Recently, Space-Time Block Coded OFDM (ST-OFDM) that applies Space-Time Block Code (STBC) to OFDM has been proposed. Space-Frequency Block Coded OFDM (SF-OFDM) has been also proposed where the block codes are formed over the space and frequency domain. ST-OFDM and SF-OFDM are known as the schemes that achieve good performance over the multipath fading environments and the fast fading environments, respectively. For the systems with two transmit antennas, the orthogonal conditions required to separate the received signals are that in ST-OFDM, the frequency responses of the consecutive two OFDM symbols are almost identical and that in SF-OFDM, the frequency responses of the adjacent two subcarriers are almost identical. In practical fading environments, however, these conditions of the orthogonality sometimes cannot be satisfied. In those environments, the received signals cannot be well separated and the performances are degraded. Recently, the diagonalized maximum likelihood decoder (DMLD) of new zero-forcing (ZF) type was proposed for the space-time block coded single carrier QPSK system to maintain the orthogonality of STBC under the fast fading environments and the flat fading environments, where the channel separation in DMLD is performed by the ZF algorithm using two receive signals at time index 2n, 2n+1 (Space Time Code: STC) or two subcarriers (Space Frequency Code: SFC). Note that the matrix generated after the channel separation is not an identity matrix but the matrix proportional to an identity matrix. We show that ST/SF-OFDM with DMLD outperform ST/SF-OFDM in terms of Bit Error Rate (BER).

Space-time block coded orthogonal frequency division multiplexing (ST-OFDM) has been proposed as an attractive solution for a high bit rate data transmission in a multipath fading environment. Space-frequency block coded OFDM (SF-OFDM) has been also proposed as another solution. These two systems utilize STBC with a 22 transmission matrix, using two transmit antennas. In ST-OFDM the block codes are formed over the space-time domains. In SF-OFDM the block codes are formed over the space-frequency domains. If we apply STBC with a 44 transmission matrix to OFDM, using four transmit antennas, we can expect the performance improvement. However, when the block codes are formed over space-time (frequency) domains with four transmit antennas, the conditions of the orthogonality become more strict. We can expect that if the block codes are formed over space-time-frequency domains with four transmit antennas, that is, if we implement space-time-frequency block coded OFDM (STF-OFDM), the condition of the orthogonality is more relaxed. In this paper, we apply STBC with a 44 transmission matrix to OFDM and propose STF-OFDM. We evaluate the performance of the three types of systems (ST-OFDM, SF-OFDM, STF-OFDM). We show that the best system with respect to the error rate performance differs in the different channel conditions. When the effect of the Doppler spread is large and the effect of the delay spread is small, SF-OFDM has the best error rate performance, and STF-OFDM and ST-OFDM follow in order. When the effect of the delay spread is large and the effect of the Doppler spread is small, ST-OFDM has the best error rate performance, and STF-OFDM and SF-OFDM follow in order. We also show that STF-OFDM is attractive in wireless communications. STF-OFDM is more tolerant than ST-OFDM with respect to the Doppler spread and SF-OFDM with respect to the delay spread, respectively.