# Compact Quad-Port MIMO Antenna with Ultra-Wideband and High Isolation
## 2 Design of UWB Antenna Unit
### Design Procedure  
To achieve the UWB communication band (3.1-10.6 GHz) specified by FCC, the basic monopole antenna is designed for improvement, and undergoes five steps in total, as shown in Figures 2 and 3. The rectangular monopole antenna in Figure 2 is the initial reference antenna, named Ref. Antenna, and the dielectric substrate is made of Teflon (PTFE) with a thickness of 1.524 mm, dielectric constant \(\varepsilon_{r}=2.1\) and loss tangent angle tan \(\delta=0.0002\). Using the cylindrical approximation method [20], the approximate dimensions of the rectangular radiating patch (\(l\times w\)) and the rectangular ground plane (\(l^{\prime}\times w^{\prime}\)) of Ref. Antenna can be calculated as follows:  
\[l=0.24\times\lambda\times s \tag{1}\]  
Figure 3: Design steps of UWB antenna: (**a**) Ref. Antenna; (**b**) first step; (**c**) second step; (**d**) third step; (**e**) Pro. Antenna; (**f**) perforated antenna model. Figure 2: Rectangular patch planar monopole antenna estimated using the cylindrical approximation. \[s=\frac{h/r}{1+h/r}=\frac{h}{h+r}=\frac{\omega}{\omega+l/2\pi}=\frac{2\pi\omega}{2 \pi\omega+l} \tag{2}\]  
Combined with Formulas (1) and (2), consider the influence of the feed gap (\(g\)) between the background and radiation patch, \(g\) is incorporated into the height (\(h\)) of the cylinder, \(w\) needs to be revised to \(w+g\) in the Formula (2), the lowest resonant frequency (\(f_{L}\)) can be approximated by calculating the following [21]:  
\[f_{L}=\frac{144}{w+w^{\prime}+g+\frac{l}{2\pi\sqrt{\epsilon_{eff}}}+\frac{l^{ \prime}}{2\pi\sqrt{\epsilon_{eff}}}}(GHz) \tag{3}\]  
At the beginning of the design, Formula (3) can be used to obtain the initial dimensions of the antenna structure, and then simulation software is used to optimize and improve the parameters to improve the design efficiency. The dimensional parameters of Ref. Antenna are obtained as follows: \(l=w=21.8\) mm, \(l^{\prime}=25.6\) mm, \(w^{\prime}=4.8\) mm, \(g=1.4\) mm, as shown in Figure 3a. The lowest resonant frequency estimated by Formula (3): \(f_{L}=3.85\) GHz. It can be seen that the red curve from the reflection coefficient curve given in Figure 4 is indeed resonant around 3.85 GHz, in agreement with the calculation. The purple line in Figure 4 represents S\({}_{11}\) = \(-10\) dB. The operating bandwidth of the reference antenna is only 1.4 GHz (3.07-4.47 GHz), which cannot meet the design requirements of UWB technology, so further improvement is needed. The coplanar waveguide feeding structure has many advantages over other feeding methods. First, the single-sided structure makes it easy to connect in series or parallel with other microwave devices, facilitating integration with both passive and active microwave devices. Second, the symmetric ground state of CPW also allows for miniaturized circuits and improved radiation patterns. Third, the primary mode transmitted by the coplanar waveguide is a quasi-TEM mode with no minimum resonance frequency, which can transmit both odd and even modes, thus providing new ideas for the design of new antennas. Finally, the dispersion properties of CPW are also higher than those of the microstrip, which is suitable for broadband implementations of microwave circuits and antennas, and for the study of UWB antennas. Based on the above analysis, it can be seen that the coplanar waveguide feed has many advantages over the microstrip line feed, so the first step of antenna structure improvement is to convert the microstrip line feed into CPW feed, as shown in Figure 3b. The size and position of the feed line and the two grounds in the CPW structure are optimized  
Figure 4: Variation curve of the reflection coefficient during the design process. and analyzed to achieve a good 50 \(\Omega\) impedance matching.