  Multi-Input Multi-Output (MIMO) techniques have been incorporated with
Orthogonal Frequency Division Multiplexing (OFDM) for broadband wireless
communication systems. Bit-Interleaved Coded Multiple Beamforming (BICMB) can
achieve both spatial diversity and spatial multiplexing for flat fading MIMO
channels. For frequency selective fading MIMO channels, BICMB with OFDM
(BICMB-OFDM) can be employed to provide both spatial diversity and multipath
diversity, making it an important technique. In our previous work, the
subcarrier grouping technique was applied to combat the negative effect of
subcarrier correlation. It was also proved that full diversity of BICMB-OFDM
with Subcarrier Grouping (BICMB-OFDM-SG) can be achieved within the condition
R_cSL<=1, where R_c, S, and L are the code rate, the number of parallel streams
at each subcarrier, and the number of channel taps, respectively. The full
diversity condition implies that if S increases, R_c may have to decrease to
maintain full diversity. As a result, increasing the number of parallel streams
may not improve the total transmission rate. In this paper, the precoding
technique is employed to overcome the full diversity restriction issue of
R_cSL<=1 for BICMB-OFDM-SG. First, the diversity analysis of precoded
BICMB-OFDM-SG is carried out. Then, the full-diversity precoding design is
developed with the minimum achievable decoding complexity.
