## 4 Experimental Validation and Results Analysis
### Experimental Results and Analysis
According to the DPD structure introduced in the previous sections, the GMP model is applied to model the APA system and generate the predistorted signal. Figure 12 shows the AM-AM and AM-PM curves of this APA system. The predistorted signal forms an inverse relationship with the original APA output signal, which makes the combined pre-distorter and the APA approximately linear. The time-domain signal comparison in Figure 13 reveals that the most effective strategy of the DPD technique is to pre-amplify the signal at high  
Figure 10: The communication window occupied by the proposed method. Figure 9: Improvement results of ACPR and EVM for different input power levels from VSG: (**a**) \(P_{nt}\): \(-25\) dBm; (**b**) \(P_{nt}\): \(-24\) dBm. amplitude so that after the nonlinear APA gain compression, the same linear gain can be achieved as at other low amplitude. Figure 11: Frequency and time domain noise reduction results with STS method: (**a**) frequency domain; (**b**) Time domain. Empirically and based on several attempts to obtain the minimum normalized mean square error (NMSE)  
Figure 12: Measured AM-AM and AM-PM curves with the proposed technique for 100 MHz OFDM signal: (a) AM-AM; (b) AM-PM. Figure 13: Time domain indication of the pre-distorted signal. \[\text{ACPR (dB)}=10\lg\left[\frac{P_{adj\_n\_L}(w)+P_{adj\_n\_R}(w)}{P_{ ch\_main}(w)}\right], \tag{20}\]0  
where \(y(n)\) is the actual output of the APA, and \(g(n)\) is the output of the APA obtained by model fitting. Thus, the optimal parameters selected for the GMP model are 3, 5, 2, 3, 2, 3, 2, 2, which represent the nonlinear order and memory depth of the MP sub-model, lagging envelope term, and leading envelope term, as well as the additional degrees of freedom of the lagging and leading term. In this paper, experiments were also conducted on the MP model for comparison. For fairness, the nonlinear order and memory depth were chosen as three and five, respectively, which are consistent with the MP sub-model of the GMP model. As can be seen from the results in Figure 14 and Table 1, for the case of stronger nonlinearity (input power level: \(-24\) dBm), the application of the proposed JSG-DPD method improves the upper and lower ACPR average performance by nearly 4 dB for a training sequence superposition of 1000 or 100 times with the GMP model, especially the EVM performance by more than 7.5%, which undoubtedly enhances the quality of the transmitted signal significantly. The ground station is more concerned about the improvement status of EVM than ACPR. When the number of training sequence superposition is 10, there is also an improvement of nearly 6.5% in EVM, which is still promising. In contrast, the results without the STS method improved the EVM slightly. In addition, for the results of the MP model, the improvement in EVM is not as good as that of the GMP model, with a difference of about 0.2% to 0.4%. Nevertheless, it is noteworthy that using the MP model without the STS method still improves the ACPR by 2.5 dB, while the ACPR results with the GMP model without the STS method have deteriorated to the extent that it seriously affects the signal transmission in the adjacent channels. For the case of slightly weaker nonlinearity (input power level: \(-25\) dBm), applying the proposed JSG-DPD method, the EVM performance is improved by 6.3% to 6.9% for the training sequence superpositions of 1000, 100, and 10 times with the GMP model. For the results of the MP model, the improvement of EVM is not as good as that of the GMP model,