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Unmanned aerial vehicles (UAVs) have been widely utilized for their various advantages. However, UAVs exhibit high mobility and energy storage restrictions in some applications, which can compromise the quality and reliability of communication links. This is a challenge that future aircraft and low-orbit aircraft will inevitably encounter. To effectively address the issue of dynamic Doppler spread in air-to-ground communication, this paper creatively introduces four-dimensional spherical code modulation into the orthogonal time–frequency space with an index modulation (OTFS-IM) system. The fundamental concept of the four-dimensional spherical code is elaborated in detail. Multiple resource symbols can be jointly used to increase the modulation dimension, thereby achieving a larger minimum Euclidean distance between constellation points. Furthermore, detailed analysis is conducted on the bit error rate (BER) and the peak-to-average-power ratio (PAPR) expressions of the proposed system to evaluate its performance and provide theoretical guidance. The proposed scheme not only adapts well to high-speed scenarios but also achieves better power consumption efficiency. The simulation results demonstrate that our proposed scheme outperforms conventional methods. Its robustness and generalization ability are also validated.