Abstract Spatial antenna diversity has been important in improving the performance of the wireless communication systems and supporting high data rate services. Many of the space-time coding schemes applied to multi-antenna systems assume that perfect synchronization to achieve the expected performance gain. However, the inaccuracy of frequency offset estimation caused by the mismatch of the oscillators between the transmitter and receiver and/or Doppler shift would degrade the performance. In this thesis we investigate the problem of frequency offset estimation in multiple-transmit-antenna systems to find out whether space diversity can provide diversity gain to frequency offset estimation or not. The performance of the maximum likelihood (ML) estimator and the Cramer-Rao lower bound (CRLB) are shown and also the asymptotic CRLB. The optimal training sequences designed based on obtaining the optimum performance are discussed.