This paper discusses a cyclic prefixed single carrier frequency-domain equalization (SC-FDE) scheme with two types of transmit diversity. Firstly, we propose a SC-FDE system with space-frequency block coding (SFBC). The transmit sequence of the proposed system is designed to have spatial and frequency diversities, which is equivalent to the SFBC. The corresponding combining receiver is derived under a minimum mean square error (MMSE) criterion. It is shown that the proposed system significantly outperforms the SC-FDE system with space-time block coding (STBC) over fast fading channels, while providing lower computational complexity than orthogonal frequency division multiplexing (OFDM) combined with SFBC. We verify the performance of two-branch transmit diversity systems including the proposed one through bit error rate (BER) analysis. Secondly, as a scheme that combines STBC and SFBC, a space-time-frequency block code (STFBC) SC-FDE system is presented. Computer simulation results show that the proposed STFBC SC-FDE system has better immunity to the distortion caused by both fast fading and severe frequency selective fading, compared to the SC-FDE system with the STBC or the SFBC scheme. Complexity analysis is also conducted to compare their computational loads of the transceiver. It is shown that the proposed STFBC SC-FDE system has lower computational complexity than the STFBC OFDM system.