# Miniaturized Antenna Array-Based Novel Metamaterial Technology for Reconfigurable MIMO Systems
## 4 Results, Discussion, and Validation
To realize the effects of using the proposed MTM on the proposed antenna performance, a comparison study is summarized at the end of the discussions to focus on the role of the proposed MTM unit cell. In Table 4, the summary is listed to show the complete picture of such a discussion in terms of frequency bandwidth, gain, and coupling. The antenna array performance with and without the proposed MTM is included in Table 4 at fixed separation distances for both considered cases. Now, to present a complete picture of the proposed antenna array performance, the authors evaluated the channel capacity (CC) and the bit error rate (BER) under the assumption of constructing an antenna array of 64 \(\times\) 64 elements, theoretically only; for such an assumption, we tried to perform an analytical validation of such antenna feasibility for massive MIMO systems. The calculated CC and BER are based on measured results from the antenna elements in terms of gain, bandwidth, and mutual coupling. The channel is affected by white Gaussian noise and the transmitted power was changed from \(-20\) to 20 dBm. In such circumstances, the maximum bit error rate was found to be about 0.15, and the channel capacity was found to reach 2 Gbps. The obtained results are presented in Figure 17.  
The evaluated BER and CC were calculated using the following mathematical expressions [26]:  
\[BER=erfc\Big{(}\sqrt{2E_{b}/N_{o}}\Big{)}CC=BW\times(MN)\;log_{2}(1+SNR)\]  
where _erfc_ is the complementary error function, \(E_{b}\) is the bit energy, \(N_{o}\) is noise power, and \(BW\) is the available bandwidth. In those calculations, a digital modulation schema based on quadrature-amplitude modulation (QAM) with an effective coverage was applied to indicate the effects of that on BER. The considered BER in this case is defined as the number of acceptable errors at the prepared tolerates. In such a case, typically, it is a number between 0.1 and 0.000001. This ratio is very much affected by the signal-to-noise ratio (SNR), which is measured in dB. It was found from the results in Figure 17a that a high SNR provides low BER, while a low SNR would increase BER. It is obvious that frequency bands with higher gain are better than those with a low gain to provide a lower chance of errors due to the noise effects. Later, the proposed antenna array CC spectra were evaluated and shown in Figure 17b. It was found that the proposed antenna array CC capacity increases from 1.5 to 4.5 Gbps with a frequency increase. Finally, the proposed antenna array performance was compared with the published results in the literature in terms of antenna bandwidth, gain, size, reconfigurability, and substrate type. It was observed that the proposed antenna array shows a maximum-size reduction with excellent configuration technique and performance in comparison with the previous one listed in Table 5. Such a reconfiguration technique requires no biasing circuit or wiring system, while most of the old traditional techniques came up with high biasing complexity and wiring systems. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case** & **BW/GHz** & **Gain/dBi** & **Efficiency** & **DG** & **ECC** & **Coupling/dB** \\ \hline Without MTM & 3.2–4.65 & 1.1 & 20\% & 5.3 & 0.24 & \(-3\) \\ With MTM & 3–5.5 & 4.5 & 83\% & 10 & 0.01 & \(-20\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The proposed antenna performance with and without MTM introduction at fixed antenna sizes and separation distances for both cases. Figure 17: Channel performance calculations at different frequency bands: (**a**) BER and (**b**) CC.