**3. Results and Discussion**

The fabricated four-port MIMO antenna is shown in Figure 6A (top view) and Figure 6B (bottom view). Using an Agilent PNA-X N5242A vector network analyzer (VNA), the S-parameters are measured. The radiation pattern is measured in an anechoic chamber by using a Nanjing Lopu Co. antenna measurement system. The measurement scenario of the proposed antenna is given in Figure 7 to show the measurement environment. The simulated and measured return loss for the designed antenna is represented in Figure 8A. The figure representation clearly shows that the simulated *S*<sup>11</sup> results of all the four ports are the same due to its similar structure, and good impedance bandwidth of 57% is achieved between the frequency range of 3.2 GHz to 5.8 GHz.

**Figure 6.** Fabricated prototype of the proposed antenna design: (**A**) top view and (**B**) bottom view.

On the other side, measured return-loss results of the proposed antenna show utmost similar results with good bandwidth of 54% covering the frequency range from 3.2 GHz to 5.6 GHz. The measured return-loss results show a slight difference in the frequency range. This difference is primarily due the fabrication process and slight alteration in the dielectric constant of the substrate.

Similarly, the simulation and measured isolation results between the antenna elements are shown in Figure 8B, and isolation between the antenna elements are greater than 16 dB throughout the expected frequency, which demonstrates that all the four antenna elements work independently. A sequence of parameter analyses is presented on the proposed MIMO antenna system to understand the process of the design principle. In Figure 5, the purpose of the rectangular slot at the ground plane is studied with *S*<sup>11</sup> and *S*<sup>12</sup> measurements by etching with and without the slot in the ground layer. The use of slot C in the ground not only improves the isolation to −22 dB but also enhances the frequency bandwidth. As slot C in the ground plane increases, the frequency bandwidth of the MIMO antenna gradually increases with the frequency range gradually moving back from 4.3 GHz to

3.3 GHz, and similarly the bandwidth also increases from 0.4 GHz to 2.5 GHz, as shown in Figure 9A. Similarly, to understand the effects of using slot E etched in the ground plane, the dimensions of slot E are adjusted from 2 mm to 7 mm while maintaining all other parameter values unchanged. It can be seen in Figure 9B, that the return-loss *S*<sup>11</sup> gradually decreases to −10 dB covering the entire frequency range from 3.3 GHz to 5.8 GHz.

Figure 10B shows the working principle of the proposed four-port antenna with the surface current distribution for different frequency bands. This indicates that with the proposed antenna design, the surface current almost does not transfer between the nearby antenna elements at 3.4 GHz, 4.8 GHz, and 5 GHz. This feature assures good isolation between the antenna elements.

**Figure 7.** MIMO antenna measurement setup in an anechoic chamber.

**Figure 8.** Simulated and measured results of the proposed antenna: (**A**) *S*11, *S*22, *S*33, *S*<sup>44</sup> and (**B**) *S*13, *S*23, *S*23, *S*24.

**Figure 9.** Parametric Analysis: (**A**) *S*<sup>11</sup> [dB] vs. Frequency [GHz] for slot C parameter values, (**B**) *S*<sup>11</sup> [dB] vs. Frequency [GHz] for slot E parameter values.

**Figure 10.** Current distributions in 3.4 GHz, 4.8 GHz and 5.2 GHz. (**A**) Step 2 design antenna; (**B**) final proposed antenna.

Figure 11A–D depicts the simulated and measured 2D YZ-plane and XZ-plane radiation patterns with port 1 excited at 3.4 GHz and 4.8 GHz. The other ports are connected to the 50–ohm match load. It is obvious that the radiation patterns of both the simulated and measured are similar while port 1 is excited and are radiating omnidirectionally. The peak gain achieved by all the four ports lies between 2.4 to 4.9 dBi over the entire operational bandwidth and the average radiation efficiency obtained is 93%. From Figure 11A,B, it can be seen that the maximum measured gain of 2.6 dBi is achieved in the YZ and XZ planes. Similarly, a maximum measured gain of 4 dBi at 4.8 GHz is achieved, as shown in Figure 11C,D.

**Figure 11.** Simulation and measured radiation pattern for port 1: (**A**) 3.4 GHz at YZ plane, (**B**) 3.4 GHz at XZ plane, (**C**) 4.8 GHz at YZ plane, and (**D**) 4.8 GHz at XZ plane.

The ECC and the diversity gain (DG) are important parameters to assess the performance of the MIMO system. The mutual coupling and return loss at the ports can be used to determine ECC, which helps to find the diversity performance of the MIMO antennae [23,24], and is given in Equation (1):

$$|\rho\_{\mathbf{e}}(\mathbf{i}, \mathbf{j}, \mathbf{N})| = \frac{\left| \sum\_{n=1}^{N} \mathcal{S}\_{i,n}^{\*} \mathcal{S}\_{n,j} \right|}{\sqrt{\left| \Pi\_{k(=i,j)} \left[ 1 - \sum\_{n=1}^{N} \mathcal{S}\_{i,n}^{\*} \mathcal{S}\_{n,k} \right] \right|}} \tag{1}$$

The correlation can also be measured from MIMO antenna's far-field radiation patterns [25], as given in Equation (2):

$$\text{ECC} = \frac{\left| \int \int\_0^4 \left[ E\_i(\theta, \phi) \* E\_j(\theta, \phi) \right] d\Omega \right|^2}{\int \int\_0^4 \left| E\_i(\theta, \phi) \right|^2 d\Omega \int \int\_0^4 \left| E\_j(\theta, \phi) \right|^2 d\Omega} \tag{2}$$

where *i* and *j* are the antenna elements and *N* is the number of antennae. *Ei*(*θ*, *φ*) and *Ej*(*θ*, *φ*) are the three-dimensional radiation patterns of *i*th and *j*th antenna and Ω is the solid angle. The acceptable and standard value of ECC should be less than 0.5 for portable devices. Similarly, the antenna DG is a well-known performance parameter used to verify the efficacy of the diversity [26]. It can be defined as the ratio of rise in SNR of mixed signals from multiple antennae to the SNR from a single antenna in the system. The DG can be calculated using Equation (3):

$$DG = \sqrt[10]{1 - |\mathbb{E}\mathbf{C}\mathbf{C}|^2} \tag{3}$$

It can be observed that the ECC is less than 0.005 and DG is greater than 9.9 dB in the 3.4 to 6.5 GHz frequency band, as shown in Figure 12. This signifies good diversity performance and shows good performance results in the achieved frequency band. Table 2 provides a comparison between the proposed wideband MIMO antenna and other antenna designs [27–34] found in the literature. This comparison clearly indicates that the proposed antenna design is exceedingly competitive with other designs discussed in the literature in terms of impedance bandwidth, size, and isolation, along with good values of ECC and diversity gain.

**Figure 12.** (**A**) Envelope correlation coefficient [dB] vs. frequency [GHz] (**B**) diversity gain [dB] vs. frequency [GHz].



**Table 2.** *Cont.*
