Bit-Interleaved Coded Multiple Beamforming with Imperfect CSIT

This paper addresses the performance of bit-interleaved coded multiple beamforming (BICMB) [1], [2] with imperfect knowledge of beamforming vectors. Most studies for limited-rate channel state information at the transmitter (CSIT) assume that the precoding matrix has an invariance property under an arbitrary unitary transform. In BICMB, this property does not hold. On the other hand, the optimum precoder and detector for BICMB are invariant under a diagonal unitary transform. In order to design a limited-rate CSIT system for BICMB, we propose a new distortion measure optimum under this invariance. Based on this new distortion measure, we introduce a new set of centroids and employ the generalized Lloyd algorithm for codebook design. We provide simulation results demonstrating the performance improvement achieved with the proposed distortion measure and the codebook design for various receivers with linear detectors.We show that although these receivers have the same performance for perfect CSIT, their performance varies under imperfect CSIT.