In this thesis work, fixed WiMAX based on IEEE 802.16d PHY layer with underlying OFDM technology has been studied. Due to overlapped subcarriers, OFDM system is very sensitive to synchronization errors. Synchronization is important for the receiver to successfully demodulate the received data. Different synchronization tasks have been presented using both single antenna and multiple antennas techniques. Timing synchronization is used for frame detection and the symbol boundaries whereas coarse frequency synchronization is used to estimate the frequency offset. Frequency response of the channel is also estimated. OFDM, when combined with multiple antennas at both the transmitter and the receiver increase the system capacity, meeting the requirement of Shannon capacity. In this thesis, in case of MIMO, Alamouti STBC scheme is use to transmit the data and interleaved carriers are used to transmit the preambles.