# Issues with Modeling a Tunnel Communication Channel through a Plasma Sheath
## 4 Simulations of the Tunnel Radio Communication Channel  
A numerical simulation of a prospective telemetric and control radio line for a spacecraft was performed to analyze the efficiency of overcoming blackout. Optimal reception of radio signals is usually performed using matched filtering [19]. The frequency response of a matched filter directly depends on the spectral density of the signal and noise. The plasma sheath and resonator distort the radio signal due to the absorption of signal energy in certain frequency ranges. The amplitude-frequency and phase-frequency response curves of the \"plasma + resonator\" system are depicted in Figure 7. It is seen that the system's frequency response is quite uneven. The matched filter was designed as a finite impulse response (FIR) filter with tap coefficients representing a complex-conjugate  
Figure 7: Amplitude–frequency and Phase–frequency responses of the structure shown in Figure 3 for the following parameters: \(a=0.5\) cm, \(\epsilon_{d}=700\), \(b=318\) nm, \(z_{\text{rs}}=0.115\) cm, \(c=1\) cm, \(\epsilon_{c}=10\), \(d=10\) cm. impulse response of the \"plasma + resonator\" system. The numerical simulation of the radio signal reception via the proposed resonator was conducted using the scheme depicted in Figure 8. An RF channel was implemented as signal attenuation due to energy loss in the atmosphere. Signal energy loss was calculated using the ITU-R P.618-13 recommendation taking into account the loss caused by signal propagation in the atmosphere, the influence of clouds, and precipitation for the 2.632 GHz operating frequency. The considered system, consisting of the plasma sheath and resonator, was implemented as the FIR filter with tap coefficients representing the impulse response of the \"plasma + resonator\" system. The modulator was designed to form a binary shift-keying (BPSK) signal with a direct sequence spread spectrum (DSSS). The spreading sequence is a maximum-length sequence (MLS). The demodulator was designed using a coherent scheme. The model has been used to conduct a noise immunity investigation for signal-code constructions that meet telemetric and control radio line requirements. For this purpose, estimates for the bit error rate (BER) and signal-to-noise ratio (SNR) were included in the model (that is very common for a variety of tasks) [20; 21; 22; 23; 24; 25]. SNR was estimated as the ratio of the spectral power density in the band of the signal to the spectral power density outside this band. BER was estimated as a ratio of the number of incorrectly decoded bits to the total number of transmitted bits. The signal properties are presented below in Table 1.  
According to ITU-R P.618-13, the average atmospheric loss for the 2.632 GHz operating frequency is about 3 dB. However, more than 3 dB will be lost due to the imperfect synchronization scheme operation and Doppler effect compensation according to the navigation system data. The calculations lead us to the curves of the maximum communication range depending on the equivalent radiated power \(P_{Tx}\,G_{Tx}\), where \(G_{Tx}\) is gain of the transmitting \begin{table}
\begin{tabular}{l l} \hline \hline
**Property/Parameter** & **Value** \\ \hline Signal type & BPSK with DSSS \\ \hline Pseudo-random sequence length & 1024 \\ \hline Error-correcting code & convolutional turbo code, r = 1/3 \\ \hline Bandwidth, MHz & 14.8 \\ \hline Chip rate, MBd & 7.4 \\ \hline Net data rate, kbit/s & 2.2 \\ \hline Operating frequency, GHz & 2.632 \\ \hline Receiver antenna gain, dB & 0 to \(-\)10 \\ \hline Receiver noise factor, dB & 2 \\ \hline Maximum receiver temperature, \({}^{\circ}\)C & 100 \\ \hline Receiver bandwidth, MHz & 14.8 \\ \hline Required SNR in the receiving band & \(-\)28.5 (BER = 10\({}^{-4}\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Signal Properties and Channel Parameters in Simulations. Figure 8: Simulation scheme for the tunnel communication channel. antenna and \(P_{Tx}\) is radiated power.