Diversity Analysis of Bit-Interleaved Coded
Hong Ju Park, Student Member, IEEE, and Ender Ayanoglu, Fellow, IEEE
In this letter, diversity analysis of bit-interleaved coded multiple beamforming (BICMB) is extended to the
case of general spatial interleavers, removing a condition on their previously known design criteria. We provide a
method to get diversity order, simplifying the calculation of pairwise error probability (PEP). By using the Singleton
bound, we also show the maximum achievable diversity for given code rate and the number of subchannels.
When the channel information is perfectly available at the transmitter, beamforming is an attractive
technique to enhance the performance of a multi-input multi-output (MIMO) system . The beamforming
matrices can be obtained by singular value decomposition (SVD) which is optimal in terms of minimizing
the average bit error rate (BER) . Single beamforming, which carries only one symbol at a time, was
shown to achieve the full diversity order of NM where N is the number of transmit antennas and M is
the number of receive antennas , . However, multiple beamforming, which increases the throughput
by sending multiple symbols at a time, loses the full diversity order over flat fading channels. To achieve
the full diversity order in multiple beamforming, the authors in  introduced BICMB, combining bit-
interleaved coded modulation (BICM) and multiple beamforming. Design criteria for interleaving the
coded sequence were provided , .