.

Fig. 8
figure 8

S-parameter curve of the proposed single element antenna (Meas and Sim).

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Fig. 9
figure 9

Prototype of the antenna (a) front view (b) back view (c) measurement setup.

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A physical prototype of the simulated antenna was subsequently created, and the calculated findings were validated by testing with the Keysight N9916A 14 GHz VNA. The tested reflection coefficients are combined with the simulated results for comparison, as depicted in Fig. 8, which shows a minimum value of -39.13 dB across the entire operational bandwidth.

Fig. 10
figure 10

Simulated and measured (a) Gain (b) Efficiency of single antenna element.

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Figure 9 illustrates a constructed antenna. Figure 10a and b demonstrate the gain and radiation efficiency of the antenna, respectively. The antenna achieves an increase of more than 2.2 dBi across the working band, with a maximum gain of 3.4 dBi.

Additionally, the radiation efficiency remains above 84% across the entire frequency range, indicating strong performance for 5G applications. A slight drop in efficiency at higher frequencies is attributed to the lossy nature of the FR-4 substrate.

Proposed 2-Port MIMO antenna configurations

Geometry of 2-Port MIMO antenna

The 2-port antenna was configured with a single-element antenna and MIMO settings. Figure 11a and b illustrate the top and bottom sides of the antenna, which is designed for a substrate size of W×L = 60 × 28 mm2. Two antenna elements are arranged edge-to-edge, with a 21-mm space between their patches. A variety of isolation techniques and structures are used to improve isolation. In a MIMO setup, the isolation between antennas can be enhanced by augmenting the distance between the antenna elements or utilizing a decoupling structure. Augmenting the separation between antenna elements enlarges the total antenna dimensions. To improve isolation, two optimized elliptical ring-shaped structures are placed between the antenna elements, as shown in Fig. 11c. All the design characteristics and dimensions of the developed two-port antenna are summarized in Table 5.

Since it is known that a connected ground improves isolation and lessens interference between the antennas, both ground planes are connected in the suggested antenna. By linking the grounds, surface currents are prevented, and so no radiation enters the other ports. On the substrate’s back side, two ground planes are connected, and a vertical rectangular strip is coupled to these two ground planes to enhance isolation. The ground planes of the two antenna elements are connected to ensure that the MIMO antenna has the same reference voltage levels32,33,34.

Fig. 11
figure 11

2-Port MIMO antenna configurations (a) Top view (b) Bottom view (c) Isolation structure.

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Table 5 Dimensional parameters of 2-Port Antenna.
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The equivalent circuit of a two-element MIMO antenna is illustrated in the figure. The coupling between the two antenna elements is modeled by C9 and L9, while capacitors C10 and C11 represent the gaps between the decoupling structure and the antenna elements. Two antenna elements are represented by the same equivalent circuits of single antenna elements given in Fig. 6).

The values of R, L, and C parameters of the individual antenna elements are the same as the values for single antenna elements. The optimized values for the decoupling section are obtained as C10 = C11 = 0.08 pF, L9 = 0.2 nH, and C9 = 1.35 pF. The estimated reflection and transmission coefficients using HFSS and Keysight’s ADS are plotted in Fig. 12b, and both results are in good agreement.

Fig. 12
figure 12

(a) Equivalent circuit of two-port antenna (b) Reflection and transmission coefficients (HFSS and ADS).

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Results and discussion of MIMO

  1. A.

    S-Parameters and gain.

Figure 13a displays the 2-Port MIMO antenna’s observed and simulated reflection coefficients, which agree pretty well. The transmission coefficients indicate mutual coupling among the antenna elements, and Fig. 13b demonstrates that the isolation between the two elements exceeds 20 dB. The minimum isolation between antenna elements is 21 decibels. Thus, both antenna structures are well segregated from one another.

Fig. 13
figure 13

Simulated and measured (a) Reflection coefficients-Sii (b) Transmission coefficients (c) S-Parameters of antenna without decoupling structure.

