DFT-Based Beamforming Weight-Vector Codebook Design for Spatially Correlated Channels in the Unitary Precoding Aided Multiuser Downlink

The DFT-based beamforming weight-vector codebook is considered as an effective design for spatially correlated channels. In this paper, we demonstrate that when the antenna elements are uniformly spaced as well as linearly arranged, and the channels are spatially correlated, the codewords in a DFT-based beaforming weight-vector codebook approximately match the distribution of the optimal beamforming weight-vectors. As a result, the DFT-based codebook is indeed effective. Furthermore, we also demonstrate that if the antenna elements are uniformly spaced and circulary arranged, the statistical distribution of the optimal beamforming weight-vectors becomes different. We will demonstrate that in this scenario the DFT-based codebook will no longer outperform the Grassmannian codebook, which has not been shown in previous studies. Finally, an algorithm is proposed for constructing the DFT-based precoding matrix, which outperforms the conventional algorithm by ensuring the orthogonality of the precoding matrix.