###### Abstract
In the LEO satellite system, the synchronization performance is seriously affected by the large frequency shift caused by the high-speed movement of the LEO satellites. How to carry out accurate synchronization under a large frequency shift is an important problem. There have been plenty of research works on the subject of synchronization for the terrestrial communications system. Low-complexity synchronization schemes were proposed in [21; 22] by using the autocorrelation of primary synchronization signals (PSS) for a 5G system. These works reduced the complexity by sacrificing the SNR performance or processing delay. The work in [23] exploited the periodicity and the sparsity of the channel to improve the estimated performance of the channel impulse response (CIR) and of the carrier frequency offset (CFO). Most of the above research works are aimed at reducing the complexity, and they are not applicable to the high mobility of LEO satellites. In an LEO satellite system, the large frequency offset seriously affects the system performance. To achieve fine timing synchronization, a low-complexity algorithm using the Zadoff-Chu (ZC) sequence is proposed in [24]. The work in [25] proposed a robustness timing advance estimation method by a novel random-access preamble sequence, which consists of the real and imaginary part of a ZC sequence. The time and frequency synchronization methods in the downlink LEO satellite system were investigated in [26]. The PSS and cyclic prefix (CP) were used to improve the estimation performance. In order to adapt to 5G, the synchronization methodssuitable for LEO satellite single-path and multipath fading channels were proposed in [27] for an OFDM-based satellite system, which utilizes the ZC sequence and the feature of the satellite channel. In addition, several methods estimated the frequency offset without training sequences. In [28], the author presented a turbo-code-aided Doppler frequency shift correction algorithm by means of the Gaussian process model for high-mobility satellite communication without a training sequence. In this paper, we model the downlink transmission of a dual-LEO-satellite communication system and analyze the impact of the dynamic characteristics of an LEO satellite. In addition, we propose a power control algorithm and a synchronization algorithm under this system to combat the influence of the path loss and frequency offset of the LEO satellite system. It is assumed that the data transmitted by the two satellites are different, and the terminal has the function of joint receiving and processing of the dual-stream data, as shown in Figure 1. A power control scheme is proposed to solve the path loss effect. In order to resist the large frequency shift of the LEO satellites, the two-dimensional search algorithm is adopted. The PSS sequence is used for the time synchronization and coarse frequency offset estimation, and the PSS and secondary synchronization signal (SSS) sequences are combined for the fine frequency offset estimation to improve the synchronization performance. The simulation results show that the proposed schemes can not only ensure a high communication rate but also reduce the power loss. The proposed scheme can achieve more than a \(1\) Gbps data rate for a single user.