## 3 The Hybrid HM-QAM Scheme for Multi-User Scenario  
In the multi-user case, we initially assume two users for analytical simplicity, which can be expanded to scenarios with more than two users. The system model is shown in Figure 1. User 1 is located closer to the base station at distance \(d_{1}\), and User 2 is farther away at distance \(d_{2}\) (\(d_{2}>d_{1}\)). Based on distance dependence, the available bandwidths for User 1 and User 2 are \(B_{1}\) and \(B_{2}\), respectively, with the condition \(B_{1}=2B_{2}\) for simplicity. It is important to note that the fixed relationship \(B_{1}=2B_{2}\) is for analytical simplicity. In practical scenarios, dynamic bandwidth allocation based on real-time conditions such as user mobility, traffic demand, and channel conditions might be more effective. The available bandwidth for the closer user includes the available bandwidth for the farther user, and thus, the overlapped bandwidth for the two users is \(B=B_{2}\), with the remaining available bandwidth for the closer user being \(B\). We apply HM modulation schemes on the overlapped frequencies for both closer and farther users, and a QAM modulation scheme on the non-overlapped frequencies for the closer user. In the HM modulation scheme, the closer user (UE1) experiences less path loss compared to the farther user (UE2). Consequently, the modulation order for the closer user is higher than that for the farther user on the overlapped frequencies due to better channel quality allowing for higher data rates. Because of the mobility of the UAVs, the available frequencies for the closer and farther users vary, necessitating adjustments in the modulation order to match environmental conditions. In scenarios with more than two users, coordination among multiple UAVs can help optimize overall system performance, ensuring fair bandwidth distribution and minimizing interference. In the UAV THz communication system, energy efficiency is also a concern since UAVs have limited energy resources. Efficient power management and routing algorithms are essential to prolong the operational time of the UAVs while ensuring reliable THz transmissions. Although this work focuses on modulation schemes, energy efficiency will be addressed in future research. In the traditional hierarchical modulator (HM), the closer user applies the higher modulation order than the farther user. However, the farther user and closer user have the same available bandwidth and they have the same symbol rate with \(\frac{1}{2T_{s}}\), where \(T_{s}\) is the symbol duration of the closer user. The hierarchical bandwidth modulation (HBM) exploits the distance-dependence available bandwidth of the THz frequency [46]. The available bandwidth of the closer user is larger than the farther user. The symbol duration is adjusted according to the available bandwidth with \(T_{s}\) for the closer user and \(2T_{s}\) for the farther user. Hence, the symbol rate of the closer user is \(\frac{1}{T_{s}}\) and the symbol rate of the farther user is \(\frac{1}{2T_{s}}\). In HBM, although the modulation order of closer user and farther user is different, the modulation order of the closer user is the same on all the available frequencies, which is not reasonable and adaptive. Motivated by these observations, we propose the hybrid HM-QAM strategy. Besides exploiting the distance-dependence of the available bandwidth of the THz frequency, we also combine the advantages of HM and QAM. In this modulation scheme, the base station adopts the HM scheme on the overlapped frequencies between the closer and farther users and the QAM scheme on the remaining frequencies of closer users. The HM-QAM scheme is formulated as  
Figure 1: The UAV-based THz system model. \[