# A Dual-Band Flexible MIMO Array Antenna for Sub-6 GHz 5G Communications
## 4 MIMO Array Antenna
### Characteristic Mode Analysis  
The characteristic mode theory has been a popular antenna analysis tool for understanding any antenna structure's operating behavior. CMA uses information on different resonant modes, facilitating the understanding of the significant modes that influence the antenna's resonance. The CMA calculates that the whole antenna current is the vector  
Figure 16: S-parameters of the suggested antenna under bending environment (**a**) \(x\)-axis bend, and (**b**) \(y\)-axis bend.  
Figure 15: Bending analysis of the antenna in the \(x\)-axis and \(y\)-axis bends.  
addition of the nth eigen current \(J_{n}\) and modal weighting coefficient \(\beta_{n}\) that is derived from the eigenvalue \(\lambda_{n}\), which is denoted by Equation (2) [19].  
\[J=\sum_{n}\beta_{n}J_{n} \tag{2}\]  
The CM can be estimated from \(\lambda_{n}\) using Equation (3).  
\[X\left(J_{n}\right)=\lambda_{n}\ R(J_{n}) \tag{3}\]  
where \(R\) denotes the real part of the impedance matrix \(\mathbb{Z}\).  
The eigen-based parameter's modal significance (MS) and characteristic angle (CA) are investigated in the study to understand the resonance behavior of the proposed antenna. The CA determines the corresponding field current phase delays. In contrast, the modal significance indicates the normalized current mode value, where a mode resonates when the MS value is near unity. In other words, the particular mode resonates when the eigenvalue is zero or the CA is close to 180\({}^{\circ}\). Figure 17 shows the CMA parameters of the suggested MIMO antenna at both resonances. The study uses the first five fundamental modes (modes 1-5) to examine the antenna's resonance behavior. Initially, let us consider the first resonance. From the figure, the first resonance of the antenna is highly influenced by mode 1, since the modal significance approaches unity and the eigenvalue of that particular mode is zero. This can be further confirmed by the CA value, where the value approaches 180\({}^{\circ}\) for the first mode. The individual current modes contribute to the resonance when the MS value is more than 0.707 [20]. Even though all the other modes contribute to a value higher than 0.707, mode 1 is the most significant mode that helps in radiating energy and contributes much to the first resonance. In addition, it can be deduced from the figure that every mode contributes to the second resonance of the suggested antenna, which has an MS greater than 0.707. However, it is visible that modes 1 and 4 are more significant and contribute to the second resonance with an MS value equal to unity near the second antenna resonance and also over the entire second band of operation. The CA value also approaches 180\({}^{\circ}\) for these two modes, indicating the antenna's radiation.  
Figure 17: _Cont._  
The CMA has been investigated in this study to examine the resonant behavior and how the individual modes of the antenna have contributed to both of the antenna's resonances.  
The surface current distribution of all the characteristic modes (represented by mode 1 to mode 5) for both resonance frequencies is displayed in Figure 18 to enhance the clarity. The significant individual mode current contributes to achieving the desired radiation properties with bidirectional and omnidirectional patterns in the principal E and H planes, respectively.  
Figure 17: CMA analysis: (**a**) modal significance, (**b**) eigenvalue, and (**c**) characteristic angle.  
Figure 18: _Cont._