In state of the art relay-assisted transmission schemes, analysis of symbol error ratio (SER) and throughput mainly focuses on static or low-speed sources, where relay strategies and power allocation strategies are studied. However, when the sources move quickly with variable trajectories, the power allocation strategy of relays is affected by the sources' movement and time-varying channels, and should be adjusted dynamically according to the sources' trajectories with corresponding motion scenarios. Therefore, previous schemes are no longer applicable to solve the problem brought by high-speed sources because their channels and power allocation strategies are lack of correlation with the sources' movement. In this paper, taking full advantage of the flexibility of unmanned aerial vehicle (UAV) combined with multi-antenna technology, we propose two UAV-assisted relaying transmission schemes to serve high-speed moving sources. Through derivation and optimization of system's symbol error ratio (SER), new dynamic power allocation and adjustment strategies of the source and each UAV are obtained when the total power of the system is limited. Moreover, the proposed schemes utilize time-based power allocation lists to save signaling overhead. Simulation results demonstrate that our schemes outperform the compared schemes. INDEX TERMS moving sources, UAV relays, dynamic power allocation.