The proposed MIMO antenna prototype is constructed, and its |S|-parameters are tested using an Agilent E5071C VNA. In Fig. 6, both the simulated and experimental |S|-parameters are shown, indicating that the measured data matches well with the simulated data, which was obtained utilizing EM Solver Ansoft HFSS 18.0. However, there are minimal variances between the two due to SMA connector loss and manufacturing resilience.

From the observation of Fig. 6, it is clear that the simulated and measured bandwidth at -10 dB is 4.43–9.85 GHz (IBW 82.12%) and 5.26–10.83 GHz (IBW 73.8%) respectively.

Figure 7 & 8 show the radiation characteristics of the proposed MIMO antenna for frequencies of 5.8 GHz, and 9.1 GHz for both ports. For port-1 at 5.8 GHz, the XZ-plane (ϕ = 00) displays a typical monopole-like pattern, but the YZ-plane (ϕ = 900) exhibits an omnidirectional pattern (cf. Figure 7(a) & (b)). Figure 7(c) & (d) show a quasi-omnidirectional pattern with some ripples for both the XZ-plane and YZ-plane for port-1 at 9.1 GHz. The same trends are seen for port-2, however, at 5.8 GHz, the XZ-plane (ϕ = 00) shows an omnidirectional pattern, while the YZ-plane (ϕ = 900) displays a monopole-like pattern (cf. Figure 8(a) & (b)). At a higher frequency of 9.1 GHz, the quasi-omnidirectional pattern with some ripple is observed in YZ-plane (cf. Figure 8(d))

Figure 9 depicts the simulated efficiency of the antenna and the simulated and experimental gain over the entire operating frequency range of 4.43–9.85 GHz. Further, the radiation efficiency plot of the proposed model attained the maximum value of 98% in the whole operating impedance bandwidth and a peak gain of 4 dBi (simulated), and 3.37 dBi (measured) is noticed.

The simulated and measured VSWR of the antenna is determined, as illustrated in Fig. 10 Throughout the frequency range, VSWR is less than 2. (4.43–9.85 GHz). This result is supported by the examined antenna's VSWR of 1.52 (simulated) & 1.59 (measured) at 9.1 GHz. The suggested antenna has a 2:1 VSWR bandwidth of 8230 MHZ (4.08-12.31GHz).

The group delay depicts the degree of frequency-dependent alterations in sent and received signals. Figure 10 illustrates the proposed group delay time of the MIMO antenna. Its value is less than 0.9 ns for the operating bandwidth, which is acceptable for distortion-free transmission in the whole frequency range.

### Diversity Performances Parameters

The envelope correlation coefficient (ECC) is an essential metric for illustrating the degree of association among channels of communication. Figure 11 depicts the results of an analysis of ECC data in order to assess the diversity performance of the proposed MIMO antenna. When calculating the ECC, the far-field properties or scattering parameter values are taken into account. Equations 1 and 2 are used to calculate the ECC values by considering the scattering parameters and far-field parameters respectively.

$$EC{C_s}={\left| {\frac{{\left| {S_{{11}}^{ * }{S_{12}}+S_{{21}}^{ * }{S_{22}}} \right|}}{{{{\left| {\left( {1 - {{\left| {{S_{11}}} \right|}^2} - {{\left| {{S_{21}}} \right|}^2}} \right)\left( {1 - {{\left| {{S_{22}}} \right|}^2} - {{\left| {{S_{12}}} \right|}^2}} \right)} \right|}^{1/2}}}}} \right|^2}$$

1

$$EC{C_F}=\frac{{{{\left| {\iint\limits_{{4\pi }} {\left[ {{E_i}\left( {\theta ,\phi } \right) * {E_j}\left( {\theta ,\phi } \right)} \right]d\Omega }} \right|}^2}}}{{\iint\limits_{{4\pi }} {{{\left| {{E_i}\left( {\theta ,\phi } \right)} \right|}^2}d\Omega \iint\limits_{{4\pi }} {{{\left| {{E_j}\left( {\theta ,\phi } \right)} \right|}^2}d\Omega }}}}$$

2

Where Ei (θ,ϕ) & Ej (θ,ϕ) indicates the 3-D far-field radiation pattern acquired by the antenna when the antenna is excited by the power supply on port i & j respectively [32][33]. ‘Ω’ & ‘*’ represents the Hermitian product operator and solid angel respectively. For practical applications, the value of ECC should be less than 0.5. Figure 11 shows that the proposed MIMO antenna has an ECC value of less than 0.04.

Another significant element that must be evaluated is DG. In the operational bandwidth, the DG of the MIMO antennas should be high (10 dB). In terms of ECC, it is calculated as [34].

$$DG=10\sqrt {1 - EC{C^2}}$$

3

Figure 11 shows the DG of the proposed MIMO antenna, which fluctuates at a 10 dB scale across the full working spectrum.

