LAUSR

To realize massive multiple-input multiple-output (MIMO) systems, the uniform planar array (UPA) structure has been adopted to deploy a large number of antennas in a limited area of a radio unit at a base station. Subsequently, the Kronecker product (KP) codebook, consisting of horizontal and vertical-domain codebooks, was introduced to enable efficient quantization and feedback for the channel state information (CSI) under the UPA structure. In this paper, we propose advanced limited feedback schemes based on the KP codebook for massive MIMO systems. First, we propose one feedback bit allocation scheme to maximize the beamforming gain. Eigenvalues of spatial correlation channels are used to determine the numbers of feedback bits for horizontal and vertical-domain CSI, and the numbers of feedback bits to maximize the beamforming gain are derived as a closed-form expression. Moreover, we propose a novel feedback and pilot transmission scheme to reduce both the feedback and pilot overhead. The proposed feedback and pilot transmission scheme utilizes the property that the small-scale fading information can be compressed only to the horizontal-domain CSI when the spatial correlation of the vertical-domain channel is high. Simulation results show that, with the use of the proposed feedback bit allocation, the beamforming gain increases by up to 65 % compared with the fixed feedback bit allocation when the horizontal and vertical-domain spatial correlation coefficients are equal to 0.57, and the numbers of horizontal and vertical-domain antennas are 8 and 12, respectively. In addition, it is also shown that the proposed feedback and pilot transmission scheme improves the ergodic rate by up to 48 % compared with conventional feedback schemes.