**1. Introduction**

Antennas are used in several aspects of life, from human body networks to space communication. There are many antennas around us, and hence their interference with one another and with other

electronic gadgets must be reduced. Electromagnetic interference (EMI) between transmitting and receiving antennas is an important consideration for relative antenna placement [1]. Whether onboard or offboard, radiating and receiving electronic appliances such as antennas can interfere with other such devices and can reduce their application effectiveness.

Multipath propagation issues arise in conventional transmission systems due to signal degradation in the transmission medium of the transmitter and receiver. To overcome this issue, multiple-input multiple-output (MIMO) technology can be implemented [2–8]. A variety of research on MIMO antennas can be found in the literature with an aim of achieving high quality, isolated signals along with compact antenna size to overcome the aforementioned issues.

Tian et al. [9] and Liu et al. [10] discussed channel capacity to enhance antenna efficiency by reducing the mutual coupling and effects of spatial correlation under the Rayleigh fading channel assumption. Abdul et al. [11] and Khalighi et al. [12] proposed a method to identify the number of antennas at the asymmetric base station as well as in mobile units in order to increase the effectiveness of the station. Du et al. [13] addressed the need to optimize overall MIMO system capacity, which includes the unequal costs of antennas at both channels.

In antenna design optimization, algorithms inspired by natural processes have been applied, and they are genetic algorithms (GAs) [14–17], particle swarm optimization (PSO) [18,19], and their variants [20,21]. Genetic algorithm (GA)-based optimization algorithms have been utilized for antenna array positioning and have been successful in finding optimized antenna schemes [22]. These optimization algorithms do not consider the assumptions about the design, and the generation of optimal parameters is necessary to meet the defined design criteria [23].

In this work, we wanted to optimize the MIMO antenna design with respect to its EMI. The factors that affect the EMI can be classified into its structural parameters and the material properties of the substrate. This work focused on the structural parameters only. However, there are ten structural parameters, as we discuss later, making optimization challenging.

To improve the effectiveness of optimization, 2K factorial design methodology was applied in this work. This methodology is commonly employed for many experimental designs and has been shown to be the most effective experimental design methodology [24]. The 2K refers to designs with K factors where each factor has just two levels. Through this methodology, we can screen a large number of factors and identify only those parameters that are important so that the scale of optimization can be reduced.

In this work, a four-element wideband MIMO antenna was optimized. This antenna consisted of a stub, reduced ground plane, and T-shaped radiating elements, and its size was 25 mm <sup>×</sup> 25 mm <sup>×</sup> 1.6 mm. Optimization was done using 2K factorial and GA optimization algorithms, with Minitab and ANSYS High Frequency Structure Simulator (HFSS) software, respectively. EMI was considered the parameter to be optimized, and this optimization also improved the return loss and bandwidth, as will be shown in this work. Optimization helps in reducing the interference and enhancing the operating frequency and bandwidth of the antenna [25], which makes the proposed antenna suitable for various applications such as radar communication, imaging, and satellite communication.

#### **2. Antenna Design and Fabrication**

The design diagram of a single-element MIMO antenna is shown in Figure 1. This MIMO antenna is designed on RT/Duroid substrate with relative permittivity of 2.2 and dielectric loss tangent (tanδ) of 0.0009 [26], having a cross-section of 25 mm x 25 mm x 1.6 mm. A microstrip feed line of 50 ohms is utilized to provide the input supply to the antenna.

**Figure 1.** (**a**) Multiple-input multiple-output MIMO antenna with substrate, (**b**) dimensional geometry of one element in the four-element MIMO antenna, (**c**) top view of the fabricated antenna, and (**d**) back view of the ground plane. Substrate is absent in (**b**) to highlight the ground plane.

The reduced ground plane was designed at the bottom of the substrate and straight stubs of 0.3 mm width are used to establish a connection with the reduced ground plane. Figure 1a shows the MIMO antenna with the substrate understudy in ANSYS HFSS V19.0, and Figure 1b shows the structural parameters of the T-shaped antenna. Initial values of design parameters were a = 1 mm, b = 2 mm, c = 0.5 mm, d = 2 mm, tw = 3 mm, tl = 8.5 mm, ga = 11 mm, gb = 3 mm, gc = 25 mm, and gd = 0.3 mm. Figure 1c,d shows the top and back views of the fabricated MIMO antenna.

Figure 2 shows the simulated and measured return loss of the initial antenna design as shown in Figure 1. The difference between simulated and measured results may be attributed to the fabrication discrepancies and associated tolerances because of the variation of dielectric constant (εr) and loss tangent (tanδ) of the RT/Duroid substrate with frequency and relative humidity [27–29].

(**a**) Simulated return loss for initial antenna

(**b**) Measured return loss for initial antenna

**Figure 2.** Return loss of initial antenna (**a**) simulated and (**b**) measured.

A small change in design, relative permittivity, and thickness of substrate were incorporated into our antenna simulation in order to investigate the causes of the difference between the simulated and measured results. Figure 3 shows the modifications made to the antenna design, where the area under the black eclipse represents an area of change, while the red box represents a zoomed-in area. The changes were made in the angle of the patch in the antenna design (to mimic the actual antenna), dielectric constant value to 2.22 from 2.2, and substrate thickness to 1.575 mm from 1.6 mm. All these minor changes resulted in the matching of the losses between the simulated and measured results. However, negligible changes were observed in EMI, radiation pattern, peak gain, and surface current distribution, as shown in Figure 4. Hence, we proceeded with our ideal antenna design instead of the physical antenna design that contained non-ideality.

(**b**) Modified design

**Figure 3.** Antenna design for (**a**) modified and (**b**) initial antenna to match the measurement results. Area under the black eclipse represents an area of change, while the red box represents the zoomed-in area.

**Figure 4.** *Cont*.

(**c**) 2-D radiation pattern

(**d**) Peak gain

(**e**) Surface current distribution

**Figure 4.** *Cont*.

**Figure 4.** Results for modified antenna (**a**) return loss, (**b**) electromagnetic interference (EMI), (**c**) radiation pattern, (**d**) peak gain, (**e**) surface current distribution, and (**f**) mutual coupling.
