On the Performance of Channel-Statistics-Based Codebook for Massive MIMO Channel Feedback

The channel feedback overhead for massive multiple-input multiple-output 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 proved under a particular channel assumption in the literature. To provide a rigorous theoretical proof under a general channel assumption, in this paper, we quantitatively analyze the performance of the channel-statistics-based codebook. Specifically, we first 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 depends 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 number of 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.