Orthogonal frequency division multiplexing (OFDM) systems are sensitive to the carrier frequency offset (CFO), which degrades the performance of the system. Therefore, CFO estimation is an important issue in OFDM systems. The focus of this thesis is on CFO estimation in OFDM systems. This thesis first extends frequency analysis (FA) method to estimate carrier frequency offset in OFDM systems with more than two transmitting antennas. Then, we extend the FA method to multi-users. Finally, simulation results show the proposed method works in different settings.