On the Performance of Channel Statistics-Based Codebook for Massive MIMO
  The channel feedback overhead for massive MIMO systems with a large number of base station (BS) antennas is very high, since the number of feedback bits of traditional codebooks scales linearly with the number of BS antennas. To reduce the feedback overhead, an effective codebook based on channel statistics has been designed, where the required number of feedback bits only scales linearly with the rank of the channel correlation matrix. However, this attractive conclusion was only intuitively explained and then verified through simulation results in the literature, while no rigorous theoretical proof has been provided. To fill in the gap between the theoretical conclusion and simulation results, in this paper, we quantitatively analyze the performance of the channel statistics-based codebook. Specifically, we firstly introduce the rate gap between the ideal case of perfect channel state information at the transmitter and the practical case of limited channel feedback, where we find that the rate gap is dependent on the quantization error of the codebook. Then, we derive an upper bound of the quantization error, based on which we prove that the required feedback bits to ensure a constant rate gap only scales linearly with the rank of the channel correlation matrix. Finally, numerical results are provided to verify this conclusion. To the best of our knowledge, our work is the first one to provide a rigorous proof of this conclusion. 
Wenqian Shen, Linglong Dai, Yu Zhang, and Zhaocheng Wang
cs.IT math.IT