###### Abstract
Nevertheless, while OTFS has a lower peak-to-average power ratio (PAPR) than a multi-carrier system [45] and shows significant advantages in performance over OFDM [43], the PAPR of OTFS, which grows linearly with the number of symbols, is still problematic for THz transmitters. Therefore, the reference [38] proposed a discrete Fourier transform spread OTFS (DFT-s-OTFS) modulation scheme. However, these modulation schemes still do not solve the high path losses and distance-dependent bandwidth experienced by THz signals in modulation schemes due to the small wavelength and molecular absorption. References [46; 47] presented hierarchical bandwidth modulation (HBM) to address these challenges, which is an extension of traditional hierarchical modulation (HM) that introduces a hierarchy in bandwidth by simultaneously servicing users at different symbol rates. We have found that there are few studies on optimizing the modulation strategy for the UAV-based THz communication. From a forward-looking perspective, it is necessary to make efforts to develop and refine modulation strategies that can better exploit the THz spectrum's properties to achieve the higher data rate for UAV communications. Motivated by these investigations, we present a new distance- and frequency-dependent adaptive modulation scheme, where the distance and frequency play the important role in the design of the modulation strategy. This work differs from previous studies in the following aspects. First, the subcarrier bandwidth, modulation order, and the transmit power are jointly utilized, which results in the non-convex optimization problem different from the convex problem in [37] fixing the subcarrier bandwidth. We propose a block-coordinated decent (BCD) algorithm to solve this problem. Second, the available bandwidth of the user is closely related to the distance. Therefore, when the user moves, the modulation scheme should be adjusted. However, the adjustment frequency of the adaptive modulation strategy can not be large due to the high overhead and complexity. Thus, it is necessary to design adjustment rules for modulation schemes and derive the adjustment probability as the user moves, which is meaningful but has not been studied in existing works. Finally, in the multi-user case, we propose a new hybrid HM-MOAM (Quadrature Amplitude Modulation with a modulation order of M) modulation by adopting HM on the overlapped frequencies between the farther and closer users because the available bandwidth of the closer user is larger and includes the available bandwidth of the farther user. The MQAM scheme is applied on the remaining frequencies of the closer user. The performance of the proposed modulation scheme is compared with existing modulation schemes, and the simulation results demonstrate the superiority of the proposed modulation scheme. The contributions of this work are summarized as follows. In the multi-user case, we propose a new hybrid HM-MQAM scheme by adopting hierarchical modulation on the overlapped frequencies between the farther and closer users and MQAM modulation scheme on the remaining frequencies of the closer user. Our results indicate that the modulation order on the resultant frequencies of the closer user is different from that on the overlapped frequencies. The data rate of the proposed modulation scheme is higher than that of the existing HBM and HM schemes. 2. We jointly optimize the subcarrier bandwidth, modulation order, and transmit power and propose the BCD method to solve the non-convex optimization problem. 3. We also design the adjustment rules of the adaptive modulation strategy when the user is moving. The adjustment probability of the adaptive modulation scheme is derived according to these adjustment rules. The remainder of this paper is organized as follows. Section 2 introduces the THz system and channel models. Section 3 proposes a new hybrid HM-MQAM scheme for the multi-user case and compares the performance of the proposed modulation scheme with that of the existing HBM and HM schemes.