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The elliptical isolator structure plays a crucial role in reducing mutual coupling. The behavior of the antenna is illustrated in Fig. 13c in terms of S-parameters, where, without an isolator structure, the isolation is low, resulting in an observed isolation of less than 12 dB within the proposed frequency range. The magnitude of the surface current reaching from one antenna to the other antenna when the first antenna is excited must be minimized to reduce the mutual coupling. This is possible by different methods, such as decoupling or isolation structures placed between antennas. Further, to quantify the isolation, the antenna is simulated without the elliptical ring. Figure 14 depicts the surface current distribution of the antenna with and without an elliptical ring isolator at three different frequencies 4.5, 5.5, and 6.5 GHz.

Fig. 14
figure 14

Current distribution of 2-Port MIMO Antenna with and without isolator (i) and (ii) at 4.5 GHz (iii) & (iv) at 5.5 GHz (v) & (vi) 6.5 GHz.

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At 4.5 GHz, the majority of the current is spread on the feed line and patch edges, indicating that the constructed antenna is a perfect radiator in the frequency band, as shown in Fig. 14 (i) and (ii). Without an isolator, a small amount of surface current can be seen near the feed line of the second antenna, indicating mutual coupling between the antenna elements. After introducing the isolator, it blocked the surface current from reaching the second antenna. Similarly, for frequency 5.5 GHz, when port 1 is excited, most of the current is concentrated around the left side of the patch, feedline, and upper edges of the ground as displayed in Fig. 14 (iii) & (iv). In the absence of a ring isolator, surface current is also concentrated on the feed line and at the lower edge on the left side of the patch of the second antenna. With the use of the elliptical structure, the current density at the second antenna is minimized, which indicates high isolation. The surface current distribution at 6.5 GHz, with and without an isolator, is shown in Fig. 14(v) and (vi). Similarly, without the isolator, a large amount of current is distributed on the non-energized antenna around the feedline and the edges of the patch, as well as the upper edges of the ground. The elliptical isolation structure and stub in the ground plane are crucial in managing surface current, as they restrict the flow of current from one antenna to the other, resulting in no leakage to the second antenna, as shown in Fig. 14(vi). It guarantees that both antennas are well isolated.

From Fig. 14, it is also clear that most of the current is blocked by the elliptical ring from reaching the non-excited antenna, and the surface current can be seen on the ring structure. However, with the introduction of the isolator, this surface current is reduced to improve the isolation. The antenna prototype is made of FR-4, and the fabricated prototype of the 2-port antenna and measurement equipment are shown in Fig. 15a–c.

Fig. 15
figure 15

Prototype and measurement setup of 2-port antenna (a) Front view (b) Bottom view (c) Measurement setup in an anechoic chamber.

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Figure 16 plots the computed and tested gain of the antenna. The antenna’s gain remains steady across the operational frequency range, ranging from 2.3 to 5.42 dBi, with a maximum gain of 5.42 dBi at 7.2 GHz.

Fig. 16
figure 16

Gain of 2-port antenna.

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  1. B.

    Radiation performance.

The computed and tested radiation patterns of the MIMO antenna in the E and H planes, including co-polar and cross-polar components, are depicted in Fig. 17 at three distinct frequencies. The measurement setup for the radiation pattern measurement is shown in Fig. 15c. The Co-polar radiation pattern in the H-plane is almost omnidirectional at all three frequencies. However, in the E-plane, the radiation patterns for 4.5 and 5.5 GHz are bidirectional, while at 6.5 GHz, they are omnidirectional. The computed and tested patterns are closely matched, except for some ripples that occurred due to fabrication and measurement tolerances. These radiation patterns make the antenna suitable for 5G communication within a wide range. Discrepancies between the computed and tested results are due to the presence of higher-order modes at specific frequencies. For ɸ=90°, the difference between co and cross polarization at 0° elevation angle is more than − 20 dB across different frequencies. H-plane follows a Similar pattern at 0°.

The results indicate a significant alignment between the computed and tested results. The measuring setup, fabrication method, and other factors all contributed to a slight discrepancy between the graphs.

2-Port MIMO antenna performance parameters

Several performance metrics, including bandwidth, efficiency, gain, and resonance property, can be used to describe the antenna. To ensure that the MIMO antenna performs well in terms of diversity, there are additional considerations. In general, the ECC, DG, MEG, and CCL are the metrics that define the performance of the MIMO antenna. It is essential to analyse these parameters in a real-time environment. Thus, these parameters are calculated by assuming a Rayleigh fading environment, as it represents rich multipath conditions in real urban and indoor conditions35,36.

