## 2 Principle Analysis of the Proposed JSG-DPD Technique
### LEO Satellite-Ground Channel  
As for LEO satellite communications, it is commonly necessary to consider the Doppler effect [15] and multipath effect [16]. The multipath effect is the propagation phenomenon of radio frequency (RF) signals arriving at the receiving antenna through various paths from the transmitting antenna. The electromagnetic waves of each path arrive at the receiver at different times, and thus at different phases. The superposition of multiple signals with different phases at the receiver results in a change in the amplitude of the received signal, which produces the so-called multipath fading. When considering that the received signal consists of only multipath signal components, the probability density function (PDF) of the signal obeys the Rayleigh distribution  
\[f_{r}(r)=\frac{r}{\sigma^{2}}\cdot\exp\left[-\frac{r^{2}}{2\sigma^{2}}\right], \tag{4}\]  
where \(r\) and \(\sigma^{2}\) denote the received signal amplitude, and the average multipath power, respectively. While considering the received signal is composed of a line of sight (LOS) signal and multipath signal, the PDF of the signal obeys the Rice distribution  
\[f_{r}(r)=\frac{r}{\sigma^{2}}\cdot\exp\left[-\frac{r^{2}+z^{2}}{2\sigma^{2}} \right]I_{0}\Big{(}\frac{rz}{\sigma^{2}}\Big{)}, \tag{5}\]  
where \(r\) indicates the received signal amplitude, \(z\) represents the LOS signal amplitude, and \(\sigma^{2}\) is the average multipath power [17]. Generally, we assume ground stations are built in non-urban open areas, thus ignoring the effect of reflections caused by buildings. Due to different atmospheric densities, scattering is typically generated in the troposphere at an altitude of about 10-20 km above the ground. For LEO satellites above several hundred km, such a link length is only 2-3% of the total link length, so the resulting multipath effect is insignificant. In addition, the inter-symbol interference (ISI) from multipath can be maximally eliminated by inserting a guard interval between OFDM symbols, where the guard interval is larger than the maximum multipath delay extension of the satellite communication channel. If the cyclic prefix (CP) is filled in the guard interval, the inter-channel interference (ICI) from multipath can also be avoided. This is the commonly used means of OFDM signal transmission. Therefore, the impact of the multipath effect is ignored in this paper. When there is relative motion between the satellite and the ground station, the transmitted carrier frequency received by the ground station is frequency shifted, which is the Doppler shift phenomenon. It is harmful to digital communication using correlation demodulation, and thus cannot be ignored. As depicted in Figure 3, the actual velocity of the satellite is \(v\), and the relative speed of the satellite to the ground station is  
\[v^{\prime}=v\cdot\sin\theta, \tag{6}\]  
which varies dynamically. The Doppler shift is defined as  
\[\Delta f_{c}=\frac{v^{\prime}}{c}\cdot f_{c}, \tag{7}\]  
where \(f_{c}\) denotes the carrier frequency, \(\Delta f_{c}\) represents the carrier frequency offset, i.e., Doppler frequency offset, and \(c=3\cdot 10^{8}\) m/s is the speed of light. According to the standard 401.0-B of the Consultative Committee for Space Data Systems (CCSDS) [18], the maximum relative motion speed between a LEO satellite and a ground station is 10 km/s, and the maximum speed change rate is 380 m/s\({}^{2}\). The maximum Doppler frequency offset of the LEO satellite-ground data transmission system based on Ka-band (28 GHz) is \(\pm\)930 kHz, and the maximum Doppler frequency offset change rate is 35 kHz/s. Therefore, the time-varying Doppler effect makes it difficult for the receiver to accurately track the carrier of the signal, which undoubtedly increases the design difficulty of the receiver. In addition, the Doppler effect causes a spreading/compression of  
\[\Delta B=\frac{v^{\prime}}{c}\cdot B \tag{8}\]  
for a transmitted signal with bandwidth \(B\).