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This correspondence proposes a new rotated codebook for a three-dimensional (3-D) multiple-input multiple-output (MIMO) system under a spatially correlated channel. To avoid the problem of high dimensionality led by a large antenna array, the rotation matrix in the rotated codebook is proposed to be decomposed by Tucker decomposition into three low-dimensional units, i.e., statistical channel direction information in horizontal and vertical directions, respectively, and statistical channel power in the joint horizontal and vertical direction. A closed-form suboptimal solution is provided to reduce the computational complexity in Tucker decomposition. The proposed codebook has a significant dimension reduction from conventional rotated codebooks and is applicable for a 3-D MIMO system with an arbitrary form of antenna array. Simulation results demonstrate that the proposed codebook works very well for various 3-D MIMO systems.

Tucker Decomposition For Rotated Codebook in 3-D MIMO System Under Spatially Correlated Channel