# Data-Aided Frequency Offset Estimation for CE-OFDM Broadband Satellite Systems
## 1 Introduction  
With the development of information technology, the space-air-ground integrated network (SAGIN) has received extensive attention. The most touted advantage of the SAGIN is its ability to enable communication anytime, anywhere. The space network of SAGIN is composed of various satellites and constellations (e.g., Geostationary (GEO), Medium Earth Orbit (MEO), and Low Earth Orbit (LEO) satellites), as well as the corresponding terrestrial infrastructures (e.g., gateways and ground stations) [10]. To support emerging applications via satellites, such as high-speed internet access and multimedia services, the high throughput broadband satellite systems have become a research hotspot [11]. Some organizations have already carried out some MEO/LEO constellation plans, such as OneWeb and SpaceX. High operating frequency and wide bandwidth, as well as a high data rate, have become the main features of the next-generation broadband satellite systems [12]. Among the key technologies of the next-generation broadband satellite systems (e.g., mobility management, routing algorithm, etc. ), the waveform design of the physics layer is essential as it affects the data rate and the peak-to-average power ratio (PAPR), as well as other system parameters. As a unique form of multicarrier modulation, the orthogonal frequency-division multiplexing (OFDM) waveform is the cornerstone of the fourth-generation (4G) terrestrial wireless systems, and the OFDM-like waveforms have already been adopted in the fifth-generation (5G) New Radio (NR) specification, including both the terrestrial and satellite networks [13]. Therefore, how to use OFDM technology in satellite systems is of great significance. In order to make OFDM technology available in satellite systems, two main problems need to be solved, which are the high PAPR caused by OFDM itself and the large carrier frequency offset (CFO)caused by the related movement between the satellite and the terminal. Among the various PAPR reduction techniques, the constant-envelope OFDM (CE-OFDM) proposed by [PERSON] et al. in [2 ] is considered as an effective method in broadband satellite systems [3 ]. The 0 dB PAPR signal is obtained by applying a nonlinear phase modulation to a real-valued OFDM signal, while the drawback is that the spectral efficiency is reduced to half that of the regular OFDM signal. Since the power resources are more precious than spectrum resources in broadband satellite systems, CE-OFDM can find important applications. The spectrum efficiency-enhanced transceiver for CE-OFDM [3 ], the CE-OFDM based mm-wave communication system [4 ], and the iterative space-frequency equalizer for CE-OFDM mm-wave systems [5 ] have been proposed in recent years, which promote the application of CE-OFDM in broadband satellite systems. However, the large CFO caused by the related movement introduces interference in CE-OFDM systems, and it needs to be estimated and compensated. The CFO estimation strategies can be grouped into two categories, namely: data-aided estimation strategies--comprising the time domain training sequences [6 ; 7 ], the frequency domain pilot symbols such as the primary synchronization signal (PSS) [8 ] and the secondary synchronization signal (SSS) [9 ] designed for the long-term evolution (LTE) network--and blind estimation strategies comprising the kurtosis-type criterion [10 ], the diagonality criterion [11 ], and the presence of null subcarriers [12 ]. Since the data-aided strategies generally have higher estimation accuracy, these strategies are more likely to be used in the communication system than the blind strategies. The time domain training symbol containing two identical halves proposed in [10 ] can be used to estimate the CFO, but the frequency acquisition range is subcarrier spacing. In order to improve the estimation range, the optimal periodic training signal is discussed in [11 ; 12 ], and the Cramer-Rao bound (CRB) is derived. However, the drawback of the time domain training signal is the decline of the spectral efficiency.