Space-frequency (SF) group codes are designed for multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems. A rather general channel model is assumed, where the channel is frequency-selective Rayleigh fading with arbitrary power-delay profile. It is shown that the SF group code has a symmetric distance structure like the space-time group code, if the group consists of diagonal matrices. A scenario where the multiple codewords are loaded onto the subcarriers of the OFDM system in parallel is considered. The optimality condition on the choice of subcarrier allocation is found, and an optimal subcarrier-allocation scheme is proposed. A transmit scheme where rotated versions of the same signal are transmitted from different transmit antennas is proposed, and it is shown that it satisfies the optimality condition. Then matrix groups are designed which guarantee that the resulting SF codes are full rank. Numerical comparisons with recently published techniques in the literature verify our improved performance.

A delayed space-frequency cyclic group code is proposed in this paper, which applies a new bandwidth and power-efficient space-frequency processing on the orthogonal-frequency- division-multiplexing (OFDM) system. The delayed orthogonality with respect to frequency tones among different transmitter antennas guarantees to exploit the full spatial and frequency diversity of the frequency-selective multi-input multi-output (MIMO) channel. In contrast with the schemes which combine the single-antenna error correcting code with delayed transmitter diversity in multi-antenna OFDM systems, this space-frequency code has a robust performance in flat-fading channel. Without a tradeoff of the diversity gain, the proposed code can be easily expanded to achieve high data rate and generalized to more than two transmit antennas.

A high rate delayed space-frequency cyclic group code is proposed in this paper, which applies a new bandwidth and power-efficient space-frequency processing on the orthogonal-frequency-division-multiplexing (OFDM) system. The delayed orthogonality with respect to frequency tones among different transmitter antennas guarantees to exploit the full spatial and frequency diversity of the frequency-selective multi-input multi-output (MlMO) channel. In addition, after partitioning the subcarriers into groups and coding each group with the proposed block code, a maximized multiplexing gain can be obtained without any diversity loss. The proposed code can also be easily generalized to multiple transmitter antenna systems.