## 3 Influence of Physical Properties of NS on Communication, Navigation, and TT&C Integration
### Atmospheric Loss in NS
#### 3.3.5 NS Multipath and Doppler  
In the NS, the presence of multiple scatterers such as hills, buildings, and the ionosphere will cause the transmitted radio waves to propagate along multiple different paths. Therefore, the signal received at the receiving end is the superposition of multiple attenuated signals of the transmitted signal. The NS multipath channel model usually includes the direct component, the ground reflection component, and the remaining multipath components. Considering that in the actual channel, the reflection paths formed by the atmospheric ionosphere and those formed by mountains, hills, and building share differ  
Figure 8: Simulation results of the attenuation coefficient, phase shift coefficient of the plasma, and the electron density distribution model of the spatially inhomogeneous plasma. (**a**) Attenuation coefficient \(k\) and phase shift coefficient \(m\). (**b**) Electron density distribution model of the spatially inhomogeneous plasma. ent time delays, they are distinguishable. Therefore, we improve the model proposed in Reference [83] and propose a four-path channel model suitable for the NS,  
\[r(t)=A_{0}[1+A_{1}\delta(t-\tau_{1})+A_{2}\underset{N\rightarrow\infty}{\lim} \underset{n=1}{\overset{N}{\sum}}a_{n}\delta(t-\tau_{2})+A_{3}\underset{N \rightarrow\infty}{\lim}\underset{n=1}{\overset{N}{\sum}}a_{n}\delta(t-\tau_ {3}) \tag{17}\]  
where \(A_{0}\) is the fading coefficient of the direct path, \(A_{1}\) is the normalization coefficient of the ground reflection path relative to the direct path, and \(A_{2}\) is the normalization coefficient of the reflection path of mountains, hills, and building. \(A_{3}\) is the normalization coefficient after removing \(A_{0}\), \(A_{1}\), and \(A_{2}\). \(a_{n}\) is the fading coefficient of different scatters. The typical value of \(A_{1}\) ranges from 0.25 to 0.75, \(A_{2}\) ranges from 0.084 to 0.01, \(A_{3}\) range from 0.084 to 0.01. Since the third and fourth components of Equation (17) are relatively small in energy, they can be equivalent to a random noise in analysis and are statistically independent from the first two components. In addition, since the Doppler shift determines important characteristics of the fading channel such as the average fading rate, the average level crossing rate, and the average fading duration, this characteristic must be reflected in the communication, navigation, and TT&C channel of high-speed NS vehicles, especially when the vehicle is operating at a high speed, the frequency shift is relatively large. The Doppler shift is mainly caused by the high-speed flight of the vehicle, so the impact caused by the Doppler shift cannot be ignored. At this time, the frequency of the signal received by the mobile terminal is \(f_{c}\) + \(f_{d}\), where the calculation equation for the Doppler shift \(f_{d}\) is as follows [84],  
\[f_{d}(t)=\frac{vf_{c}}{c}\cos\beta(t) \tag{18}\]  
where \(f_{c}\) is the signal transmission frequency; \(\beta\) is the angle between the reference station and the aircraft; \(f_{d}(t)\) is the Doppler shift. Since the speed of the spacecraft is near 5-25 Mach, and the K/Ka to be evaluated is between 18 GHz and 40 GHz, so the Doppler variation range is about 102-1133.33 KHz. Assuming the speed of the hypervelocity aircraft reaches 25 Mach and the carrier frequency is 30 GHz, then the maximum Doppler shift is \(f_{c\_max}\)\(\pm\) 850 KHz. In combination with Equations (16) and (17), Figure 9 simulates the bit error rate (BER) of four multipath channels with different delay and multipath number under the conditions of Doppler shift of 100 Hz, carrier frequency of 25 GHz, symbol number of 1 \(\times\) 10\({}^{5}\), and sampling rate of 0.1 MHz, using BPSK modulation, BER with different delay, and relative power is set for the four-path model; among them, we also provide the BER of the direct signal path, aiming to provide a basis for comparative evaluation of signal propagation in two or more paths. The relevant simulation parameters are shown in Tables 3 and 4.