# A Frequency-Domain Estimation Scheme for Frequency Offset with Large Range in OFDM Systems
## 1 Introduction
Therefore, the IFO could be estimated by the correlation operation between the transmitted pilot sequence and the received pilot sequence with cyclically shifted elements. The IFO estimation methods have been widely used in 5G NR frequency synchronization with the primary synchronization signal (PSS) [7] and the secondary synchronization signal (SSS) [8]. The FFO is estimated by the phase offset between the frequency-domain channels of two pilot OFDM symbols, which is similar to the idea of time-domain methods. Due to the \(2\pi\)-periodicity of the phase offset, the estimation range of conventional frequency-domain methods cannot cover \((-0.5,0.5]\) times of the SCS if there is more than one OFDM symbol inserted between the two pilot symbols. Another category of pilot-based works focus not only on frequency offset estimation but also on the joint estimation of frequency offset with other channel parameters, such as channel coefficients [19; 20] or timing offset [21; 22]. In these joint estimations, frequency offset and other channel parameter estimators are jointly derived, based on the maximum likelihood (ML) criterion [19], or by minimizing the estimation mean square error (MSE) [20], or separately estimated, where the frequency offset estimator is designed based on conventional time-domain methods [21; 22]. In this work, a pilot-based estimation scheme for frequency offset with large range in OFDM systems is proposed. The proposed scheme is implemented in the frequency domain. It firstly takes advantage of the \(2\pi\)-periodicity of the phase offset between two pilot OFDM symbols to estimate a set of candidate frequency offsets, which contains some large-value frequency offsets. Then, each candidate frequency offset is used to compensate the received pilot sequence, and the correlation value between the compensated and local pilot sequences is calculated. Finally, the frequency offset corresponding to the largest correlation value is output as the final estimation result. The contributions of this work are summarized as follows:  
* The estimation range of the proposed scheme covers \((-0.5,0.5]\) times of the SCS--independent of the symbol gap between the two pilot OFDM symbols--compared to conventional frequency-domain methods. Thus, the proposed scheme enables large frequency offset estimation with the pilot OFDM symbols sparsely inserted in the radio frame. * We analyze the modulus of frequency-domain compensation coefficients and provide a low-complexity implementation for the proposed scheme by simplifying the calculation of the frequency-domain compensation coefficient vector. * The effectiveness of the proposed scheme in both single-user and multi-user scenarios is shown by the simulation results based on 5G NR PUSCH, where various Doppler shifts and numbers of configured resource blocks (RB) are considered. The simulation results also show the advantages of the proposed frequency-domain method over the conventional time-domain method, since the former was less affected by the noise of the non-pilot subcarriers. In the following sections, the OFDM system model and the conventional frequency offset estimation methods are reviewed in Section 2. In Section 3, the proposed frequency offset estimation scheme and its low-complexity implementation are introduced. Section 4 illustrates the simulation system and results. Finally, we conclude in Section 5. The notations used in this paper are summarized in Table 1.