## 1 Introduction  
Due to the rapid expansion of wireless network users, the scarcity of spectrum resources has become more and more severe, and people have gradually turned their attention to the millimeter wave, which has abundant spectrum resources [1, 2]. Millimeter wave massive MIMO technology uses the physical size of the antenna array by acting the antenna spacing through the millimeter wave characteristics, which in turn helps to increase the antenna array size to obtain larger array gain to resist attenuation in propagation [3]. Thus, it significantly increases the system capacity while solving the spectrum problem. The application of massive MIMO technology increases the number of antennas to 64, 128, or even 256, which helps the system generate a directional beam by controlling the phase and amplitude of the signal transmitted by each antenna unit. This can not only effectively enhance the coverage distance of signal transmission, but also ace the interference between adjacent beams, thus greatly improves the system throughput, which has unlimited potential with the increasing number of users and the increasingly more complex signal transmission environment nowadays [4]. This technology is also suitable for applications in millimeter wave communications, which have abundant spectrum resources but are not suitable for long-distance wireless transmission. Therefore, the antenna array scale of the millimeter wave communication system is much larger than that of the traditional communication system. If the precoding scheme still follows the pure digital processing architecture of the traditional communication system, it will greatly increase the amount of data processing and complexity. Additionally, the huge digital and RF links will bring about an increase in cost and power consumption [5; 6]. Secondly, if all just use analog components when precoding, it will inevitably bring non-ideal distortion [7]. Therefore, adopting a digital-analog hybrid architecture to convert part of the digital processing work into analog domain beamforming is taken into account. Although the processing performance of the analog domain is slightly worse than that of the digital domain, it can effectively use the construction cost and power overhead of the system, and the performance difference can also be compensated by architecture design and algorithm optimization. The implementation is that the baseband still uses low-dimensional traditional digital precoding to obtain multiplexing gain, while the RF domain uses phase shifters to implement analog precoding to obtain a higher antenna array gain to realize a wider range of networks coverage and higher transmission rate performance [8]. The current integrated analog beamforming IC is specifically developed for analog phased array applications or hybrid array architectures, in which the hybrid array architecture is a combination of digital beamforming technology and analog beamforming technology. There are two types of hybrid precoding structures, respectively, called sub-connected and fully-connected according to the connection mode between RF chains and the transmit antennas [9; 10]. The sub-connected structure divides the antenna into multiple subsets, which will have a one-on-one connection to different RF chains, respectively. While in fully-connected structure, every RF chain will connect to all antennas through phase shifters [11]. Obviously, the sub-connected structure is more energy friendly in contrast, which is beneficial to improving the energy efficiency of the system. However, there exists a fundamental contradiction between energy efficiency and spectral efficiency: the improvement of energy efficiency will lead to the deterioration of spectral efficiency [12]. Therefore, further optimizing the spectral efficiency of the sub-connected structure has always been a research hotspot. [PERSON] et al. [8] documented that the millimeter wave channel can be approximated as a sparse channel.