# A Versatile Shared-Aperture Antenna for Vehicle Communications
## 2 Antenna Configuration
### Microstrip Antenna for GPS  
A microstrip antenna for GPS applications is included in the proposed shared-aperture antenna. The working frequency of a conventional square microstrip antenna is determined by the length of the radiating edge of the patch. The design parameters of the square patch antenna can be calculated according to Formulas (1)-(4).  
Given the thickness h of the antenna substrate as 1 mm and a dielectric constant of 3.5, we can initially calculate the width of the microstrip antenna \(W\) using (1), where \(f_{r}\) is the resonant frequency, and \(\varepsilon_{r}\) is the dielectric constant. Additionally, based on the effective dielectric constant \(\varepsilon_{ref}\) Formula (2) and the correction formulas for the length \(L\) of the microstrip antenna ((3) and (4)), we can preliminarily determine all the dimensions of the microstrip antenna.  
\[W=\frac{1}{2f_{r}\sqrt{\varepsilon_{0}\mu_{0}}}\sqrt{\frac{2}{\varepsilon_{r}+1}} \tag{1}\]  
\[\varepsilon_{ref}=\frac{\varepsilon_{r}+1}{2}+\frac{\varepsilon_{r}-1}{2}[1+1 2\frac{h}{W}]^{-\frac{1}{2}}\left(W/h\gg 1\right) \tag{2}\]  
\[\Delta L=0.412\frac{(\varepsilon_{ref}+0.3)(\frac{W}{h}+0.264)h}{(\varepsilon_ {ref}-0.258)(\frac{W}{h}+0.8)} \tag{3}\]  
\[L=\frac{1}{2f_{r}\sqrt{\varepsilon_{ref}}\sqrt{\varepsilon_{0}\mu_{0}}}-2\Delta L \tag{4}\]  
As shown in Figure 4, setting the radiant edge of the square patch antenna as a meandering line can effectively increase the length of its radiant edge current path. It allows for a smaller antenna size at the same radiation frequency. The antenna size is reduced from the theoretical 63 mm to 50 mm under the condition of guaranteeing the operating frequency and bandwidth performance of Ant 1. In addition, according to the Chu limit principle (5), the miniaturization of antenna size \(r\) will also lead to a further decrease in antenna bandwidth and gain. Therefore, this design also considers whether the antenna bandwidth can cover the GPS frequency band on the basis of reducing size [29].  
\[Q=\frac{f_{0}}{BW}\geq\frac{1}{\left(kr\right)^{3}}+\frac{1}{kr} \tag{5}\]  
Figure 3: Comparison of the distribution and array spacing of two shared-aperture arrays.  
The proposed microstrip antenna is then placed in a rotated configuration, as shown in Figure 2, with feed phases set at 0 degrees, 90 degrees, 180 degrees, and 270 degrees, enabling circular polarization for the microstrip antenna array.  
In addition, it is quite important to reduce antenna interference in other frequency bands as well. In general, to avoid interference at other frequencies, a narrow-band filter would be cascaded to the antenna. In addition, there are also integrated designs that incorporate the filter structure into the antenna. For an antenna with filter effect, the gain of the antenna presents band-pass characteristics, which can reduce the interference of the antenna in other frequency bands.  
The use of a high dielectric constant and thin substrate can effectively improve the quality, so that the patch antenna has a narrower bandwidth. It can be understood that the medium with low dielectric constant has a weaker binding on electromagnetic energy, and the reduction in thickness also weakens the binding on electromagnetic energy in the structure, and the performance of the antenna is more selective in terms frequency. When designing GPS microstrip antennas, thinner substrates are used to design first-order high-quality narrow-band microstrip antennas. Figure 4 and Table 1 provide the specific dimensions of the microstrip antenna. According to Figure 5, the antenna has the effect of a filter antenna and has a radiation null at low frequency 1.4 GHz.