Fast algorithm of LTE RACH detection based on sparse fourier transform

In this paper, we present a fast algorithm of time synchronization between User Equipment (UE) and Base Station (BS) which is suitable for Long Term Evolution (LTE) Random Access Channel (RACH). The algorithm reduces the complexity more than 1.5 times. Further, if the SNR is above a threshold, the algorithm allows to extremely reduce the complexity of synchronization more than 3 times. The presented method uses the sparse nature of a time synchronization problem, where the spike of a cross-correlation between received signal and local RACH preamble indicates correct time delay.