Abstract: Abstract： A maximum likelihood (ML) frequency estimation algorithm for the long term evolution (LTE) uplink is proposed. By the quantitative analysis on the performances of the ML algorithm and the algorithm based on the phase difference between two training sequences (phase difference algorithm), a combined frequency offset algorithm is also proposed. The simulation results show that the proposed ML algorithm and combined algorithm cover a sufficient estimation range for the high speed train (HST) scenario compared with the phase difference algorithm. Moreover, the proposed ML algorithm is not vulnerable to the frequency hopping in the LTE uplink. At SNR=10 dB, when the number of users is smaller than 4, the two proposed algorithms can both provide 10-4, or even smaller, mean square error (MSE) of normalized frequency offset estimation. At the environment of only one user, the combined algorithm provides 5 dB improvement over the ML algorithm in performance.