Highlights What are the main findings? This paper designs an Asynchronous Non-Orthogonal Multiple Access (A-NOMA)-enhanced two-step random-access framework compatible with the current Fifth-Generation (5G) communication protocol, redesigns the random-access preamble sequence, and realizes Doppler frequency offset estimation via paired indexing preambles. A successive interference cancellation algorithm combined with frequency offset and phase compensation is designed for demodulation. The framework adopts A-NOMA technology to improve spectrum efficiency and two-step random access to reduce random-access latency, thus enhancing access efficiency and lowering resource consumption. This paper redesigns the 5G Sidelink Synchronization Signal Block (S-SSB) to adapt to a wider range of application scenarios with flexible adjustment capability and designs a receiving algorithm considering frequency offset estimation and compensation with a complete link-level algorithm constructed. In view of the practical constraint of limited onboard energy of Unmanned Aerial Vehicles (UAVs), a downsampling-based synchronization detection algorithm is designed, which divides synchronization detection into coarse and fine estimation stages to reduce computational complexity on the premise of ensuring synchronization accuracy. What are the implications of the main findings? This paper provides an end-to-end technical solution for the synchronization communication of UAV swarms in the space-air-ground integrated network, solving the synchronization challenges caused by high mobility and long-distance transmission, and improving the communication reliability and stability of UAV swarms in scenarios such as emergency communication and remote-area coverage enhancement. The designed synchronization scheme is compatible with existing 5G communication standards, enabling a smooth transition with terrestrial 5G networks, and providing a referable physical-layer design idea for the implementation of UAV communication technologies in 5G-Advanced (5G-A) and 6G Non-Terrestrial Networks (NTNs). The optimized design based on A-NOMA and downsampling in this paper improves the utilization rate of spectrum resources while reducing the hardware and energy overhead of UAVs, providing technical support for the lightweight, low-cost deployment and long endurance of UAV swarms. The paper reveals the influence of user quantity, asynchrony, frequency offset and resource overlap on the system performance in UAV swarm synchronization communication and provides important simulation and experimental basis for subsequent resource allocation, multi-user scheduling and protocol optimization of UAV communication.Highlights What are the main findings? This paper designs an Asynchronous Non-Orthogonal Multiple Access (A-NOMA)-enhanced two-step random-access framework compatible with the current Fifth-Generation (5G) communication protocol, redesigns the random-access preamble sequence, and realizes Doppler frequency offset estimation via paired indexing preambles. A successive interference cancellation algorithm combined with frequency offset and phase compensation is designed for demodulation. The framework adopts A-NOMA technology to improve spectrum efficiency and two-step random access to reduce random-access latency, thus enhancing access efficiency and lowering resource consumption. This paper redesigns the 5G Sidelink Synchronization Signal Block (S-SSB) to adapt to a wider range of application scenarios with flexible adjustment capability and designs a receiving algorithm considering frequency offset estimation and compensation with a complete link-level algorithm constructed. In view of the practical constraint of limited onboard energy of Unmanned Aerial Vehicles (UAVs), a downsampling-based synchronization detection algorithm is designed, which divides synchronization detection into coarse and fine estimation stages to reduce computational complexity on the premise of ensuring synchronization accuracy. What are the implications of the main findings? This paper provides an end-to-end technical solution for the synchronization communication of UAV swarms in the space-air-ground integrated network, solving the synchronization challenges caused by high mobility and long-distance transmission, and improving the communication reliability and stability of UAV swarms in scenarios such as emergency communication and remote-area coverage enhancement. The designed synchronization scheme is compatible with existing 5G communication standards, enabling a smooth transition with terrestrial 5G networks, and providing a referable physical-layer design idea for the implementation of UAV communication technologies in 5G-Advanced (5G-A) and 6G Non-Terrestrial Networks (NTNs). The optimized design based on A-NOMA and downsampling in this paper improves the utilization rate of spectrum resources while reducing the hardware and energy overhead of UAVs, providing technical support for the lightweight, low-cost deployment and long endurance of UAV swarms. The paper reveals the influence of user quantity, asynchrony, frequency offset and resource overlap on the system performance in UAV swarm synchronization communication and provides important simulation and experimental basis for subsequent resource allocation, multi-user scheduling and protocol optimization of UAV communication.Abstract With the deployment and application of the Fifth-Generation (5G) mobile communication technologies and the ongoing research and development of the Sixth-Generation (6G) mobile communication technologies, the space-air-ground-sea integrated network has become the core development vision for future communications. As aerial nodes, Unmanned Aerial Vehicles (UAVs) can be applied in a wide range of scenarios, including emergency rescue, surveying and mapping, environmental monitoring, and communication coverage enhancement. In terms of communication coverage enhancement, the space-air-ground integrated network, with UAVs as a key component, can provide seamless communication coverage for the full-domain three-dimensional space such as remote areas, deserts, and oceans. Benefiting from advantages such as low cost and high flexibility, UAVs have become a critical research focus, and the one-hop Base Station (BS)-relay UAV-slave UAV architecture for communication coverage enhancement has emerged as an important development direction. However, the high mobility and wide coverage characteristics of UAVs also pose significant synchronization challenges. Aiming at the uplink synchronization problem on the sidelink between slave UAVs and the relay UAV, a two-step random-access scheme based on Asynchronous Non-Orthogonal Multiple Access (A-NOMA) is designed to mitigate the Doppler Frequency Offset (DFO), improve access efficiency, reduce resource consumption, and accommodate the asynchrony among different users. This scheme leverages the existing preamble sequences of the Physical Random Access Channel (PRACH) and realizes DFO estimation in combination with the pairing index. On this basis, a Successive Interference Cancellation (SIC) algorithm based on DFO and phase compensation is designed to complete the demodulation of user data. For the downlink synchronization problem on the sidelink between slave UAVs and the relay UAV, the frequency offset estimation performance is improved by redesigning the resource allocation scheme of the Sidelink Synchronization Signal Block (S-SSB). Meanwhile, considering the energy constraint of UAVs, a downsampling-based detection scheme is designed to reduce UAV power consumption, and a full-link algorithm is developed to support the practical implementation of the proposed scheme.