# Quad Element MIMO Antenna for C, X, Ku, and Ka-Band Applications
## 3 MIMO Performance of the Proposed Antenna  
The MIMO performance of the proposed antenna system is investigated in terms of S-parameter, ECC, DG, radiation pattern, efficiency, gain, MEG, TARC, CCL, and CC. The measured \(-10\) dB impedance bandwidth of the proposed MIMO antenna system are 3-15.5 GHz (% bandwidth of 116.27), 26.4-34.3 GHz (% bandwidth of 32.45), and 36.1-48.9 GHz (% bandwidth of 32.74). Over the entire frequency bands in OFB1, OFB2, and OFB3 the simulated minimum values of port isolation are 15.7 dB, 23.2 dB, and 23.2 dB, respectively; however, the measured minimum values of port isolation are 15 dB, 22 dB, and 22.3 dB, respectively. The simulated and measured S-parameter is depicted in Figure 6a. The envelope correlation coefficient (\(\rho_{i,j}\)) can be used for assessing the diversity efficiency of the MIMO antenna system. The value of the ECC that is closest to zero implies that the MIMO antenna system has strong isolation and excellent diversity gain. Equation (5) [45] is used to calculate the measured ECC for a MIMO antenna system in this work. \[ECC=\rho_{i,j}=\frac{\left|\iint_{4\pi}\left[\overset{\rightarrow}{M_{i}}( \theta,\varphi)\cdot\overset{\rightarrow}{M_{j}}(\theta,\varphi)\right]d \Omega\right|^{2}}{\left[\iint_{4\pi}\left|\overset{\rightarrow}{M_{i}}( \theta,\varphi)\right|^{2}d\Omega\right]\cdot\left[\iint_{4\pi}\left|\overset{ \rightarrow}{M_{j}}(\theta,\varphi)\right|^{2}d\Omega\right]} \tag{5}\]  
where, \(\overset{\rightarrow}{M_{i}}(\theta,\varphi)\) indicates the 3D radiation pattern when antenna '\(i\)' is excited, and \(\overset{\rightarrow}{M_{j}}(\theta,\varphi)\) indicates the 3D radiation pattern when antenna '\(j\)' is excited. The solid angle is denoted by the symbol \(\Omega\). The degree of the improvement of the MIMO system is determined by diversity gain (DG). ECC can acquire the DG [46] calculation using Equation (6). \[DG_{i,j}=10\sqrt{1-ECC_{i,j}} \tag{6}\]  
The simulated and measured ECC and DG over the frequency bands OFB1, OFB2, and OFB3 are depicted in Figure 6b. The simulated ECC and DG over the frequency bands OFB1, OFB2, and OFB3 are better than (0.213, 8.87 dB), (0.002, 9.89 dB), and (0.017, 9.91 dB), respectively, whereas the measured ECC and DG over the frequency bands OFB1, OFB2, and OFB3 are better than (0.1, 7.86 dB), (0.034, 9.97 dB), (0.04, 9.82 dB), respectively. Figure 5: Fabricated antenna: (**a**) top view and (**b**) bottom view. Figure 7 depicts the simulated and measured two-dimensional (2-D) radiation patterns of Ant1-Ant4 at the frequencies 11.1 GHz, 31.6 GHz, 37.8 GHz, and 46.8 GHz in the XZ plane. At the frequency 11.1 GHz, 31.6 GHz, 37.8 GHz, and 46.7 GHz, the co-polar major lobe direction of Ant1-Ant4 are (184\({}^{0}\), 183\({}^{0}\), 176\({}^{0}\), 177\({}^{0}\)), (93\({}^{0}\), 148\({}^{0}\), 266\({}^{0}\), 212\({}^{0}\)), (162\({}^{0}\), 136\({}^{0}\), 198\({}^{0}\), 224\({}^{0}\)), and (185\({}^{0}\), 128\({}^{0}\), 175\({}^{0}\), 232\({}^{0}\)), respectively. Based on the observations, it is discovered that the radiation patterns of (Ant1, Ant3) and (Ant2, Ant4) are complementary to each other in the XZ plane. Such complementary radiation pattern qualities enable a low value of ECC between antennas and are also useful in producing self-isolated MIMO antenna systems. In Figure 8, the total efficiency and gain of Ant1 is illustrated. The simulated average efficiency and gain of Ant1 over the frequency bands OFB1, OFB2, and OFB3 are (49.1%, 1.76 dB), (58.2%, 4.65 dB), and (50.5%, 5.07 dB), respectively, whereas the measured average efficiency and gain over the frequency bands OFB1, OFB2, and OFB3 are (44.3%, 1.54 dB), (48.1%, 4.42 dB), and (44.9%, 4.85 dB), respectively. Figure 6: (a) S-parameter (simulated and measured), (b) ECC and DG (simulated and measured). Figure 8: Simulated and measured gain-efficiency versus frequency plot. Figure 7: Radiation pattern of antennas @11.1 GHz, @31.6 GHz, @37.8 GHz, and @46.8 GHz in _X_Z plane.