# Propagation Characteristics of Modulated EHF Signal in the Wake Region of Plasma Sheath
## 2 Characteristics of EHF Wave in Plasma Sheath
### Spatiotemporal Evolution Characteristics of EHF Wave in the Wake Region of Plasma Sheath  
Figure 2 shows the time-varying curves of the total transmission coefficient (top panels) and phase shift (bottom panels) of EHF signals with carrier frequencies of 94 GHz, 140 GHz, and 225 GHz in the tail channels 1-6. Note that the time resolution of the curves in Figure 2  
Figure 1: (**a**) Schematic diagram of stratified propagation of oblique incident plane wave at the tail of plasma sheath and (**b**) signal transmission channels at the tail of plasma sheath. is \(10^{-5}\) s, and that the transmission coefficient and phase shift at each time point are obtained by Equation (4). Figure 2 reveals that, for a specific carrier frequency, the greater the angle between the channel and the tail of the vehicle, the greater the transmission coefficient. For example, for the carrier frequency of 94 GHz, the total transmission coefficient increases significantly from an average of about 0.45 at an angle of \(36^{\circ}\) (channel 1) to an average of about 0.78 at \(58^{\circ}\) (channel 6). The increase in the total transmission coefficients from channel 1 to channel 6 is mainly due to the polarization loss [13]. In addition, as shown in Figure 2a-c, for a specific channel, the total transmission coefficient increases with the increases in carrier frequency. For instance, for channel 6, the transmission coefficient increases from about 0.78 at 94 GHz to about 0.84 at 225 GHz. Moreover, from Figure 2a-c, we can also find that the transmission coefficients of different combinations of carrier frequency and channel fluctuate with time, but that the fluctuation amplitude is small. Among them, the fluctuation amplitude of 3-6 channels at 94 GHz is the largest, reaching about 0.1, and the fluctuation amplitude of 5-6 channels at 225 GHz is the smallest, with only about 0.02. Overall, when 225 GHz carrier frequency and channel 6 (with a relatively large angle \(\alpha\)) are selected, the maximum and most stable transmission coefficient performance can be obtained. In general, the total transmission coefficients always vary with time, and the total transmission coefficients for higher frequencies is generally higher than that of lower frequencies. The reason for this is that the plasma sheath is dispersive lossy media to EHF signals. For signals of normal incidence, the polarization loss is zero. Then, the absorption led by the collisions between free electrons and neutral particles becomes the main mechanism for the energy loss in EHF signals. The total absorption rate depends on the electron density, collision frequency, and the wave frequency [11]. High frequencies suffer less absorption than that of lower frequencies [24]. As shown in Figure 2d-f, different from the transmission coefficient, the phase shift fluctuates much more severely with time. The phase shift curve looks very messy, but it can still be seen that, for a specific carrier frequency, the fluctuation of phase shift is significantly more intense with an increase in angle \(\alpha\). It should be noted that the phase shifts are measured in the range from -pi to pi, as it is not necessary to take the ambiguity  
Figure 2: The time curves of the total transmission coefficients and phase shifts of the tail channels. (**a–c**) Total transmission coefficients of EHF signals with carrier frequencies of 94 GHz, 140 GHz, and 225 GHz, respectively; (**d–f**) Phase shifts of EHF signals with carrier frequencies of 94 GHz, 140 GHz, and 225 GHz, respectively. of whole cycles into account in the present modulation-demodulation problem. Once the phase varies from a value of smaller than pi to greater than pi, it would register as a sharp decrease in Figure 2, although it is still a continuous variation. The temporal variation of phase shift is led by the temporal variation of the wavelength in the plasma sheath. The plasma sheath is dispersive media, and its cutoff frequency is normally at the EHF band.