## 5 DBF Performance
### Beam Synthesis Performance and Steering Tests  
The aim of the final test was to study the performance of the beams. As the system is fully polarimetric, the DBF has to be characterized for the four Stoke's parameters. As the antennas of the system have only two polarizations, vertical and horizontal, the third and fourth parameters are measured by cross-correlating these inputs. The beams of the third and fourth parameters are identical among them because they are the real and imaginary parts, respectively, of the cross-correlation of the horizontal and vertical beams. Then the analysis is focused in the horizontal (H) and vertical (V) polarizations, and the cross-correlation (VH). To compute the MBE and the beamwidth of beams synthesized in different directions, the whole pattern was measured by scanning across the azimuth angle (\(\varphi\)) range and the elevation angle (\(\theta\)) range. The synthesized beam was steered from \(-20\,^{\circ}\)to \(+20\,^{\circ}\)in \(5\,^{\circ}\)steps, in total nine different beams. For the sake of clarity only five of these normalized DBF results are presented in Figure 16, these beams correspond to the horizontal polarization scanning across the \(\theta\) angle. Synthesized beams in Figure 16 shows a side lobe level (SLL) of \(-17\) dB, in the best case, the \(0\,^{\circ}\)steering beam, and a \(-16\) dB in the worse case, for the \(\pm 20\,^{\circ}\)angle. Furthermore, in some beams there is a misalignment of \(\pm 2\,^{\circ}\)due to the residual calibration error, which does not impact the instrument's performance. Tables 1 and 2 summarize the results in terms of MBE and beamwidth for the V, H and VH beams. For all the possible steering angles the MBE is better than 91% and the best result is for \(0^{\circ}\) where the MBE reaches a value of 95.6% for HV, 94.8% for H and 93.4% for the V polarization. On the other hand, the worst results were, as expected, when the angle of steering is high (\(\pm 20\,^{\circ}\)). Note that the  
Figure 16: PAU-RAD DBF results. Measured normalized array factors in dB for multiple beams (H-pol and scanning the \(\theta\) domain range). design specification was to have a MBE higher than 94%, which has been achieved for the 0 \({}^{\circ}\)steering beam and was almost fulfilled for all steerable beams. The other design parameter was the beamwidth. In this case the best performance was again for the 0\({}^{\circ}\) steering angle when the \(\Delta\theta_{\text{-3 dB}}=22.8\,^{\circ}\) for H, \(\Delta\theta_{\text{-3 dB}}=22.4\,^{\circ}\) for V and \(\Delta\theta_{\text{-3 dB}}=23.33\,^{\circ}\) for HV. Again, the worst results were for the largest steering angles when the beamwidth values reach the maximum of \(\Delta\theta_{\text{-3 dB}}=25.5\,^{\circ}\). TZhe beamwidth requirements were therefore fulfilled in almost all cases. In addition, Table I shows that the HV beams showed the best performance in terms of MBE, but the largest beamwidth. This is due to the way this beam is created from the cross-correlation of the H and V beams. Once the steering capabilities and excellent performance of the instrument had been demonstrated, Figures 17-19 analyze the polarimetric nature of the beams. For brevity purposes only the 0 \({}^{\circ}\)steering angle has been shown. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Polarization**} & \multicolumn{1}{c}{**H**} & \multicolumn{1}{c}{**V**} & \multicolumn{1}{c}{**HV**} \\
**Beam steering** & & & & \\ \hline \(-20\,^{\circ}\) & 92.5\% & 91.8\% & 94.2\% \\ \(-15\,^{\circ}\) & 93.2\% & 92.6\% & 95.0\% \\ \(-10\,^{\circ}\) & 93.2\% & 92.7\% & 95.1\% \\ \(-5\,^{\circ}\) & 93.3\% & 92.9\% & 95.2\% \\ \(\mathbf{0\,^{\circ}}\) & **94.8\%** & **93.4\%** & **95.6\%** \\ \(5\,^{\circ}\) & 92.9\% & 92.5\% & 95.0\% \\ \(10\,^{\circ}\) & 92.8\% & 91.9\% & 95.0\% \\ \(15\,^{\circ}\) & 92.7\% & 91.7\% & 94.2\% \\ \(20\,^{\circ}\) & 92.3\% & 91.2\% & 93.8\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: MBE for the synthesized beams.