# Propagation Characteristics of Modulated EHF Signal in the Wake Region of Plasma Sheath
## 4 Discussion  
Previous studies have mostly focused on the communication \"blackout\" on the wall or the nose of the vehicle. Only a few studies have analyzed the tail communication performance, mainly for Ka band, and the plasma sheath parameters were simply set (e.g., only typical values of electron density at certain heights were used) [36; 37; 38]. Moreover, when the electron density of the plasma sheath reaches about \(10^{20}\) m\({}^{-3}\), the Ka band signal cannot penetrate the plasma sheath. Based on the dynamic time-varying plasma sheath model, the communication performance of EHF signals in the tail channels of the reentry vehicle is investigated for the first time in this study. Our results indicate that, when an EHF band is adopted in the tail of the plasma sheath and the electron density is in the magnitude of \(10^{19}\) m\({}^{-3}\), the transmission coefficient can be greater than 0.7, even if the carrier frequency is 94 GHz. It can be seen from Section 2 that the transmission coefficient increases and the phase shift fluctuates more violently as angle \(\alpha\) increases. As is illustrated in Section 3, when 2 PSK modulation with a carrier frequency of 140 GHz or 225 GHz, or 4 QAM (QPSK) modulation with a carrier frequency of 140 GHz, and channel 6 are adopted, better BER performance can be obtained. Figure 4 illustrates the BER variation with the threshold of the 2 ASK and 2 PSK systems, the schematic diagram of 2 FSK non-coherent demodulation, and its waveforms of the nodes. As can be seen from Figure 4a, the optimal threshold of the 2 PSK system is 0, which is independent of amplitude, while the optimal threshold of the 2 ASK system is half of amplitude, which is closely related to amplitude. In addition, the demodulation method of the 4 QAM (QPSK) system is similar to that of 2 PSK, and the threshold is also 0, which is independent of amplitude. As can be seen from Figure 4b,c, the 2 FSK communication system does not need to set the decision threshold artificially, as it makes a decision based on the size of the two quadrature demodulation signals. The bandwidth of 2 ASK, 2 PSK, and 4 QAM (QPSK) modulation systems is twice the symbol rate, while the bandwidth of 2 FSK is the absolute value of the difference between the two carrier frequencies plus twice the symbol rate. The frequency band utilization of a communication system is defined as the amount of information transmitted on a unit frequency band per second. The bandwidth utilization of 2 ASK and 2 PSK is 0.5 bit/s/ Hz), and that of 4 QAM (QPSK) is 1 bit/s/Hz), while that of 2 FSK is less than 0.5 bit/s/Hz). Therefore, for the four modulations involved in this article, 4 QAM (QPSK) has the highest bandwidth utilization, while 2 FSK has the lowest bandwidth utilization. Based on the above analysis, it can be concluded that the 2 PSK system can be selected if the anti-noise performance of the system is considered first, while the 4 QAM (QPSK) system can be selected if the bandwidth utilization is considered first. In addition, the BER is also closely related to the channel electron density level and channel length. Better BER performance in channel 6 may be controlled by these two factors. Here, we further analyze the maximum electron density and channel length of all channels at some selected moments, and the results are illustrated in Figure 5. According to Figure 5, the maximum electron density decreases with an increase in \(\alpha\) after 1.2 ms. Generally, in the early stage of sheath evolution (before 1.2 ms), compared with the fluctuation of electron density of channels with \(\alpha<60^{\circ}\), the fluctuation of electron density of channels with \(\alpha\geq 60^{\circ}\) is more serious, and the lengths of channels with \(\alpha\geq 60^{\circ}\) are very long. When \(2^{\circ}\leq\alpha\leq 50^{\circ}\), the maximum electron density is relatively larger and may result in worse BER performance, even if the length of the channel is small.