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Kronecker product‐based codebook design and optimisation for correlated 3D channels
Author(s) -
Wang Ying,
Jiang Lisi,
Chen Yongce
Publication year - 2015
Publication title -
transactions on emerging telecommunications technologies
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.366
H-Index - 47
ISSN - 2161-3915
DOI - 10.1002/ett.2914
Subject(s) - codebook , linde–buzo–gray algorithm , algorithm , kronecker product , product (mathematics) , mathematics , computer science , beamforming , discrete fourier transform (general) , kronecker delta , mathematical optimization , fourier transform , statistics , geometry , mathematical analysis , physics , fourier analysis , quantum mechanics , fractional fourier transform
Discrete Fourier transform (DFT) codebook has been favoured by long term evolution because of its simplicity and effectiveness for two‐dimensional multi‐input multi‐output channels. In order to further explore vertical freedom, a Kronecker product‐based codebook (KPC), which is the Kronecker product of a horizontal DFT codebook and a vertical one, has been proposed. However, how to effectively design the codebook is still a challenge, because neither its effectiveness nor optimisation has been studied. In this paper, we demonstrate that the codewords in the KPC approximately match the distribution of the optimal beamforming vectors under spatially correlated three‐dimensional channels, showing the effectiveness of such codebook structure. Moreover, because the maximal cross‐correlation amplitude ( I m a x ) of the original KPC is high, we investigate the structure of the codebook and then find a criterion of constructing the optimal KPC to achieve the lowest I m a x , namely the Welch bound. Furthermore, considering the optimal codebook only exists under certain conditions, a modified discrete stochastic approximation algorithm is used to construct a near‐optimal codebook. Simulation results show that our algorithm greatly reduces I m a x and respectively provides 1 and 0.5 dB coding gain compared to the traditional DFT codebook and the original KPC, which confirms the efficiency of the codebook design. Copyright © 2014 John Wiley & Sons, Ltd.