# Miniaturized Antenna Array-Based Novel Metamaterial Technology for Reconfigurable MIMO Systems
## 3 MTM Analysis and Discussion  
As shown in Figure 1, the suggested MTM structure is built from a 1D array with four unit cells (b). The third iteration of the Minkowski fractal describes the form of each individual unit cell. A circuit model is developed to describe the performance based on a transmission line theory to analyze the suggested unit cell features. In essence, a circuit model with a mix of right- and left-hand branches may be created from such a unit cell, as illustrated in Figure 2a.  
In terms of mathematics, the suggested unit cell was examined from various orientation angles at normal and tangential electric field incidences. Yet, in this inquiry, the planned unit cell iteration was raised from the first to the fourth with a single step. This was done to make sure that the performance of the suggested unit cell is improved by the iteration effects. As a result, the suggested unit cell is situated inside a fictitious waveguide to track the S-parameter spectra at the targeted frequency range. With the application of two electrical and two magnetic barriers to the virtual waveguide, the effective medium theory is invoked in this simulation process. A similar procedure is used to simulate the creation of transverse electromagnetic modes as a plane wave [10].  
Now, after inserting the proposed unit cell with different orientations and different iterations, the calculated S-parameters, in terms of S\({}_{12}\) and S\({}_{11}\) spectra, are shown in Figure 2b. The suggested unit cell was discovered to offer a cut-off frequency for the frequency bands from 3 up to 5.3 GHz. The proposed unit cell performance in terms of permittivity and permeability is presented in Figure 2c. It was found that the proposed unit cell realizes multiple bands with \(-\varepsilon\)r and \(-\mu\)r within the frequency band of interest. Such an observation realizes that the unit cell is an excellent candidate for mutual coupling reduction to suite MIMO applications; that is very useful for size reduction [5]. Next, as a result, the suggested unit cell was nominated as an outstanding option for coupling reduction in MIMO array systems as a result of this accomplishment. The comparable circuit model based on the developed RLC network, which is often built as an interdigital capacitor (IDC) in series connected to a compact series inductor (CSI) and Hilbert fractal, is used to analytically determine the suggested sensor design based on an equivalent circuit model. The lumped elements Richard model [10] was used to create the suggested structure equivalent circuit model. A 50 input impedance RF source is coupled in series with a R-L-C parallel branch to form the suggested circuit architecture, as seen in Figure 2. An inductive segment LT and capacitive air gaps Cgap, which were previously shown in Figure 2, set apart the primary transmission line. The recommended S-parameters for the circuit model were reviewed and contrasted with those obtained using CST MWS, considering the lumped components indicated that were simulated in Advanced Devices Simulator (ADS). Table 2 contains a list of the assessed RLC parts.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Value** & **Abbreviation** \\ \hline Xg & 3 & Separation distance \\ Yg & 3 & Ground plane length \\ Xm & 4 & Monopole width \\ D & 12 & Separation distance between antenna elements \\ \hline \hline \end{tabular}
\end{table}
Table 1: Antenna geometrical details.  
Figure 2: The proposed MTM structure circuit model: (**a**) equivalent circuit, (**b**) S-parameters results, and (**c**) retrieved electromagnetic properties in terms of \(\epsilon_{\rm r}\) and \(\upmu_{\rm r}\).