The scattering characteristics-derived reflection coefficient is inadequate to forecast antenna performance under MIMO limitations. The total active reflection coefficient (TARC) is an important metric for understanding how one antenna element affects the performance of other antenna components [35]. The TARC for the 2-port MIMO antenna can be calculated by Eq. 4.

$$TARC=\frac{{\sqrt {\left( {\left( {{{\left| {{S_{11}}+{S_{12}}{e^{j\theta }}} \right|}^2}} \right)+\left( {{{\left| {{S_{21}}+{S_{22}}{e^{j\theta }}} \right|}^2}} \right)} \right)} }}{{\sqrt 2 }}$$

4

Figure 12 shows that the TARC value is less than − 20 dB throughout the whole working bandwidth (4.43–9.85 GHz) and is consistently less than − 20dB over a broad range of elevation angle values (theta).

The channel capacity loss (CCL) measure calculates the maximum speed at which a message may be sent across a communication channel before the transmission is interrupted. S-parameters are used to calculate the CCL by Eq. 5 [36].

$$\begin{gathered} CCL=-{\log _2}\det \left( {\begin{array}{*{20}{c}} {{a_{11}}}&{{a_{12}}} \\ {{a_{21}}}&{{a_{22}}} \end{array}} \right) \hfill \\ {a_{11}}=1-\left( {{{\left| {{S_{11}}} \right|}^2}+{{\left| {{S_{12}}} \right|}^2}} \right) \hfill \\ {a_{22}}=1-\left( {{{\left| {{S_{22}}} \right|}^2}+{{\left| {{S_{21}}} \right|}^2}} \right) \hfill \\ {a_{12}}=-\left( {S_{{11}}^{*}{S_{12}}+S_{{21}}^{*}{S_{12}}} \right) \hfill \\ {a_{21}}=-\left( {S_{{22}}^{*}{S_{21}}+S_{{12}}^{*}{S_{21}}} \right) \hfill \\ \end{gathered}$$

5

Figure 13 shows the antenna's CCL. CCL should be 0.5 bits/sec/Hz for optimal diversity performance [33]. Figure 13 shows that CCL is within the allowed range for the designated operating band.

The suggested dual-port MIMO antenna compared to existing antennas for the same wireless application are investigated in terms of dimensions, operating bands, and minimal isolation as seen in Table II. In the investigation, it was found that the suggested design is highly small and performs similarly.

Table II. Performance comparison of proposed and existing MIMO antennas for the same applications

Dimension (mm) | Operating Band (GHz)/ Impedance bandwidth (%) | Overall Isolation (dB) | Average Efficiency (%) | Average Gain(dBi) | ECC | DG | CCL | Applications |

0.27λ0 × 0.32λ0 × 0.008 λ0 [37] | 3.1–10.6/109 | 25 | 95 | 5 | 0.001 | NR | NR | C & X |

0.41 λ0 × 0.33λ0 × 0.01 λ0 [12] | 2.5–11/125 | 15 | 69.2 | 2.11 | 0.01 | NR | NR | X |

0.29λ0 × 0.6λ0 × 0.01λ0 [38] | 3–20/147 | 23 | 80.2 | 3.7 | 0.001 | 9.99 | 0.32 | C, X, and Ku |

0.24λ0 × 0.4λ0 × 0.01λ0 [39] | 3.52–9.89/95 | 22 | NR | 3.08 | 0.005 | 10 | 0.4 | X |

0.30λ0 × 0.30λ0 × 0.008 λ0 [40] | 3.08–10.9/111 | 20 | NR | 5 | 0.013 | 9.51 | 0.3 | C and Ku |

0.37 λ0 × 0.93 λ0 × 0.03 λ0 [41] | 6.6–7.6,8.3–10/2.81,18.5 | 22 | 80 and 70 | 5,1.7 | 0.015 | 9.9 | NR | C and X |

0.44 λ0 × 0.44 λ0 × 0.01 λ0 [42] | 3.3-13.75/122 | 18 | 89 | 5.5 | 0.012 | 9.998 | 0.2 | C and X |

0.21λ0 × 0.37λ0 × 0.008 λ0 [43] | 3.16–10.6/108 | 15 | 90 | 4 | 0.1 | 9.99 | 0.2 | C and X |

0.2λ0 × 0.44λ0 × 0.008 λ0[44] | 3.3–3.65,4.8–5.5/10,13.6 | 18 | 92.2,97 | 3.8,5.9 | 0.002 | 9.9 | 0.5 | S and C |

0.41 λ0 × 0.25×0.01 λ0 [7] | 2.5–14.5/141 | 20 | NR | 4.3 | 0.04 | 7.4 | NR | C, X and Ku |

0.13 λ0 × 0.68 λ0 × 0.02 λ0**[Proposed]** | **4.43–9.85 /82.12** | **18** | **98%** | **4** | **0.04** | **9.98** | **0.3** | **C & X** |