# Highly Compact 4 \(\times\) 4 Flower-Shaped MIMO Antenna for Wideband Communications
## 3 2-Port MIMO Antenna Design  
In this section, a single antenna is copied to compose the 2 \(\times\) 2 MIMO antenna, where antenna 2 is placed side-by-side with antenna 1 as shown in Figure 3a. The spatial distance between the two radiators is 14.6 mm, and they are designed on the same substrate FR4 epoxy (\(\varepsilon_{\text{r}}\) = 4.4) with a total area of 15 \(\times\) 30 mm\({}^{2}\). The insertion and return losses are investigated in Figure 4a, and it can be noticed that the antenna succeeded in obtaining the desired frequency band with a range from 5.7 GHz to 11 GHz with S\({}_{11}\) below \(-\)10 dB and the lowest value of S\({}_{11}\) is \(-\)19 dB at 6.45 GHz; in addition, the obtained S\({}_{21}\) result is below \(-\)15 dB for the same achieved frequency band. Although the isolation is acceptable since it is below \(-\)15 dB, further enhancement is required, and it could be achieved by inserting decoupling stubs between the two radiators, as depicted in Figure 3b. The presented decoupling stub is similar to an inverted fork with three rectangular slots of length 3.4 mm in the main fork arm (10.2 mm). The overall area of the decoupling stub is 4 mm \(\times\) 14 mm, and two of these stubs are added on the top and the bottom layers of the substrate for improved isolation between the two radiators. The effect of the decoupling stubs on the two-port MIMO antenna performance is demonstrated in Figure 4b. It can be observed that the achieved S\({}_{11}\) is below \(-\)10 dB from 6 GHz to 11 GHz with a minimum value of \(-\)18.5 dB at 6.6 GHz, and S\({}_{21}\) outcome is improved after using the fork-shaped stubs with a value below \(-\)20 dB starting from 6.4 GHz till the end of the obtained frequency band which confirms the positive influence of the newly added isolation stubs on the MIMO antenna outcomes. As well, the realized gain and the radiation efficiency with and without the decoupling stubs are displayed in Figure 4c,d, which show that the antenna has gain fluctuated between 4 dBi and 5 dBi with decoupling stubs, from 3 dBi to 4 dB without stubs while the efficiency fluctuates from 80% to 95% with stubs and from 90% to 95% without stubs. Figure 3: \(Cont.\)  
Figure 2: The outcome of the single element: (**a**) \(S_{11}\); (**b**) gain and radiation efficiency. Another arrangement of the two MIMO radiators is utilized to investigate its influence on impedance-matching performance. The new arrangement is accomplished by putting the two radiators face-to-face within a constrained area of 15 \(\times\) 30 mm\({}^{2}\), so the shortest distance between the two radiators is 5.7 mm, as demonstrated in Figure 5a. The outcomes of the face-to-face two-port MIMO antenna are shown in Figure 6a, and it is clear that the antenna covers the same frequency range (6-11 GHz) with S\({}_{11}=-21.5\) dB at 7 GHz. Furthermore, the mutual coupling between elements is less than \(-18\) dB over the obtained frequency band. In order to investigate the effect of the isolation stub used before, it will be necessary to investigate the effect of the isolation stub used before, it will be necessary to investigate the effect of the isolation stub used before. Figure 4: The 2-port (side-by-side) MIMO antenna: (**a**) S\(-\)parameters outcomes without decoupling stubs; (**b**) S\(-\)parameters outcomes with decoupling stubs; (**c**) gain; (**d**) radiation efficiency. Figure 3: Layout of the 2-port (side-by-side) MIMO antenna: (**a**) without decoupling stubs; (**b**) with decoupling stubs. inserted between the two radiators on the top and bottom sides of the substrate, as depicted in Figure 5b. It is evident from the outcomes in Figure 6b that the antenna radiates in the range from 6 GHz to 11 GHz efficiently, with a significant improvement in the mutual coupling between radiators of less than \(-20\) dB over the achieved frequency band.