# Miniaturized Antenna Array-Based Novel Metamaterial Technology for Reconfigurable MIMO Systems
## 3 MTM Analysis and Discussion
### Design Methodology
#### 3.1.4 MIMO Array Performance  
Now, the proposed antenna was designed to be configured as an array with two elements, as shown in Figure 1. Therefore, to specify the effects of coupling on the proposed antenna performance, the separation distance (D) between the antenna elements was changed from 10 to 25 mm. As seen in Figure 8a, the proposed antenna array S\({}_{11}\) spectra are insignificantly affected by increasing D. This is a usual response because the fact of changing S\({}_{11}\) spectra is relative to varying the antenna elements' dimensions [12]. However, in the case of S\({}_{12}\) spectra, the manner of the antenna mutual coupling variation is different; it is increased with decreasing the distance between the antenna elements, as shown in Figure 8b.  
Our philosophy in this research was to reduce the antenna element size within a miniaturized array configuration by adding MTM defects. Such an addition can be implemented to minimize the separation distance ultimately to 6 mm with coupling effects in terms of S\({}_{12}\) below \(-\)20 dB, as seen in Figure 9. Such a performance was compared to the antenna array with and without MTM defects. The fact of reducing the mutual coupling with low separation distance is that such MTM defects apply a high surface impedance by producing a negative dielectric constant (\(-\epsilon_{\mathrm{r}}\)) over the frequency bands of interest. Therefore, the propagated surface current toward the array center is a decayed mode with a significant attention factor [17].  
Figure 8: The obtained S-parameters spectra for the proposed antenna array with changing D: (**a**) S\({}_{11}\) and (**b**) S\({}_{12}\) spectra.  
Now, the proposed antenna array is introduced to a metamaterial unit cell column in the back panel to eliminate the mutual coupling between the antenna edges. In our design, we introduced the proposed unit cell parametrically, from one to four with the step of the one-unit cell, to minimize the mutual coupling altimetry. Therefore, it is observed from the evaluated S-parameters results, in Figure 10, that a significant enhancement in the antenna bandwidth is achieved after the proposed metamaterial introduction (see Figure 10a) with an increasing metamaterial unit cell number. Consequently, the antenna mutual coupling was found to decrease when increasing the unit cell number that maintains the separation distance between the antenna elements about 0.1 \(\lambda\) at 3.5 GHz. Therefore, we found from the proposed parametric study that the minimum S\({}_{12}\) reduction is achieved when four-unit cells are introduced to the proposed array, as seen in Figure 10b. Such a reduction, it is good to mention, was found to be overall in the frequency band from 3.5 to 5.5 GHz with S\({}_{12}\) below \(-\)20 dB and S\({}_{11}\leq-\)10 dB. It is concluded from these results that the proposed metamaterial array behaves as a stop-band filter to reject most of the frequencies within the frequency band of interest, as discussed later.  
We next evaluated the antenna TRAC using the effective antenna gain for the optimal antenna performance with different signal phase excitations at Port 2 of 0\({}^{\circ}\), 30\({}^{\circ}\), 60\({}^{\circ}\), and 90\({}^{\circ}\). The obtained results are depicted in Figure 11a, showing a significant effect of changing the signal phase difference on the evaluated TRAC in terms of impedance bandwidth. Such an observation is attributed to sever variation in the phase change due to the effects of mutual coupling at random phase signals [9].  
The antenna radiation efficiency was evaluated for both cases of with and without MTM introduction. The calculated results are presented in Figure 11b, showing a significant enhancement after introducing the proposed MTM structure. This enhancement is attributed to the fact of reducing the capacitive and inductive losses by the proposed MTM introduction [7].