## 4 Conclusions  
The study has extensively analyzed a digital beamforming transceiver front-end for LEO satellite communications. It adopts the paradigm of the digital twin to assess how impairments affect the performance of the transmitting and receiving chains. For system antenna designers, such an evaluation highlights the most critical subsystem parameters of the RF and digital chain, thus permitting a trade-off between them. In the first part of the paper, we developed a thinned array antenna, implementing a specific tapering feed. The antenna was fully characterized. The radiation characteristics, along with the information about elements' mutual coupling, were included in the system-level analysis of both the receiving and transmitting systems.  
The system-level analysis highlighted the effect of the mutual coupling between antennas, and its twofold drawback: first, for the pattern, an overall gain reduction and a slight modification of the side-lobe level; second, an amplitude and phase scaling of the complex envelope that needs to be fixed at the receiver in the digital domain.  
In terms of the transmitter front-end, the system-level analysis highlighted a set of values leading to an EVM better than 1.5% RMS considering standard conditions. In terms of the receiver front-end, the analysis highlighted a set of minimum features in terms of phase noise, ENOB, and I/Q imbalance, which provide a BER better than \(10^{-4}\). The sensitivity can hardly be reduced below \(-95\) dBm in the standard front-end setting; better sensitivity can be achieved with digital modulation coding.  
An additional consideration is related to the impact of the antenna feed tapering on the average transmitting chain Power-Added Efficiency (PAE). In particular, according to the data reported in Table 3, the transmitting channels experience different peak power levels due to the feed tapering established during the antenna design. For this reason, using the same PA module for all the TX channels would result in a large number of those PAs operating with large power back-off, about 4.8 dB in our case; consequently, this results in a low average PAE. Scaling the PA size, the peak PAE would occur at the actual value of the peak power. According to the tapering strategy, we can consider that a significant number (N) of PAs are effectively driven with a reduced peak power. It results in those PAs reaching a maximum efficiency equal to (PAE-\(\Delta\)). Thus, considering the total number of the channels (\(N_{\text{E}}\)), considering two sizes of PAs, the gain in average PAE can be calculated by  
\[\text{PAE}_{Gain}=\frac{\text{PAE}}{(\text{PAE}-\Delta)+\frac{N}{N_{E}}\Delta} \tag{1}\]  
where \(N\) out of \(N_{\text{E}}\), is the number of PAs with a reduced size. The Figure 2 reports the normalized amplitude of the feeding with respect to the position of the array element in the lattice. Thus, the strategy of the PA down-scaling could consider that lower-sized PAs correspond to normalized feeding less than one. In the case under consideration, we can estimate PAE = 20%, \(\Delta\) = 10%, \(N\) = 156 (i.e., the number of elements with a tapering coefficient less than or equal to 1), and \(N_{E}\), being the PAE\({}_{Gain}\), is about 1.33.  
Conceptualization, G.L., A.C. ([PERSON]), G.G. and A.C. ([PERSON]); Methodology, G.L., M.R., S.M., V.P., A.C. ([PERSON]) and S.S. All authors have read and agreed to the published version of the manuscript. This research was funded by Thales Alenia Space--Italy, via Saccomuro 24, Rome, Italy.  
Not applicable.  
Data Availability Statement: Data are contained within the article. Additional data can be provided--if not restricted--by mailing with corresponding authors.  
Conflicts of Interest: Authors [PERSON], [PERSON] and [PERSON] were employed by the company Thales Alenia Space Italy. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.