This master thesis aims for Inter-carrier interference (ICI) mitigation in orthogonal frequency division multiplexing (OFDM) system by considering designs of frequency domain cyclic extension(FDCE) and optimal windowing pulse shape. Although OFDM system has been put forward in the 1970s, it has just emerged in 4G. In the early stage, it has been restricted by its high computational complexity. With the discovery that modulation and demodulation process of OFDM can be realized by discrete Fourier transform (DFT) and inverse discrete Fourier transform (IDFT), it is widely used in 4G and 5G-New Ratio (NR). Based on OFDM system, a variety of derivative systems are further proposed and applied. With the development of 5G technology in the mobile communication, the requirement of signal propagation between high-speed mobile user and base station (BS) is higher and higher. With the increase of the moving speed of objects, the frequency shift caused by Doppler eff ect can not be underestimated. ICI caused by Doppler shift is becoming more and more serious. Therefore, how to eliminate the ICI caused by Doppler shift has become an inevitable potential problem. In this thesis, two eff ective approaches for ICI mitigation have been explored and studied. By adding FDCE and optimal windowing pulse shape, the system performance is analyzed and the system simulation is constructed in MATLAB.