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.

💡 Research Summary

This paper investigates the performance of Bit‑Interleaved Coded Multiple Beamforming (BICMB) when the transmitter has only limited, imperfect channel state information (CSIT). While most limited‑feedback works assume that the precoding matrix is invariant under any unitary transformation, this property does not hold for BICMB because the singular value decomposition (SVD) of the channel is non‑unique: the right singular matrix V can be multiplied by any diagonal unitary matrix D without changing the channel representation. Consequently, the conventional Euclidean distance‑based codebook selection (which simply finds the codebook entry closest to V) is sub‑optimal for BICMB.

The authors first formalize the non‑uniqueness of V (Theorem 1) and then derive an optimal Euclidean selection criterion (SC‑OE). For each candidate codebook matrix (\hat V_i), the optimal diagonal unitary matrix (D_{\text{opt}}) is computed by aligning the phases of the inner products between the columns of V and (\hat V_i). The resulting distance measure is \