## 3 Measurement Results of the Proposed Antenna
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Research**} & **Operating** & \multirow{2}{*}{**Bandwidth**} & **Bore-Sight** & \multirow{2}{*}{**Array Spacing**} & **Number of** & **Unit Cell** \\  & **Band** & & **Gain** & & **Elements** & **Height** \\ \hline
[9] & S & 13.2\% & 12.6 dBi & 0.54 \(\lambda\) & 8 & 0.1 \(\lambda\) \\
[9] & X & 11.7\% & 13.7 dBi & 0.51 \(\lambda\) & 32 & 0.1 \(\lambda\) \\
[10] & S & 11.6\% & 14.0 dBi & 0.73 \(\lambda\) & 4 & 1.4 \(\lambda\) \\
[10] & X & 18.9\% & 21.0 dBi & 0.69 \(\lambda\) & 36 & 1.4 \(\lambda\) \\
[11] & C & 4.6\% & 10.0 dBi & 0.55 \(\lambda\) & 4 & 0.1 \(\lambda\) \\
[12] & X & 4.6\% & 12.0 dBi & 0.72 \(\lambda\) & 4 & 0.1 \(\lambda\) \\
[12] & S & 50.3\% & 10.7 dBi & 0.30 \(\lambda\) & 4 & 2.2 \(\lambda\) \\
[15] & Ka & 33.9\% & 14.8 dBi & 3.0 \(\lambda\) & 4 & 2.2 \(\lambda\) \\
[15] & S & 3.2\% & 20.0 dBi & 1.0 \(\lambda\) & 32 & 0.02 \(\lambda\) \\  & C & 4.6\% & 20.8 dBi & 1.2 \(\lambda\) & 32 & 0.02 \(\lambda\) \\ This work & S & 13.6\% & 5.4 dBi & 0.34 \(\lambda\) & 4 & 0.1 \(\lambda\) \\  & X & 13.4\% & 13.4 dBi & 0.51 \(\lambda\) & 16 & 0.1 \(\lambda\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the proposed antenna’s performances with previous studies. Figure 9: 2D radiation patterns of the proposed antenna: (**a**) S-band element in the \(zx\)-plane; (**b**) S-band element in the \(zy\)-plane; (**c**) X-band element in the \(zx\)-plane; (**d**) X-band element in the \(zy\)-plane. Figure 10 represents the beam-steering performance of the \(2\times 2\) array configuration. To verify the beam-steering performance of the proposed antenna, the active element patterns (AEP) for all array elements are measured in a full anechoic chamber. To measure the AEP for each element of the array, a network analyzer with an RF cable is connected to only one element, and all other elements are terminated. After repeating this procedure for all elements, the total array gain of the proposed antenna is calculated using the obtained AEPs based on the following equation [30; 31]:  
\[P_{array}(\theta,\phi)=\frac{\sum\limits_{n=1}^{N}\overline{w_{n}v_{n}}( \theta,\phi)}{\sqrt{\sum\limits_{n=1}^{N}|w_{n}|}}, \tag{1}\]  
where \(v_{n}\) and \(w_{n}\) represent the complex AEP vector and the weighting vector of the \(n_{\text{th}}\) element, respectively. In the S-band, the array gains in the bore-sight direction based on the measurement and simulation are 5.4 and 6.1 dBi, respectively. Furthermore, the maximum gain varies from 5.4 dBi to 3.5 dBi when the main beam is steered from \(\theta\) = 0\({}^{\circ}\) to 45\({}^{\circ}\). In the X-band result, the measured array gain in the bore-sight direction is 13.4 dBi, which is in good agreement with the simulation result of 14.5 dBi. Herein, the bore-sight gain decreases from 13.4 dBi to 11.6 dBi under the same beam-steering conditions. Figure 11 shows the total active reflection coefficients (TARCs) [32] and the envelope correlation coefficients (ECCs) [33] of the proposed \(2\times 2\) array. The average TARCs for Port 1 and Port 8 (port numbers are marked in Figure 5) are observed when the main beam is steered from \(\theta\) = 0\({}^{\circ}\) to 45\({}^{\circ}\). The average TARCs are \(-9.5\) dB in the S-band and \(-11.8\) dB in the X-band, as shown in Figure 11a,b. In addition, the ECCs for the S-band (from Port 1 to Port 4) and for the X-band (from Port 5 to Port 8) are also examined. The average ECCs for the nearest element are observed as 0.07 in the S-band and 0.002 in the X-band, as shown in Figure 11c,d. The result demonstrates that the proposed shared-aperture antenna is suitable for MFR applications. Figure 10: Beam-steering characteristics of the proposed antenna: (**a**) S-band; (**b**) X-band.