## 3 Design of Array Antenna
### 4 Antenna Array and Measurements  
As mentioned earlier, the purpose is to achieve a gain of 12 dBic with minimal AR less than 1.5 dB in the angular width of \(\pm 10^{\circ}\). Thus, the SP feed can easily be extended to the large CP array for high-gain applications. Using the compact and uniform features, the presented 2 \(\times\) 2 SP feed and array elements can be repeated and iteratively extended to the larger scale array. Figure 7 shows the configuration and prototype of 4 \(\times\) 4 array using the group-and-repeat process based on the module unit of the presented 2 \(\times\) 2 feed of 0.35\(\lambda_{g}\)\(\times\) 0.35\(\lambda_{g}\) along with the prototype. The overall size of the array is 3.48\(\lambda_{g}\)\(\times\) 3.48\(\lambda_{g}\) \begin{table}
\begin{tabular}{l l l l l} \hline
**Ref.** & **Type** & **ARBW(\%)** & **CP** & **C-to-C** & **Distance** \\  & & & **Gain(dBic)** & **(\(\lambda_{\theta}\))** & \\ \hline
[17] & Single Layer & 15.5 & 8.25 & 0.5 \\ \hline
[18] & Single Layer & 7.6 & 10.04 & 0.99 \\ \hline
[19] & Single Layer & 1.3 & 13.5 & 0.87 \\ \hline
[20] & Single Layer & 58 & 8.9 & 0.72 \\ \hline
[21] & Single Layer & 50 & 7.8 & 0.46 \\ \hline
[22] & Multi-Layer with air gap & 17.5 & 14.25 & 0.74 \\ \hline
[23] & Single Layer & 11.2 & 9.8 & 0.4 \\ \hline
[Prop.] & Single Layer & 6.935 & 11.5 & 0.535 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of the proposed single-feed 2 \(\times\) 2 CP array antenna with the earlier onesThe simulated and measured results for the reflection coefficients, realized gain, and AR of the design are compared in Figure 8. Improvements in the IBW, AR, and LHCP gain have been observed. The \(S_{11}\) of the proposed antenna array is measured using the Agilent 85052D network analyzer. The measured IBW for \(S_{11}\leqq-10\) dB is essentially greater than 19.5%, as shown in Figure 8a. The behavior of the simulation and measured reflection coefficients are similar but differ by large values, which can be attributed to the fabrication tolerance. The simulated and measured AR and gain of the array are shown in Figure 8b. The measured ARBW of the array is based on the requirement of the application (AR \(\leqq\) 1.5 dB) is 7.23% (7.86 GHz to 8.45 GHz). However, the measured 3 dB ARBW of the array is 8.8% (7.8 GHz to 8.52 GHz). The gain varied between 12.5 dBic and 15.5 dBic in the 3 dB ARBW. A standard dual-polarized horn antenna was used to measure the total gain characteristics of the proposed design. Figure 9 shows the simulated and measured LHCP gain in the angular width of \(\pm 10^{\circ}\) in \(\phi=0^{\circ}\) and \(\phi=90^{\circ}\) planes. Five frequency samples were chosen to depict the performance across the bandwidth. The overall difference in the measured and simulated LHCP gain is 0.5 dB. It can be observed that the measured LHCP gains at all frequencies are higher than 12.5 dBic in the \(\phi=0^{\circ}\) plane, as shown in Figure 9c, whereas in \(\phi=90^{\circ}\) plane, the measured LHCP gains are higher than 12 dBic as seen in Figure 9d. Similarly, the simulated and measured AR of the array are plotted in Figure 10. The measured AR performance in \(\phi=0^{\circ}\) plane shows that the AR lies below 1.5 dB for all frequencies in \(\pm 10^{\circ}\) span, but at 8.05 GHz it is slightly above 1.5 dB at \(+10^{\circ}\). In \(\phi=90^{\circ}\) plane, AR values for all frequencies are lower than 1.5 dB in the desired angular width except 8.05 GHz that crosses 1.5 dB level by 0.15 dB at \(+10^{\circ}\) and \(-10^{\circ}\) of the angular space. The co- and cross-pol (X-pol) radiation patterns of the array antenna are measured and compared with simulated results in Figures 11 and 12 in two planes, \(\phi=0^{\circ}\) and \(\phi=90^{\circ}\), respectively, at five frequency samples. The measured co-pol patterns agree well with simulated results.