# Triple-Band Notched Ultra-Wideband Microstrip MIMO Antenna with Bluetooth Band
## 4 Results and Discussion
### Diversity Analysis Characteristics (ECC, DG, and TARC) for Proposed UIWB-MIMO Antennas  
ECC represents the envelope correlation coefficient between the radiated antennas in the MIMO configuration. There are two methods of calculating the ECC. One is obtained from the S-parameter characteristics using Equation (6), while the other is obtained from the far-field pattern using Equation (7) [16]. ECC represents an important parameter that indicates the level of separation between the antennas in the MIMO structure. A low level of ECC indicates that there is a high level of separation. Ideally, the value of ECC should equal zero. Practically, the accepted limits of ECC are less than 0.5. The ECC based on the far-field results is more accurate than that based on the S-parameter as it includes the field coupling of the closely spaced antenna elements. Figure 24 shows the ECC curve generated from the far-field results. It is depicted from Figure 24 that the peak value of ECC generated from the far-field results does not exceed 0.05. Therefore, a very high degree of ECC is expected to be more accurate than that based on the S-parameter characteristics. Figure 23: The simulated gain versus the operating frequency range. Figure 22: The simulated far-field radiation pattern at port (4). (a) E-plane and H-plane at \(f\) = 2.4 GHz; (b) E-plane and H-plane at \(f\) = 4 GHz; (c) E-plane and H-plane at \(f\) = 6.6 GHz; (d) E-plane and H-plane at \(f\) = 10 GHz. of separation and isolation between the antennas in the proposed MIMO configuration is obtained. Moreover, there is an important parameter used in the UWB-MIMO antenna to measure the diversity performance, called the diversity gain (DG). Equation (8) was used to generate the DG curve. Figure 25 shows the diversity gain versus the operating frequency. \[ECC_{ij}=\frac{|S_{ii}^{*}S_{ij}+S_{ji}^{*}S_{jj}|^{2}}{(1-|S_{ii}|^{2}-|S_{ji}|^{ 2})(1-|S_{jj}|^{2}-|S_{ij}|^{2})} \tag{6}\]  
where \(S_{ii}\) and \(S_{jj}\) are the reflection coefficients at port \(i\) and port \(j\), respectively, while \(S_{ij}\) and \(S_{ji}\) are the isolation between port \(i\) and port \(j\). \[ECC_{ij}=\frac{|\int_{0}^{2\pi}\int_{0}^{\pi}XPR\cdot E_{\theta i}\cdot E_{ \theta j}^{*}\cdot P_{\theta}+E_{\phi j}\cdot E_{\phi j}^{*}\cdot P_{\phi})d \Omega|^{2}}{\int_{0}^{2\pi}\int_{0}^{\pi}XPR\cdot E_{\theta i}\cdot E_{\theta i }^{*}\cdot P_{\theta}+E_{\phi i}\cdot E_{\phi i}^{*}\cdot P_{\phi})d\Omega \times\int_{0}^{2\pi}\int_{0}^{\pi}XPR\cdot E_{\theta j}\cdot E_{\theta j}^{* }\cdot P_{\theta}+E_{\phi j}\cdot E_{\phi j}^{*}\cdot P_{\phi})d\Omega} \tag{7}\]  
where \(ECC_{ij}\) is the envelope correlation coefficient between port \(i\) (i.e., antenna \(i\)) and port \(j\) (i.e., antenna \(j\)). The suffixes \(i\) and \(j\) represent the port numbers. In the case of \(i\) = 1 and \(j\) = 2, the calculated \(ECC\) is named \(ECC\) 1-2, which represents the \(ECC\) between port 1 and port 2. XPR is the cross-polarization ratio, and \(P_{\theta}\) and \(P_{\phi}\) are the angular density functions of the obtained wave in the \(\theta\)-plane and \(\phi\)-plane, respectively. \(E_{\theta i}\) and \(E_{\phi i}\) are the electric field components in the \(\theta\)-plane and \(\phi\)-plane for port \(i\), respectively. \(E_{\theta j}\) and \(E_{\phi j}\) are the electric field components in the \(\theta\)-plane and \(\phi\)-plane for port \(j\), respectively. \[DG=10\sqrt{1-(ECC)^{2}} \tag{8}\]  
Another important parameter in terms of diversity characteristics is the total active reflection coefficient (TARC). The total active reflection coefficient (TARC) parameter shows the active operating spectrum for the proposed MIMO radiator configuration. Equation (9) is used to calculate the TARC parameter from the S-parameters. \[\Gamma_{a}^{t}=\sqrt{\frac{(|S_{11}+S_{12}e^{i\theta}|^{2})+(|S_{21}+S_{22}e^ {i\theta}|^{2})}{2}} \tag{9}\]  
where \(S_{11}\) and \(S_{22}\) are the reflection coefficients at port 1 and port 2, respectively.