# Data-Aided Frequency Offset Estimation for CE-OFDM Broadband Satellite Systems
## 2 Broadband Satellite System Architecture and Propagation Environment  
A broadband satellite communication system has the advantages of a high data transmission rate and the support for a large number of user terminals. According to [10], the broadband satellite system architecture includes the satellites, the forward link transmission unit (FL-TU) and the return link reception unit (RL-RU) with a gateway (GW) to the external terrestrial networks, and the satellite terminals (ST) that can receive the satellite signals and convert them to signals (e.g., Wi-Fi) available for user terminals (UT). Figure?? describes the broadband satellite system architecture.  
In Table??, the slices of available spectrum for broadband satellite communication services are listed. It can be seen that the broadband satellite systems have more abundant spectrum resources than the traditional L/S band satellite systems. However, one of the disadvantages of using high operating frequencies is a significant path loss. In order to achieve high antenna gain to combat the significant path loss, the antennas of ST and TU/RU are generally required to point directly to the satellite. As people are more willing to access the terrestrial network in the urban environment, satellite communications are generally used in rural areas. Therefore, in this paper, the channel is considered as a flat fading, which is dominated by the light of sight (LOS) path.  
Another disadvantage of the high operating frequency is the large CFO. In satellite systems, the CFO consists of two main parts: the phase noise caused by the non-ideal oscillator, and the Doppler frequency offset caused by the high speed related movement between the satellite and the terminal. The detailed analysis of the phase noise and the effect of phase noise on the CE-OFDM signal can be found in [10] and [11], respectively. The conclusion is that the phase noise will interfere with the CE-OFDM signal in the form of additive noise, resulting in the degradation of bit error rate (BER) performance. The effect of Doppler frequency offset to the CE-OFDM signal is presented in [10]. The author in [10] shows that the range of normalized Doppler frequency offset in the LEO system is about \((-2\times 10^{-5},2\times 10^{-5})\), which is normalized to the carrier frequency. The maximum Doppler frequency  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Band** & **Uplink** & **Downlink** \\ \hline Ka-band & 27.5–31 GHz & 17.7–21.2 GHz \\  & 42.5–43.5 GHz & \\ Q/V-band & 47.2–50.2 GHz & 37.5–42.5 GHz \\  & 50.4–51.4 GHz & \\ W-band & 81–86 GHz & 71–76 GHz \\ \hline \hline \end{tabular}
\end{table}
Table 1: Available spectrum for broadband satellite communication services.  
Figure 1: Broadband satellite system architecture.  
offset will be \(\pm\)400 kHz to \(\pm\)1600 kHz with the operating frequency changing from a Ka-band to a W-band. Therefore, the CFO estimation strategy needs to support a large estimation range. In this paper, we assume that the non-ideal factors in the propagation environment include the Doppler frequency offset and the phase noise, as well as the flat fading channel, and we leave the estimation of the phase noise and the channel for further study.  
The notations used in this paper are defined as follows. We use superscripts \((\cdot)^{*}\), \((\cdot)^{T}\), \((\cdot)^{H}\) to denote the conjugate, the transpose, and the conjugate transpose, respectively. The bold-faced, small letter \(x\) is a vector, and the capital letter \(X\) is the matrix. \(I_{N\times M}\) and \(0_{N\times M}\) represent the identity matrix and the zero matrix of dimension \(N\times M\), respectively. \(X_{i,j}\) is the entry in row \(i\) and column \(j\) of \(X\). \(diag(x)\) is the diagonal matrix. \(\Re\{\cdot\}\) and \(\Im\{\cdot\}\) denote the real part and the imaginary part of a complex value, respectively. The determination of \(X\) is \(det(X)\) and the modulo operator is \(|\cdot|\).