## 3 Model of the Digital Beamforming Architecture in System-Level CAD
### TX Chain Analysis  
The results of the TX signal processing chain analysis are provided in terms of signal quality, i.e., its EVM. For this analysis, the chain was implemented considering the digital \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Cases** & \multicolumn{2}{c}{\(\mathbf{\theta_{0}=0^{\circ}}\)} & \multicolumn{2}{c}{\(\mathbf{\theta_{0}=30^{\circ}}\)} & \multicolumn{2}{c}{\(\mathbf{\theta_{0}=52^{\circ}}\)} \\ \hline  & **G (dB)** & **SLL (dB)** & **G (dB)** & **SLL (dB)** & **G (dB)** & **SLL (dB)** \\ \hline zero coupling & 29.98 & 22.48 & 29.68 & 24.68 & 27.69 & 21.57 \\ numerical coupling & 28.55 & 22.25 & 29.28 & 21.42 & 27.15 & 19.45 \\ degraded coupling & 27.32 & 21.11 & 28.83 & 18.87 & 26.45 & 19.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Antenna gain (G) and the side-lobe level (SLL) comparison. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(\theta_{0}\) & \(\pm 52^{\circ}\) & \(\pm 30^{\circ}\) & \(\pm 15^{\circ}\) & 0 & \(\pm 52^{\circ}\) & \(\pm 37^{\circ}\) & \(\pm 22^{\circ}\) \\ \hline \(\phi_{0}\) & \(90^{\circ}\) & \(90^{\circ}\) & \(90^{\circ}\) & N.A. & \(45^{\circ}\) & \(45^{\circ}\) & \(45^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Directions used for multibeam analysis. Figure 10: Multibeam performances for 13 beams. (**a**) Contour polar plot; (**b**) cut aligned along \(\phi_{0}=45^{\circ}\); (**c**) cut aligned along \(\phi_{0}=90^{\circ}\). Only the cases of no coupling and numerical coupling are considered for the cuts. signal processor, the DAC, the mixer, the LO, and the PA; all of them defined by the parameters defined in Table 5.  
The antenna (feed tapering and coupling for each array element) is included in the TX signal performance evaluations. The test signal adopted for the transmitter chain testing consists of a 16-QAM (quadrature amplitude modulation) modulated signal, 12.5 MHz symbol rate, over-sampling factor equal to 8, and power level capable of driving at maximum power the PAs stage. The transmitter was evaluated both in the nominal state and in an \"ideal\" state. In the latter the subsystems behave ideally on the entire frequency range and signal dynamic. In ideal conditions the ENOB is set to 16, there are no imbalances, no phase noise, and mixer and LO are ideal. Only the PA linearity exhibits non-ideal, nominal, conditions. Table 8 reports the comparison between the two cases. It is apparent that, indeed, standard conditions are very close to the ideal case; thus, they can be both considered as a benchmark for further analyses, see Table 9.  
Starting from the nominal state, the impact of the phase noise on the transmitted signal quality is analyzed first. Figure 10(a), reports the influence of the phase noise on the EVM. Results are reported as a function of the phase noise amplitude, spanning the range \(-158\) to \(-84\) dBc/Hz at 1 MHz. From the figure it can be observed that, as expected at the nominal value of \(-120\) dBc/Hz, the signal quality is consistent with the ideal case, while degrading the phase noise to \(-108\) dBc/Hz and higher has a significant impact on the EVM. Concerning the impact of the DAC-induced noise and signal quality degradation, we considered the effective number of bits for the conversion. The simulation results for the transmitted signal are provided in Figure 10(b), where a significant influence of the ENOB on the EVM is observed for values below 6 bit. Conversely, considering ENOB exceeding the nominal value, the EVM improves. The next analysis considers the impact of the up-converter stage on the signal quality. For this purpose Figure 12 reports the influence of the up-converter imbalance in terms of amplitude (AM) and phase (PH) on the EVM. The EVM shows a stronger dependency on the magnitude imbalance rather than on the phase imbalance, and, for phase variations in excess of \(\pm 15\%\) with respect to nominal values, (Table 5), its dependency on phase becomes negligible with respect to those related to amplitude.