In this paper, we propose a channel estimation scheme in a backhaul system based on long term evolution (LTE)-Advanced. The proposed method uses the fast Fourier transform (FFT) interpolation scheme for a user moving at a high speed. This FFT interpolation scheme converts the channel frequency response obtained from a least square (LS) or minimum mean square error (MMSE) channel estimation scheme to a time domain channel impulse response by calculating the inverse FFT (IFFT). Simulation results show that the proposed channel estimation scheme can improve the normalized mean square error (NMSE), error rate, and throughput of conventional systems.