## 3 Model of the Digital Beamforming Architecture in System-Level CAD
### RX Signal Chain  
For the receiving chain, system performance was evaluated in terms of the bit error rate (BER) as a function of several critical parameters. The corresponding block diagram is shown in Figure 8b. The main subsystems of the RX chain include the antenna array (accounting for mutual coupling effects), the LNA, a down-conversion stage with a local oscillator, the ADC, the DBN, and a demodulator configured for BER estimation. The nominal values listed in Table 5 also apply to the receiver configuration. The receiving chain assumes that the incoming signal arrives from the direction pointed by the antenna beam. The incident power on the array was simulated by considering an Incident Power Flux Density (IPFD) in the range \([-63,\,-102]\) dBW/m\({}^{2}\) corresponding approximately to \([-66.5,\,-105.5]\) dBm available to each single element. The first analysis considers the effect of inter-element coupling, which introduces an alteration to the waveform that modifies the BER to an unacceptable BER = 0.077. The comparison of the received band-pass signal in both the cases with and without coupling is shown in Figure 15, reporting both magnitude, Figure 15a, and phase, Figure 15b. By relating the two time domain magnitudes and phase pairs, it is possible to find a complex coefficient for the received signal to compensate for the mismatches between the two couples of plots, which is due to antenna element coupling. This coefficient comprises both a magnitude scaling and a phase delay; it can be effectively computed by using a calibration process, which takes into account a simple pilot signal like, for instance, a BPSK signal. For the considered case--i.e., broadside--this coefficient is 1.0667 exp (j18\({}^{\circ}\)). After this correction, the re-evaluated BER is equal to 0. The presence of this calibration signal is common in many communication systems, and follows policy and constraints depending on the radio access technology. Figure 14: Constellations comparing different transmitting power levels. (**a**) Transmitting power 10 dBm (Nominal), EVM = 1.35%. (**b**) Transmitting power 18 dBm, EVM = 4.3%. Figure 13: EVM versus output power at PA, in in nominal conditions and degraded. Figure 16 reports the influence of phase noise on the BER, considering the same phase noise values considered in the transmission chain. When the amplitude of the phase noise is higher than \(-110\) dBc\(/\)Hz at 1 MHz offset from the carrier, the impact of phase noise on the BER is not negligible. Figure 17 reports the influence of the LNA's noise figure (NF) on the BER. Considering an NF equal to the nominal value--i.e., 1.4 dB--the BER is acceptable. Conversely, an NF equal to or exceeding 2 dB leads to unacceptable BER values. Figure 16: Influence of the phase noise on the BER, nominal conditions consider phase noise = \(-120\) dBc\(/\)Hz at 1 MHz offset from the carrier. Figure 17: Bit error rate as a function of noise figure. Figure 15: Waveforms of the ideal received signal (RX), with coupling, compared to the ideal received nominal signal (nominal). (**a**) Magnitude; (**b**) phase. In Figure 18, the impact of the effective number of bits (ENOB) on the BER is presented. The results indicate that when ENOB decreases below 4, the BER degrades significantly. Conversely, with an ENOB of 4 or higher, the BER remains within acceptable limits. These findings are particularly relevant in the context of system complexity reduction, as the power consumption of an ADC is a nonlinear function of both the sampling rate and ENOB. Therefore, minimizing the ENOB is essential for the efficient implementation of a digital beamforming receiver architecture. The analysis presented above assumes a received input power of \(-66\) dBm, the upper bound of the considered operating range. To extend this evaluation, an additional analysis is conducted for input power levels spanning the range \([-66,\,-105]\) dBm.