## 4 Experimental Validation and Results Analysis
### Experimental Results and Analysis  
Generally, to obtain higher drain efficiency, the PA is required to operate in 2-3 dB gain compression; thus, we choose two input power levels of \(-\)24 dBm and \(-\)25 dBm from VSG for testing. The nonlinear characteristics of such points are meaningful and significantly impact the quality of the transmitted signal without DPD techniques. Figure 7: Schematic diagram of the experimental setup. For the JSG-DPD technique proposed in this paper, it is necessary to trade-off the model performance and the frame length occupation to select a suitable length of training sequences to model and linearize the APA. Therefore, we first conduct experiments in the noiseless scenario to determine the length of training sequences by observing the improvement of ACPR and EVM. The expression of ACPR and EVM are as follows  
\[\text{ACPR (dB)}=10\lg\left[\frac{P_{adj\_n\_L}(w)+P_{adj\_n\_R}(w)}{P_{ ch\_main}(w)}\right], \tag{20}\]  
where \(P_{adj\_n\_L}(w)\), \(P_{adj\_n\_R}(w)\) are the signal power of the left channel and the right channel adjacent to the main channel, respectively, and \(P_{ch\_main}(w)\) is the power of the signal of the main channel (transmit channel). \[\text{EVM}=\sqrt{\frac{\frac{1}{N}\sum\limits_{n=1}^{N}e_{n}}{\frac{1}{N}\sum \limits_{n=1}^{N}\left({I_{n}}^{2}+{Q_{n}}^{2}\right)}}\times 100\%, \tag{21}\]  
where the vector error signal \(e_{n}=\left(\tilde{I}_{n}-I_{n}\right)^{2}+\left(\tilde{Q}_{n}-Q_{n}\right)^{2}\), \(I_{n}\), \(Q_{n}\) are the expected signal's quadrature components, and \(\tilde{I}_{n}\), \(\tilde{Q}_{n}\) are the two quadrature signals of the real measurement, respectively. Since this part of the test is performed at the ground station (before the satellite launch), the prior knowledge about APA and an almost noise-free experimental scenario can be obtained. The experimental results are shown in Figure 9. For these two input power levels, the improvement of both ACPR and EVM is optimal for a training sequence length of 40,000. Although the EVM improvement may be better after the training length exceeds 100,000, an extra-long frame length is needed to obtain a slight improvement. Especially after hundreds or thousands of superpositions, the slight performance improvement is negligible in comparison to the cost of the frame length. Hence, the training sequence length is chosen to be 40,000 after a trade-off. Figure 8: The LAB picture of the measurement setup. In order to verify the effect of AWGN on the transmitted signal without loss of generality, an SNR of 10 dB is assumed for each satellite transit to establish communication with the ground station. In actual communication scenarios, as shown in Figure 10, when the angle between the satellite and the ground station is 5 degrees from the horizontal, the communication is established, and the communication distance is the longest and the SNR is the smallest. It is at this moment that our proposed method starts to operate. The relative position between transceivers will change, which will lead to fluctuations in SNR. The SNR variation throughout the communication window may exceed 10 dB [41], but our proposed method is only used when communication is just established. The SNR fluctuation range is approximately 10 dB to 10.5 dB, which is not a large enough fluctuation to affect the experimental results. Therefore, for the convenience of the calculation, we assume a constant SNR of 10 dB. The unprocessed received signal at this point is shown in Figure 11a, and the critical sidelobe information of the APA nonlinear system is completely drowned in the noise. After 10, 100, and 1000 superimposed training sequences, the sidelobe information is gradually revealed. As the time domain signal results shown in Figure 11b, the noise reduction processed signal and the original signal almost overlap. Hence, the nonlinear characteristics of the APA system can be extracted.