The transmit diversity and OFDM system are the promising schemes for fourth generation wireless communication. Recent studies have shown that combination of two schemes produce improved and reliable performance. In general, the combined schemes can be categorized as either Space Time Block Coded OFDM(STBC-OFDM) and Space Frequency Block Coded OFDM(SFBC-OFDM). In this thesis, we define the two problems of above schemes when the system employs four transmit antennas. First is about inefficient code rate. Both STBC-OFDM and SFBC-OFDM use the complex orthogonal matrix. However Tarokh  has proven that there is no such complex orthogonal matrix which can achieve code rate of one when system employs more than two transmit antennas. So as a solution, we apply the quasi-orthogonal matrix which is proposed by Jafarkhani to the SFBC-OFDM system. we increase the throughput by 25 percent compared to previous 3/4 code rate orthogonal matrix. In the low mobility environment, performance of the QOSFBC-OFDM(quasi-Orthogonal SFBC) is worse than the STBC-OFDM because of the imperfect orthogonality, As the mobility increase, the QOSFBC-OFDM is superior than the STBC in high SNR. Second problem is that both schemes(STBC-OFDM, SFBC-OFDM) show the different performance according to the channel condition.  shows that SFBC-OFBM outperforms STBC-OFDM in the fast fading channel. Meanwhile STBC-OFDM performs better in the frequency selective channels. Thus, we conclude that the better of two schemes regarding to overall BER performance varies according to channel condition. In this thesis, we propose the switching criterion using normalized delay spreads and normalized Doppler frequency in order to keep the best performance in any channel environments.