Fig. 17
figure 17

Co- and Cross-polar radiation pattern (a) at 4.5 GHz, (b) 5.5 GHz, (c) 6.5 GHz.

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Envelope correlation coefficient (ECC) and diversity gain (DG)

To achieve better diversity performance, the envelope correlation coefficient (ECC) of the MIMO antenna should have a value of 0.537,38. This value may be determined by using the equation provided in39 Using a farfield radiation pattern.

ECC is an essential parameter of the MIMO antenna that delineates the isolation between the channels. The simulated and practical ECC for the proposed antenna is observed to be below 0.051 in the operational band, as shown in Fig. 18a. The observed and simulated values of the ECC align effectively. To determine the diversity gain (DG) of the antenna, the envelope correlation coefficient (ECC) can be utilized, as provided in40. The larger value of DG reveals the quality and reliability needed to enhance the performance of the MIMO antenna. It can be seen from Fig. 18b that both the simulated and practical DG values are equal to or greater than 10 decibels, respectively, for the complete operating band, which meets the criteria for better antenna performance.

Mean effective gain (MEG) and channel capacity loss (CCL)

Another parameter that indicates the gain behaviour of the MIMO antenna is MEG. It also helps in measuring the antenna-channel mismatch. It refers to the proportion of the power that is received by a MIMO antenna in comparison to the power that is received by an isotropic antenna41. To compute the MEG, the equation provided in39 is used.

The optimal MEG value is -3 dB, which is attained in this instance, and the variance between MEG1 and MEG2 is approximately ± 0.005 for the suggested antenna. The simulated and tested graphs of mean effective gain (MEG) are plotted in Fig. 19a.

Channel capacity between the transmitter and receiver reduces the rate of information conveyed across the channel. It is the upper limit up to which the data or information with nearly zero loss can be communicated in any communication channel27. The threshold value of the CCL (bps/Hz) is 0.4 b/s/Hz and may be determined using the equation given in26.

Fig. 18
figure 18

Envelope correlation coefficient (ECC) and diversity gain (DG).

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CCL also guarantees the optimal limit on the message transmission rate across the channel. As shown in Fig. 19b, the CCL value for the proposed antenna is below 0.4 b/s/Hz across the entire operating frequency range.

Fig. 19
figure 19

Simulated and measured (a) Mean effective gain (b) CCL.

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4-Port MIMO antenna

The suggested antenna is arranged in a 4-port configuration. The geometry of the suggested simulated 4-port antenna is illustrated in Fig. 20. Four individual antenna elements are placed orthogonally and simulated on a FR-4 substrate of size 60 × 60 mm². A modified star-shaped design with a circle in the middle is placed at the center of the substrate to mitigate the mutual coupling between antennas.

Fig. 20
figure 20

Geometry of 4-Port MIMO antenna (a) Front view, (b) Bottom view, (c) Isolator.

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The edge-to-edge distance between the antenna elements is 14 mm. The antenna operates within the frequency range of 3.8 to 7.42 GHz. The simulated S-parameters of the antenna are shown in Fig. 21. The isolation within the operating frequency of the antenna exceeds 21 dB. The optimized design parameters of the four-port antenna are summarized in Table 6.

Table 6 Optimized design parameters of 4-port antenna.
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Figure 21 illustrates that the antennas are efficiently isolated from each other. The maximum isolation is 45 dB between antenna elements.

Fig. 21
figure 21

Simulated S-parameters of the suggested antenna.

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4-Port Port MIMO parameters

To show the diversity performance of the MIMO antenna, it is essential to find the key MIMO parameters. In this section, the key MIMO parameters (ECC, CCL, DG, and MEG) are plotted across the entire operating frequency range, computed between antenna 1 and 2, and between antenna 2 and 3. The ECC and diversity gain plot is shown in Figs. 22a and b and 23.

Fig. 22
figure 22

Simulated (a) ECC and (b) Diversity Gain of 4-port Antenna.

