# A New Design of Codebook for Hybrid Precoding in Millimeter-Wave Massive MIMO Systems
## 1 Introduction  
Millimeter-wave massive MIMO, which is very suitable for 5G wireless communication transmission, has been extensively studied in the past ten years [1]. Although digital precoding can achieve excellent performance in the system, the digital precoding consumes a lot of energy and the hardware cost is quite expensive, owing to the requirement that each antenna element needs to be connected to one dedicated RF chain, which is impractical in the mmWave massive MIMO systems. In order to overcome these obstacles, we utilize hybrid precoding techniques at the cost of reduced spectral efficiency. Therefore, it is vital to design a hybrid precoding algorithm that can promote the spectral efficiency for mmWave MIMO systems. Over the past decade, hybrid precoding technology in the mmWave massive MIMO system has been diffusely researched. By regarding the mmWave channel as sparse channel, the construction of hybrid precoding is transformed into the sparse matrix reconstruction in [2], although the hybrid precoding matrix is easy to construct, the adopted orthogonal matching pursuit (OMP) algorithm causes error accumulation, which causes the decrease of system spectral efficiency. The transceiver is designed for energy efficiency maximization in [3] by dividing the joint design of the hybrid precoder and the combiner into twosubproblems, and further, using the OMP algorithm to design the hybrid precoder, then improving the design of the hybrid precoder based on random error modeling in order to adapt to the situation of imperfect CSI. With the aid of the internal connection between the analog codebook and digital codebook, an iterative algorithm is designed jointly by digital codebooks and analog codebooks in [4] based on the dictionary learning algorithm and reconstruction algorithm, which can be applied to the phase shifter with arbitrary resolution, but the algorithm has not improved the spectral efficiency. According to the different connection modes between radio frequency (RF) chains and antennas, the hybrid precoding scheme is mainly divided into full connection, partial connection, and hybrid connection. In [5; 6], a hybrid precoding scheme based on the partial connection structure is proposed, which reduces the number of phase shifters by connecting each RF chain with partial antennas, thus, effectively reducing the hardware complexity. However, the hybrid precoding based on partial connection structure will bring some loss of spectral efficiency. Hybrid-connected hybrid precoding is a trade-off between full connection and partial connection. The antennas are divided into multiple subarrays by RF chain, and each subarray is fully connected. Reference [7] proposes a successive interference cancellation hybrid precoding scheme for hybrid-connected hybrid precoding. According to the relationship between the transmitted data stream and the number of RF chains, the form of digital precoding matrix is designed first, and then the analog precoding matrix is decomposed into a submatrix by using the block diagonal characteristics of the analog precoding matrix. Finally, the hybrid precoding matrix is obtained, which is better than the partially connected hybrid precoding scheme. Compared with partial connection and hybrid connection, fully-connected hybrid precoding has better spectral efficiency performance because all RF chains are connected to each antenna at the transmitter, which can provide higher degree of freedom for the transmitted signal. It is closer to the full digital precoding scheme, but its hardware complexity is high. Therefore, in recent years, some researchers have explored the use of machine learning and deep learning methods to realize the hybrid precoding algorithm based on full connection structure, in order to reduce the hardware cost. For example, in [8], they propose a novel method based on deep learning, which designs the hybrid beamforming vector by jointly optimizing the channel measurement vector, and achieves better spectral efficiency.