With the development of 5G new radio (NR) applications in high-speed scenarios, such as 5G non-terrestrial networks (NTN), the Doppler shift in the systems is significant. In this paper, an estimation scheme for frequency offset with large range in orthogonal frequency division multiplexing (OFDM) systems is proposed. The proposed scheme 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. It then uses the autocorrelation of the pilot sequence to determine the final estimated frequency offset. This method allows for a large estimation range, independent of the symbol gap between the two pilot OFDM symbols. Moreover, the low-complexity implementation of the scheme is provided. The simulation results based on 5G NR physical uplink shared channel (PUSCH) show the effectiveness of the proposed scheme in both single-user and multi-user scenarios, where various Doppler shifts and numbers of configured resource blocks (RB) are considered. The simulation results also show that the proposed frequency-domain method outperforms the conventional time-domain method with additional computation complexity.

A polar code with repeating bits (RB polar code), where a part of frozen bits only repeat their preceding information bits is proposed. In the code construction, we propose cluster pairwise error probability (CPEP) to measure the competitiveness of the correct path against the error paths, and apply CPEP as the optimization criterion for the code construction, aiming to reduce the elimination probability of the correct path in a successive cancellation list (SCL) decoder. In the simulations, the constructed RB polar codes are combined with the cyclic redundancy check (CRC) code, and outperform their counterparts of CRC-concatenated polar codes over various codeword lengths, code rates and puncturing patterns.