# Design of a Compact Multiband Monopole Antenna with MIMO Mutual Coupling Reduction
## 2 Design of Antenna Structure
### MIMO Antenna Mutual Coupling Reduction  
In this section, the authors introduce an effective method to suppress MIMO mutual coupling. The design targets for suppression are frequencies at 2.46 GHz and 3.47 GHz because lower frequencies easily produce mutual coupling interference, causing data errors in the MIMO antenna. The material of the MIMO antenna is the same as that of the single antenna, FR4, with the same characteristic parameters. The coordinates are also the same as in Figure 1.  
The configuration and dimensions of the MIMO antenna structure are shown in Figure 6. The distance between antenna 1 and antenna 2 is 30 mm, which corresponds to a quarter-wavelength of the lowest resonance frequency 2.46 GHz. The 30 mm distance is considered for a scenario where WiFi-7 standard access points (APs) need to place 16 antennas [1] within a limited space. However, because the two antennas are close to each other, the lower two frequencies experience strong mutual coupling. Therefore, the design targets for suppression are these frequencies. The two antennas are placed opposite each other and share a common ground. The middle of the ground has two meander slits, with the slits having a common open end on both sides. The length of the upper meander slit is 41 mm, and the lower meander slit is 29 mm, corresponding to half-wavelengths at 2.46 GHz and 3.47 GHz, respectively. Here, the length of the slits is calculated using the same method as Equation (1), with the only change being the constant coefficient adjusted to 2. The effective permittivity derivative is calculated using Equation (2) and set to approximately 2.2. Here, \(\varepsilon_{r}\) represents relative permittivity. \[\varepsilon_{eff}=\sqrt{\varepsilon_{r}+1} \tag{2}\]  
Figure 5: The radiation efficiency, radiated power, and gain of the compact multiband monopole antenna. Figure 7a shows the simulation S-parameters of the MIMO antenna. The reflection coefficients \(S_{11}\) and \(S_{22}\) are the same, and their bandwidths are similar to the single element, with the only difference starting at the higher band from 4.2 GHz. Figure 7b exhibits the detailed transmission coefficient or isolation \(S_{21}\), with and without slits on the ground. Comparing the \(S_{21}\) with and without slits shows mutual coupling suppression from \(-6.5\) dB and \(-6.8\) dB to \(-29.4\) dB and \(-18.5\) dB at 2.46 GHz and 3.47 GHz, respectively. The suppression is 22.9 dB and 11.7 dB, corresponding to a reduction in mutual coupling by 195 and 14.8 times. In the higher frequency band, the mutual coupling is always under \(-15\) dB, indicating sufficient distance between elements. However, there is a peak at \(-12\) dB at 6.5 GHz because the effective wavelength (\(\lambda_{e}\)) is 19.86 mm at 6.5 GHz (\(\lambda_{e}=\frac{C_{0}}{f_{0}\sqrt{c_{e}}}\)). The 30 mm antenna separation distance is approximately \(1.5\lambda_{e}\), which excites resonance and causes stronger mutual coupling, resulting in peak isolation at \(-12\) dB. A more direct way to observe the effect of the method for reducing mutual coupling is from the current distribution of the MIMO antenna. Figure 8 shows the current distribution of the MIMO antenna. Observing Figure 8a, one can see that antenna 1's electromagnetic interference causes an inductive current on antenna 2 when antenna 1 is excited at 2.46 GHz and antenna 2 is terminated. However, in Figure 8b, there is no inductive current on  
Figure 6: The configuration and dimensions of the MIMO antenna structure, including two mean-der slits. Figure 7: The S-parameters of the MIMO antenna. (**a**) The full band. (**b**) The partial band. antenna 2; instead, the conductive current is observed on the upper meander slit. Therefore, the authors believe that the mutual coupling path consists of two components: one from the electromagnetic (EM) wave and the other from the common ground.