## 3 Model of the Digital Beamforming Architecture in System-Level CAD  
This section introduces the implementation of the entire system architecture in a system-level commercial CAD with the goal of creating a digital model of the system and thus assessing the impact of non-idealities on the overall characteristics of the transmitter and receiver chains.  
Each chain is composed of behavioral models representing the individual subsystem components, namely, the low-noise amplifier (LNA), the power amplifier, the local oscillator (LO), the mixer, and the analog-to-digital/digital-to-analog converters (ADCs/DACs).  
Figure 6: Elements considered for the mutual coupling analysis; not all numbers of feeding ports are reported in the figure. (**a**) \(S_{0}\) Tile and immediate neighbors numeration. (**b**) \(S_{I}\), but for symmetry, results apply to any outer tile, numeration.  
Figure 7: Behavior of the mutual coupling for both: the central sector when port 1 is fed (**a**) and the peripherical sector when port 15 is fed (**b**).  
Additionally, the system includes both analog and digital filters at various stages of the architecture. All channels within the digital beamforming (DBF) network are identical in structure and their behavior is dictated by the known parameter spread.  
The block diagrams of the transmitter and receiver systems, as implemented in the CAD system simulator, are reported in Figure 7(a), the transmitter, and Figure 7(b), the receiver.  
The subsystems are modeled by built-in models taking into account the most relevant non-idealities of each element. These include I/Q mixer imbalances, amplifier compression, LO phase noise, effective number of bits of the ADC (analog-to-digital converter), as well as cross-coupling between antenna array elements. Concerning the latter, its effect is considered by including the cross-coupling matrix in terms of transmission scattering coefficients for each element. The matrix is then inserted between the block defining the array lattice and the receiver/transmitter front-end.  
System-level performance is assessed through a comprehensive evaluation involving the radiation pattern under both single- and multibeam scanning configurations, the EVM, and the bit error rate (BER). These metrics respectively characterize the quality of the transmitter and receiver subsystems. Concerning EVM analysis, a virtual probe was integrated into the model to collect the signals feeding each array element. This setup enables the examination of how the individual contributions of the transmit chain combine to form the overall radiated waveform. By injecting a modulated test signal, the BER at the receiver back-end can be evaluated, thereby capturing the effects of receiver non-idealities arising from the superposition of signals across all channels. The radiation pattern is computed by mapping the element patterns across the antenna lattice and applying the corresponding excitation signals derived from the full chain simulation.  
A summary of all simulation parameters is provided in Table 5. Hereinafter, these parameters are referred to as the nominal conditions.  
Figure 8: Block diagram of the digital beamforming system implemented in the CAD for the system-level analysis; suitable probe and test signal are highlighted in the picture. (**a**) Transmitter: a probe at the antenna array element section is highlighted. (**b**) Receiver: a test signal illuminating the antenna array is highlighted.