Narrowband Internet of Things (NB-IoT) aims to provide wide coverage for a massive number of low-cost devices. Therefore, an NB-IoT physical random access channel (NPRACH) preamble based on a single tone signal with frequency hopping was designed, enabling the base station to estimate the time-of-arrival (ToA) values for realizing uplink synchronization among multiple users. However, due to residual carrier frequency offset (RCFO) in the NPRACH preamble, it is crucial to keep the accuracy of the ToA estimation. Recognizing this urgency, in this paper we first judiciously investigate the effect of the hooping distance on ToA estimation. With which, we propose an efficient receiving algorithm to improve the accuracy of ToA estimation. The main aim of the algorithm is to treat two consecutive symbol groups as a whole and then carry out difference calculations on the two newly constituted symbol groups to construct a more logical frequency hopping distance. Extensive numerical results validate the superiorly of our proposed scheme compared against conventional strategies, showing that the probability of the ToA estimation obtained by this method is 99% within the acceptable error range.

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