## 5 Discussion  
The proposed concept could be used to advance smart structure and actuator technology. Although the SMA springs used here are one-way, i.e., they can only be changed in one direction, two-way springs would enable two-way variation. In addition, we used copper tape for a fast demonstration of the proposed antenna. It was possible because of simple conductive patterns. For complicated conductive patterns and robustness, the conductive patterns can be realized by additive manufacturing technology such as inkjet printing [45; 46], aerosol jet printing [47], or screen printing [48].  
This antenna can be used as the multiple-input multiple-output (MIMO) antenna. We investigated the MIMO spatial diversity by simulating two array antennas. MIMO systems can obtain high capacity by using multiple antennas. However, minimizing interference between antennas is one of the important factors for MIMO, as coupling between multiple antennas can lead to poor performance. [49] For the MIMO system, the envelope correction coefficient (ECC) is an important parameter indicating the interference between antennas.  
The ECC can be calculated as follows [50]:  
\[\rho_{e}=\frac{\left|S_{11}{}^{*}S_{12}+S_{12}{}^{*}S_{22}\right|^{2}}{\left(1- \left|S_{11}\right|^{2}-\left|S_{21}\right|^{2}\right)\left(1-\left|S_{22} \right|^{2}-\left|S_{12}\right|^{2}\right)} \tag{5}\]  
Figure 12a,b shows the distance (\(A_{\text{d}}\)) between the centers of the two array antennas for each mode. The Radius (C\({}_{2}\)) of the array antenna in each mode is 20.5 mm, and the  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Ref.** & **Tuning Tech.** & **Method** & \begin{tabular}{c} **Tuning** \\ **Range (\%)** \\ \end{tabular} & \begin{tabular}{c} **Size (nm)** \\ **(W \(\times\)** **I \(\times\)**H)** \\ \end{tabular} & **Gain (dBi)** & **Efficiency (\%)** & \begin{tabular}{c} **DC Biasing** \\ **Circuit** \\ \end{tabular} & **Complexity** & **Cost** \\ \hline [40] & Electrical & Pin-diode & 49 & \(127\times 127\times 2.54\) & \(-1.1\) & 47 & Yes & High & High \\ \hline [41] & Electrical & Varactor-diode & 25 & \(150\times 150\times 1.524\) & N/A & N/A & Yes & High & High \\ \hline \multirow{2}{*}{[11]} & Optical & \
\begin{tabular}{c} Photoconductive \\ switch \\ \end{tabular} & 25 & \(4.56\times 48.94\times\text{N/A}\) & 8–9 & N/A & No & High & High \\ \hline \multirow{2}{*}{[42]} & Mechanical & Microfluidic & 70 & \(100\times 100\times 3.175\) & 6.98-7.34 & 80.5-88.0 & No & Low & Low \\ \hline \multirow{2}{*}{[43]} & Mechanical & MEMS switch & 149 & \(45\times 41.8\times 7.126\) & 1.2-3.3 & 75-85 & No & High & Low \\ \hline \multirow{2}{*}{[44]} & Thermal & SMA & 148 & \(60\times 50\times 1.6\) & \(-17.13\)-3.18 & N/A & No & Low & Low \\ \hline \multirow{2}{*}{
\begin{tabular}{c} This \\ work \\ \end{tabular} } & \multirow{2}{*}{Thermal} & SMA spring & 30 & \(60\times 60\times 5\) & 4.26-6.41 & 51.44-75.5 & No & Low & Low \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison table of frequency reconfigurable antennas with different tuning technologies.  
Figure 11: Simulated and measured radiation efficiency at different tangential loss: (**a**) circular disk mode and (**b**) circular sector mode.  
S-parameter when the distance (\(A_{\text{d}}\)) between the antennas was changed to 42, 45, and 50 mm is shown in Figure 12c. In general, the MIMO system has good isolation if the mutual coupling level (\(S_{21}\)) is lower than \(-15\) dB. [49] When the distance (\(A_{\text{d}}\)) between two antenna elements was larger than 45 mm, \(S_{21}\) was lower than \(-15\) dB. Figure 12d shows the calculated ECC from Equation (5). The ECC value when the distance (\(A_{\text{d}}\)) is 42 mm was 0.0004 for the circular disk mode at 2.41 GHz, and the circular sector mode is 0.019 at 3.25 GHz, respectively. The MIMO arrangement of the proposed antenna had good diversity performance for a MIMO antenna. [49]