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Hybrid beamforming offers a low hardware complexity for millimeter wave massive multiple-input multiple-output systems, which is divided among the analog radio frequency precoding and digital baseband precoding. In order to provide channel state information for the base station, channel feedback is essential, especially in frequency division duplexing systems. However, in large antenna systems, the size of channel matrix is huge, and the overhead of feedback complete channel is not acceptable. To reduce the feedback overhead for hybrid beamforming, leveraging the property that the millimeter wave path angles of departure vary more slowly than the path gains, we propose a two-timescale hybrid beamforming/combining algorithm for downlink multi-streams millimeter wave systems. We analyze the performance of the proposed algorithm with perfect channel state information, and the analytical and simulation results show that proposed algorithm can achieve the same performance of full digital singular value decomposition algorithm. We also analyze the rate gap between the proposed algorithm with perfect channel state information and limited feedback. The rate gap caused by quantization of radio frequency and baseband precoder codebooks are decoupled, and the quantization error is analyzed. At last, we provide a closed-form expression of relationship between feedback bits and rate gap.

A Novel Two-Timescale Limited Feedback Hybrid Beamforming/Combining Design for Millimeter Wave Systems