  Multiple beamforming is realized by singular value decomposition of the
channel matrix which is assumed to be known to both the transmitter and the
receiver. Bit-Interleaved Coded Multiple Beamforming (BICMB) can achieve full
diversity as long as the code rate Rc and the number of employed subchannels S
satisfy the condition RcS<=1. Bit-Interleaved Coded Multiple Beamforming with
Constellation Precoding (BICMB-CP), on the other hand, can achieve full
diversity without the condition RcS<=1. However, the decoding complexity of
BICMB-CP is much higher than BICMB. In this paper, a reduced complexity
decoding technique, which is based on Sphere Decoding (SD), is proposed to
reduce the complexity of Maximum Likelihood (ML) decoding for BICMB-CP. The
decreased complexity decoding achieves several orders of magnitude reduction,
in terms of the average number of real multiplications needed to acquire one
precoded bit metric, not only with respect to conventional ML decoding, but
also, with respect to conventional SD.
