In narrow band-Internet of Things (NB-IoT) systems, a preamble of physical random access channel (NPRACH) is based on a single-tone waveform combined with frequency hopping, which is appropriate to achieve the goals of IoT, such as long battery lifetime and extended coverage. Since the hopping pattern of a preamble is predetermined, it is possible to estimate time-of-arrival (ToA) using phase difference. The accurate ToA is very important for device positioning and uplink signal decoding. In this paper, we design a new frequency hopping pattern of NPRACH preamble which fully utilizes all feasible hopping distances for a given number of subcarriers in NPRACH. The proposed hopping pattern maintains the compatibility with the standard system, by keeping the NPRACH structure in standard with minimal change. The simulation results show that the proposed hopping pattern greatly improves the accuracy of ToA estimation without additional system overhead.
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