# Research on Waveform Adaptability Based on Lunar Channels
## 4 Numerical Results
In both TDD and FDD modes, we conducted a comprehensive comparison of phase shift keying (PSK), amplitude phase shift keying (APSK), and quadrature amplitude modulation (QAM) modulation schemes across various orders in both the uplink and downlink scenarios. In the TDD, The performance comparison is shown in Figure 4a-d. In the FDD, The performance comparison is shown in Figure 5a-d. CCDF stands for Complementary Cumulative Distribution Function. Specifically, for APSK modulation, we examined orders 4, 5, and 6, for PSK orders 2, 3, and 4, and for QAM orders 2, 4, and 6. Additionally, we scrutinized the PAPR for different modulation schemes at order 4. In the downlink, communication utilizes OFDMA, whereas the uplink employs SC-FDMA. The impact of modulation order on PAPR remains consistent across the same modulation scheme. At modulation order 4, SC-FDMA exhibits the optimal PAPR performance under PSK modulation. For the OFDMA, the optimal PAPR performance is achieved with QAM modulation. Figure 3: Performance comparison of different modulation methods. (**a**) Performance comparison of different modulation methods for 20 M bandwidth. (**b**) Performance comparison of different modulation methods for 10 M bandwidth. Figure 4: Comparison of PAPR for different modulation schemes and orders. (**a**) Comparison of PAPR for different modulation schemes under 20 MHz bandwidth. (**b**) Comparison of PAPR for different modulation orders of QAM under 20 MHz bandwidth. (**c**) Comparison of PAPR for different modulation orders of APSK under 20 MHz bandwidth. (**d**) Comparison of PAPR for different modulation orders of PSK under 20 MHz bandwidth. Figure 5: _Cont._  
The impact of different modulation schemes on BER performance is shown in Figure 6a-d. Based on the simulated results of CP lengths obtained earlier, we chose 144 CP for TDD and 72 CP for FDD as the system parameters for modulation scheme simulation. We conducted a detailed comparative analysis of the BER performance for QAM, APSK, and PSK with the same order of modulation in both uplink and downlink transmissions. In this process, OFDMA was used for uplink communication, while SC-FDMA was employed for downlink communication. It is worth noting that the simulation results clearly indicate that, across all modulation schemes, the BER performance for downlink transmission is superior to that for uplink transmission. Among the same-order modulation schemes, QAM modulation exhibits the most superior BER performance. Between APSK and PSK, the performance of APSK is significantly better than that of PSK. Therefore, in the design of the transmission system, we opt for the 4 QAM modulation scheme, which demonstrates the optimal performance. Figure 5: Comparison of PAPR for different modulation schemes and orders. (**a**) Comparison of PAPR for different modulation schemes under 10 MHz bandwidth. (**b**) Comparison of PAPR for different modulation orders of QAM under 10 MHz bandwidth. (**c**) Comparison of PAPR for different modulation orders of APSK under 10 MHz bandwidth. (**d**) Comparison of PAPR for different modulation orders of PSK under 10 MHz bandwidth. Figure 6: _Cont_