# Research on Waveform Adaptability Based on Lunar Channels
## 4 Numerical Results  
In this section, we assess and analyze the waveform performance designed for lunar communication. The key simulation parameters are outlined as follows. In both Frequency Division Duplex (FDD) and Time Division Duplex (TDD), the uplink and downlink bandwidths are set at 20 MHz and 10 MHz, respectively. The subcarrier spacing is configured as 15 KHz. Under the 20 MHz condition, the number of subcarriers and samples per symbol are specified as 1333 and 2048, respectively. For the 10 MHz scenario, the corresponding figures are 666 subcarriers and 1024 samples per symbol. Each subframe spans a time of 1 ms, incorporating 14 OFDM symbols. We conducted separate simulation experiments to evaluate the Peak-to-Average Power Ratio (PAPR) and Bit Error Rate (BER) performance under TDD and FDD. The impact of different Cyclic Prefix (CP) lengths on BER performance is shown in Figure 2a-d. Based on the simulated attenuation in the lunar communication environment, we \begin{table}
\begin{tabular}{c c c} \hline \hline
**Communication Requirements** & **Lunar Lander** & **Lunar Exploration Rover** \\ \hline Type of data & Voice communication, image transfer & Voice communication, image transfer \\ Data rate & High & Middle \\ Real-time requirements & High & Middle \\ Scope of activities & None & 6 km \\ Transmit power & High & Middle \\ carrying capacity & High & Middle \\ Mobility & None & High \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Communication requirements for lunar surface activities. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Frequency & 2.5 GHz \\ Number of Subcarriers & 1333 \\ FFT Length & 2048 \\ Number of OFDM Symbols per Frame & 7 \\ Pilot Interval & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. experimentally verified the optimal CP lengths in two duplex modes to complete the overall design of the communication system. In both TDD and FDD modes, the communication bandwidth for uplink and downlink on the lunar channel is set at 20 MHz and 10 MHz, respectively, with a delay of \(4.557\times 10^{-6}\) s in the multipath channel. For the uplink communication, OFDMA is used, while SC-FDMA is used for the downlink communication. In Figure 3, we compare the performance under different modulation schemes, including 16 APSK, 32 APSK, and 64 APSK, for both 10 MHz and 20 MHz scenarios. It can be observed that the performance difference across various bandwidths is not significant; however, the modulation scheme has a substantial impact on the variation of the bit error rate. Figure 2: BER performance versus the length of CP. (**a**) Uplink BER performance versus the length of CP in 20 MHz bandwidth. (**b**) Downlink BER performance versus the length of CP in 20 MHz bandwidth. (**c**) Uplink BER performance versus the length of CP in 10 MHz bandwidth. (**d**) Downlink BER performance versus the length of CP in 10 MHz bandwidth. We simulated and calculated the BER performance under different CP lengths and plotted the curves for comparison. In the TDD, we set CP lengths to 0, 36, 72, 100, and 144. The cumulative time is greater than 140 CP, so we observe that when CP equals 144, the BER performance steadily improves with increasing Signal-to-Noise Ratio (SNR). When the cumulative CP time is less than the delay, BER performance remains unchanged. For the FDD, we set CP lengths to 0, 18, 36, and 72. The cumulative time is greater than 70 CP, so we observe that when CP equals 72, BER performance steadily improves with increasing SNR. When the cumulative CP time is less than the delay, BER performance remains unchanged. From the curve analysis, it is determined that the lower limit of the added CP length to ensure communication system performance is the upper limit of the delay, which is one symbol period.