# A Frequency-Domain Estimation Scheme for Frequency Offset with Large Range in OFDM Systems
## 1 Introduction  
OFDM modulation has been widely used in practical communication systems such as 5G NR systems [1]. Nowadays, the applications of 5G NR technology are developed from conventional terrestrial networks to non-terrestrial networks (NTNs) [2] in order to achieve massive and global connectivity. In low earth orbit (LEO) satellite-based NR-NTNs, the Doppler effect between LEO satellites and terrestrial users is significant due to the high speed of the LEO satellites. A large Doppler shift can cause inter-carrier interference (ICI) and degrade the demodulation performance of OFDM systems. Therefore, frequency offset estimation, tracking, and compensation modules are generally adopted at the receiver to reduce the effect of frequency offset. The existing estimation methods for frequency offset could be classified into two categories, i.e., one comprises pilot-based methods, and the other includes blind methods [3]. Pilot-based methods usually take advantage of the autocorrelation of the pilotsequence or the phase offset between the channels of two pilot symbols [4; 5; 6; 7; 8; 9] which are known to both the transmitter and receiver and are also named as reference signals in 5G NR specification [1]. Blind methods estimate frequency offset without the additional overhead of pilot symbols and therefore achieve higher spectrum efficiency compared to pilot-based methods [3]. The authors in [3] further classified the blind methods into statistical approaches and deep learning-based approaches. Statistical approaches generally exploit the inherent structure of OFDM symbols, such as the cyclic prefix (CP), to estimate frequency offset [10; 11; 12], where the CP is the repetition of the tail of one OFDM symbol. Deep learning-based approaches estimate the frequency offset by varieties of neural networks, and have attracted much attention in recent years [13; 14; 15; 16; 17; 18] due to their flexibility and powerful ability to analyze complex channel characteristics. In practical communication systems, such as 5G NR, the pilot symbols are often configured in the radio frame to assist in demodulation at the receiver. Compared to blind methods, pilot-based methods can achieve accurate estimation without a longer observation window for the received signal, and can control the frequency offset estimation range by simply adjusting the symbol gap between the two adjacent pilot OFDM symbols [3]. Therefore, pilot-based methods show much practical value in 5G NR systems. Pilot-based methods could be classified into time-domain methods [3; 4; 5; 6] and frequency-domain methods [7; 8; 9]. One basic idea of time-domain methods is to use two identical pilot OFDM symbols in the radio frame [3], or construct one pilot OFDM symbol with several repeated time-domain parts [4; 5; 6]. With the special structure of the pilot symbols, the frequency offset can be estimated by the phase offset between repeated signals. In particular, in CP-OFDM systems, frequency offset can be estimated by the CP instead of pilot symbols [10; 11; 12]. One disadvantage of time-domain methods is their restricted application in multi-user scenarios, where the NR base station communicates with different users by assigning them different frequency resources. Since the received time-domain signal at the base station is the superposition of different users' signals, their frequency offsets cannot be directly estimated by the received time-domain signal when their frequency offsets are different. Frequency-domain methods take advantage of the autocorrelation of the pilot sequence to estimate the integer frequency offset (IFO) [4; 7; 8] and the phase offset between the channels of two pilot OFDM symbols to estimate the fractional frequency offset (FFO) [9]. The IFO and FFO denote the frequency offsets, which are the integer and fractional times of the subcarrier spacing (SCS), respectively. The IFO makes the transmitted frequency-domain sequence cyclically shift at the receiver.