## 5 Simulation Results and Analysis
### Results and Discussion  
We observe the convergence of the WMMSE-based precoding algorithm. Figure 4 presents the convergence of the WMMSE-based precoding algorithm in the system with the nonlinearity of the PAs, where \(L\) and \(K\) are set as 8 and 2, respectively. This result confirms the effectiveness of the WMMSE-based precoding algorithm in CF-mMIMO-assisted LEO SATCOM systems. In addition, with a larger number of satellite antennas, the system exhibits a higher EE when the transmit power budget is saturated. Figure 5 demonstrates the EE performance versus transmit power constraint \(P\) with different satellite transmit antenna numbers and different transmit architectures. With the nonlinearity of the PAs taken into account, the trend of the value of EE is essentially the same for different numbers of satellite antennas as the transmit power budget increases. Firstly, the EE performance for \(N=64\) is superior to that for \(N=16\). In both cases, as the transmit power budget increases, the value of EE gradually rises, eventually saturates and no longer tends to increase significantly. As the transmit power budget \(P\) gradually increases, the PA also gradually enters the saturation region, and the distortion during \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter (Each Satellite)** & **Value** \\ \hline Satellite orbital altitude & 600 km \\ Downlink carrier frequency & \(f_{c}=12.6\) GHz \\ Bandwidth & \(B_{w}=0.25\) GHz \\ Shadow fading variance & \(\sigma_{\delta t}^{2}=5\) dB \\ Satellite antenna aperture radius & \(\eta=10\) wavelengths \\ NPA efficiency & \(\xi_{\max}=0.3\) \\ Maximum output power per NPA & \(P_{\max}=6\) dBm \\ Satellite antenna gain & \(G_{5}=38.5\) dBi \\ GU antenna gain & \(G_{GU}=39.7\) dBi \\ Transmit power constraint per satellite & \(P=15\) dBW \\ Basic power consumption per satellite & \(P_{o}=10\) mW \\ Power consumption per RF chain & \(P_{RFC}=338\) mW \\ Power consumption per local oscillator & \(P_{LO}=5\) mW \\ Power consumption per baseband digital precoder & \(P_{BB}=200\) mW \\ Power consumption per phase shifter switch & \(P_{SW}=1\) mW \\ Power consumption per phase shifter & \(P_{PS}=10\) mW \\ Minimum elevation angle & \(\theta_{\min}=10^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 4: EE versus the number of iterations with different satellite transmit antenna numbers and the nonlinearity of PAs. signal transmission increases. In addition, the EE performance of the system with hybrid precoders is marginally inferior to that with fully digital precoders. Figure 6 compares the EE performance of the hybrid precoding when \(N=64\) for the partially connected architectures with different quantization precision. When the transmit power budget is relatively low, the EE performance is very close regardless of whether the analog precoder has a quantization accuracy of 2 or 4. When the transmit power budget is relatively high, the EE gain from higher quantization accuracy is significantly superior to the EE gain from lower quantization accuracy. The reason lies in that the EE gain due to the increase in the transmit power budget exceeds the EE loss due to higher quantization accuracy power consumption. Figure 7 presents the ratio of EE performance to the number of RF chains \(N_{RF}\). In the system model of this paper, the effect of power consumption of RF chains on EE is more obvious. For a fixed power budget, the total rate of data transmission increases as the number of RF chains increases. However, since the increase in power consumption is more significant, the final EE shows a gradual decrease overall. Therefore, the impact of the number of RF chains on EE is not absolute and needs to be weighed against the specific power consumption model of the system. Figure 5: EE versus transmit power constraint \(P\) with different satellite transmit antenna numbers and different transmit architectures. Figure 6: EE versus transmit power constraint \(P\) for different quantization precision with \(N=64\).