## 1 Introduction  
Enhancing Low Earth Orbit (LEO) satellite communication system with the advanced technologies proposed in 5G will be a promising approach to achieve a high data rate with Gigabit per second (Gbps) broadband, low delay, and massive user access around the world [1]. It will play a key role in future services scenarios in the sixth generation (6G) era, such as Global-enhanced Mobile Broadband (G-eMBB) in areas with no coverage by Base Stations (BS), or Remote-massive Machine-type Communications (R-mMTC) convergence [2, 3, 4, 5, 6]. The incoming network is the LEO Satellite Internet Network (LEO-SIN), which have some characteristics of large constellations with more than 1000 satellite, a high-frequency band with Ku, Ka, Q, and V, and broadband with more than 100 MHz for each user [7, 8, 9, 10, 11]. The third Group Partnership Project (3 GPP) put forward the Non-terrestrial Network (NTN) project to consider the satellite network as an access network within the fifth generation (5G) since 2018 [12, 13]. Starlink has launched more than 1000 satellites to complete basic network construction and operate internet services for users since 2020 [14; 15]. The biggest concern regarding the design of LEO-SIN is mainly to make communication systems adapt to the environment with high dynamic, long delay, and serious channel degradation. Therefore, how to describe and model the satellite channel characteristics accurately, would be the key to design systems and radio interfaces for LEO-SIN. There are some proposals in the NTN project focused on the performances and improvements of Orthogonal Frequency Division Multiplexing (OFDM) waveforms, receiver synchronization in satellite scenarios with high dynamic, and long delay [16]. Some researches demonstrate that the subcarrier bandwidths and receiver synchronization need to suffer more than 100-kHz frequency offsets in LEO-SIN instead of about 20 kHz in earth [17]. The channel model is considered to describe the probability distributions of signal characteristics through channels, which can support the calculations of signals degradations of a different angle, power, delay, or phase. That is a set of continuous changes. However, in simulations or hardware implementation, all continuous signals would transfer into the form of discrete bits. Therefore, all channel characteristics in the simulations would respond to a set of discrete pulses, which superimpose on each relative filter, as shown in Figure 1.  
The Doppler Power Spectrum (DPS) is a method to describe frequency dispersion for the power superimposing from different paths with different arrival times or angles. The DPS of LEO-SIN is quite different from the DPS of the Geosynchronous Earth Orbit (GEO) satellite and Terrestrial Mobile Communication Network (TMCN). In the scenarios of the GEO satellite, there is an obvious main path, with greater power than that of other paths with long-distance degradations. The PDF of DPS of GEO obeys Rician distribution. In the scenarios of TMCN, the power of each path only has a few differences. The PDF of DPS of TMCN obeys Rayleigh distribution, whose paths have different dependent Doppler frequency offsets. The DPS of TMCN can be described by [PERSON] model. However, in the scenario of LEO-SIN, the power of the main path is not larger than other paths. So, the power of other paths cannot be ignored. In addition, there is a large Doppler-frequency Offset (DFO) delay spread for a large DFO changing rate. Some new characteristics are brought into the model of DPS in LEO-SIN, which are on the main path or not at the center point of DPS, asymmetrical DPS, and multi-path signals with random Angle of Arrival (AOA). The traditional [PERSON]'s model cannot describe the above characteristics, which have obvious deviations from real situations. Existing methods of simulation implementation of DPS are based on the superpositions of different sinusoids at a different discrete frequency, which are the methods of Sum-of-Sinusoids (SOS) [18; 19].