# An Efficient Carrier Synchronization Scheme for Demodulation Systems
## 1 Introduction  
The proliferation of bandwidth caused by the factors of low-order modulation, spatial channel spectrum resource constraint, and increasing transmission inefficiency are becoming increasingly prominent. To meet the demand of payload data transmission, we can fix the situation in three ways: channel band utilization, power consumption utilization, and signal power utilization. The data transmission efficiency is usually improved by increasing the channel band utilization. The existing satellite-ground link data transmission system is often based on the modulation method applicable to the lowest inter-satellite link gain for data transmission, which will lead to the waste of satellite-ground channel resources and satellite resources. To make full use of the satellite link resources and improve the data transmission efficiency, a variable modulation (VM) system is proposed. The VM system can switch various Modulation modes according to the gain of inter-satellite links. The receiver of a VM communication system usually adopts a low-cost oscillator, which introduces large initial carrier frequency offset (CFO) to the process of digital transmission for various reasons, such as system oscillation frequency error and Doppler shift, while the receiver of a VM communication system usually needs to achieve high phase estimation accuracy with a low signal-to-noise ratio (SNR). Carrier synchronization is often used for carrier frequency offset recovery (CFR) and carrier phase recovery (CPR). A CFR algorithm consists of a data-aided CFR algorithm and a non-data-aided CFR algorithm, and a CPR algorithm consists of a data-aided CPR algorithm and a non-data-aided CPR algorithm. The commonly used data-aided CFR algorithms are Kay, C&S, M&M, Jiang,Fitz, and L&R algorithms, and the widely used data-aided CPR algorithms are pilot-aided (PA) phase linear interpolation algorithms. The existing CFR scheme requires at least two steps, including initial frequency recovery, the coarse CFR algorithm, and the fine CFR algorithm. The CPR scheme requires at least one step, including coarse CPR and fine CPR. The four-step carrier synchronization scheme is proposed in [1], including the M&M algorithm for initial CFR, the improved L&R algorithm for coarse CFR, the pilot block interpolation for fine CFR, and the phase difference of the pilot symbols for CPR. A three-step carrier synchronization scheme is proposed in [2], which uses a Delay & Multiply (D&M) algorithm for coarse CFR, then an L&R algorithm for fine CFR, and the PA phase linear interpolator for CPR. The three-step carrier synchronization scheme is proposed, utilizing the Fitz algorithm for coarse CFR, the simple pilot block correlation algorithm for fine CFR, and the PA phase linear interpolator for CPR in [3,4]. The three-step carrier synchronization scheme that adopts the M&M algorithm for coarse CFR, the simple pilot block correlation algorithm [5] for fine CFR, and the pilot-aided block for CPR is proposed in [6]. The study of the features of the application of the coarse frequency synchronization algorithm in [7] reduces the synchronization time, but it does not reduce the complexity of the scheme. A three-step scheme is given in [8]; its purpose is not to simplify the scheme, but to optimize performance. Among them, the alternative carrier synchronization scheme proposed in [3] is less complex compared with [1,2,6], but the scheme is still more complicated. In this paper, a simplified data-aided carrier synchronization scheme for the VM system is proposed, where the CFO estimation algorithm utilizes the RLR algorithm, and the CPR utilizes the PA phase linear interpolation algorithm. In comparison with the [PERSON] [9], C&S [10], M&M [11], [PERSON] [12], Fitz [13], and L&R algorithms [14, 15, 16], the RLR algorithm is reconfigurable with higher accuracy. The residual frequency offset and residual phase offset can be reduced to the correctable range of the CPR algorithm.