Reduced Complexity Decoding for Bit-Interleaved Coded Multiple Beamforming with Constellation Precoding

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 R-c and the number of employed sub-channels 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.