Codebook Based Minimum Subspace Distortion Hybrid Precoding for Millimeter Wave Systems

Hybrid precoding is adopted for millimeter wave (mmWave) communications to offer a good trade-off between hardware complexity and system performance. In this paper, we investigate a codebook based hybrid precoder for single-user mmWave systems with large antenna arrays. We exploit the sparse nature of mmWave channels to transform the hybrid precoding design problem into a vector space distortion optimization problem which is only related to the radio frequency (RF) precoder. A near optimal solution for the RF optimization problem is derived with the assumption of the perfect channel state information (CSI) at the transmitter, which is practically very difficult to obtain. To reduce the requirement of the CSI at the transmitter, we propose the codebook based minimum subspace distortion (MSD) hybrid precoding algorithm, which obtains CSI at the combiner side and returns the index of optimal RF codewords and the baseband precoder through a limited feedback channel. Simulation results are provided and validate the effectiveness of our proposed hybrid precoding algorithm.