Kronecker product‐based codebook design and optimisation for correlated 3D channels

Abstract

AbstractDiscrete 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 (Imax) 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 Imax, 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 Imax 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.