Estimation of Residual Frequency and Time Errors on NPRACH in Nonterrestrial Networks

This article proposes a rake receiver to convey a bank of symbol-level correlators (SLCs) on each arm for joint maximum likelihood estimation (JMLE) of residual frequency error (RFE) and residual time error (RTE) after narrowband physical random access channel (NPRACH) preamble detection is completed. The proposed technique exploits multirate signal processing to decimate (i.e., downsample) the received signal for reducing subsequent computational complexity and to interpolate (i.e., upsample) in the frequency domain to enhance the accuracy of RFE estimation. Coherent accumulation of the squared magnitudes of SLC outputs further improves the signal-to-interference-plus-noise ratio (SINR). The proposed approach offers flexibility and practicality, enabling highly accurate estimation of RFE and RTE over extended ranges beyond one subcarrier spacing and beyond one symbol duration, respectively, while achieving precision at the fractional levels of a subcarrier spacing and a symbol duration. Simulation results confirm effectiveness of the proposed technique.