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The computed ECC using the farfield radiation pattern between antenna 1 and 2 is below 0.05, which is below the threshold value of 0.5. Similarly, the ECC between antenna 2 and 3 is the same. The diversity gain achieved by the MIMO antenna is also more than 9.99 across the operating frequency range from 3.7 to 7.6 GHz.

Fig. 23
figure 23

Simulated CCL of the 4-port antenna.

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Another parameter, CCL, which determines the signal alteration between the transmitting and receiving antennas, is plotted in Fig. 24. The mathematical expression mentioned in39 is used to find CCL. CCL constantly remains below 0.4 b/sec/Hz throughout the entire operational frequency range, which is the threshold for MIMO antenna performance.

A further parameter to illustrate the effectiveness of MIMO antennas is the mean effective gain (MEG). The MEG values for the proposed 4-port antenna are − 3 dB, which is within the allowed range.

Fig. 24
figure 24

Simulated mean effective gain of the 4 port antenna.

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Comparative analysis

The performance of the engineered MIMO antenna, in terms of dimensions, bandwidth, isolation, gain, and ECC, is compared with that of many previously constructed antennas and reported in Table 7.

Table 7 Comparison of proposed antenna with reported work in literature.
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Table 7 demonstrates that the suggested antenna outperforms recently produced antennas in terms of gain, bandwidth, and other parameters. The suggested antenna outperforms the one reported in9 in terms of area occupied, frequency range, isolation, and maximum gain. The antenna designed in10 is smaller in size, but it operates on two different bands with a small bandwidth. additionally, gain was not calculated. The antenna designed in22 is a 4-port antenna with a size of 66 mm × 66 mm, featuring a low bandwidth. A single-port antenna developed in21 is smaller than the proposed antenna; however, its gain and efficiency are low. The isolation between antenna elements is 17 dB in reference. The size of the two-port and single-port antennas in42,44,53 is larger than the suggested antenna. The 4-port antenna in45 is also larger and operates on two bands with a relatively narrow bandwidth. Additionally, the gain of the antenna in46 is relatively low, at 2.23 dBi. Some of the four-port antennas are developed with a smaller size, but their gain and isolation are low. The 4-port antenna reported in47 is large. Also, the isolation is about 20 dB, which is less than the proposed antenna. The suggested antenna is also superior to the antenna reported in48 in terms of isolation and bandwidth. The antenna presented in49 is smaller than the suggested antenna; however, its gain is low. Additionally, the proposed antenna occupies a smaller area than the antenna in51 and achieves better isolation and gain than the antenna in50. Similarly, the antenna in52, with a 2-port configuration, is smaller in dimensions but achieves low isolation (15 dB) between its antenna elements. Additionally, the ground planes are not connected. In comparison to other reported antennas, the suggested antenna is superior in terms of size, gain, isolation, and other performance parameters. In the future, a 4-port antenna could be fabricated and analyzed using other substrate materials, such as Rogers RO3003 or Rogers RT/duroid 5880, to enhance its performance parameters.

Conclusion

This study proposes a two-port wideband MIMO antenna. The antenna is succinct. The impedance bandwidth of the suggested antenna is measured to be 3.90 GHz. Ground planes are connected, which is a crucial requirement for implementing the antenna in real-world systems. To reduce mutual coupling, two elliptical ring-shaped structures are integrated and positioned between the antenna elements. It enhances the isolation between the antenna parts, surpassing 20 dB within the specified operating band. Various diversity performance criteria, including ECC, CCL, MEG, and DG, are assessed. Assessed ECC (< 0.05) and DG > 9.99 dB, which conforms to the acceptable parameters established in the literature. The channel capacity loss (CCL) for the developed antenna is less than 0.4 bits per second per Hz. Due to its numerous qualities, the suggested antenna is an excellent choice for 5G technologies operating at sub-6 GHz, Wi-Fi 6, INSAT-C, and V2X/DSRC services. Additionally, this 2-port antenna design was extended to 4 or more ports, which can improve data throughput and other performance parameters in MIMO systems. Additionally, the antenna can be combined with a wideband frequency-selective surface (FSS) to improve gain, bandwidth, and other performance metrics. Also, we can further optimize the design for improved isolation, bandwidth, and gain, making it more effective for next-generation communication applications.