# An Efficient Precoding Algorithm for mmWave Massive MIMO Systems
## 1 Introduction  
Symmetry concept is utilized in almost all communications systems and cellular network analyses, which is then transformed into various conclusive outcomes. As the main direction of the development of information, communication in the fifth-generation (5G) will penetrate into various fields of future society. It aims to provide users with higher data rates and multiple connections for many Internet-of-Things (IoT) devices. Compared with fourth-generation (4G), the spectrum efficiency of 5G communication is increased by 5-15 times, and energy efficiency and cost efficiency are improved by a hundred times [1]. Massive multiple-input multiple-output (MIMO) technology and millimeter wave (mmWave) communication technology plays an important role as the key technology of 5G. Massive MIMO technology uses multiple antenna units to transmit and receive transmission signals at both ends of the communication system [2; 3; 4; 5; 6]. Through spatial multiplexing, beamforming, precoding, and other technologies, the space resources of the wireless channel are fully utilized to improve thesystem Stability, reducing the system's bit error rate, simplifying signal processing and reducing system latency. Currently, 6, 15, 18, 28, 45, 60, and 72 GHz are typical candidate bands for 5G research in the industry. The 6-100 GHz frequency range is a typical millimeter-wave band [7, 8]. Communication within this range can provide higher capacity for hotspot users and support user transmission rates above 10 GB/s [9, 10, 11]. The millimeter-wave mainly propagates in space in the form of direct waves. The beam is narrow and has good directivity, but it is greatly affected by the environment, such as rainfall, sand, dust, etc., and the propagation distance is limited [12, 13]. Since the millimeter-wave belongs to a very high frequency, the wavelength is small, and a large number of antennas can be packaged in a limited physical space. The combination of the array antenna and the precoding technology can effectively compensate for the transmission loss of the millimeter-wave, increase the transmission distance, and improve the stability of the system [14]. The use of precoding techniques in massive MIMO systems can improve the spectral efficiency of the system, reduce the bit error rate, and simplify the complexity of the receiver. In the 4G communication system, traditional digital precoding technology has been widely used. In order to achieve the maximum theoretical advantage of massive MIMO technology [15], traditional digital precoding technology needs to equip each transmitting antenna with a separate Radio Frequency (RF) link. However, in a millimeter-wave massive MIMO system, due to a large number of transmit antennas, if the traditional digital precoding technology is still used, then the system hardware cost will be too high and the system power consumption will be too large. Therefore, in millimeter-wave massive MIMO systems, hybrid precoding techniques are generally used, that is, precoding processing is divided into baseband precoding (digital precoding) processing and radio frequency precoding (analog precoding) processing [16]. The solution uses only a small number of RF links to solve the high cost and high-power consumption of traditional digital precoding. Hybrid precoding is used to process the multiplexed signal through the baseband precoder, send it to the RF precoder through the RF link for constant mode phase shift, and then send it to the transmitting antenna for transmission. The hybrid precoding architecture of the millimeter-wave massive MIMO system can be divided into a shared array architecture and a separate sub-array architecture [17], in which each RF link of the shared array architecture is connected to all the transmit antennas, and the separated sub-arrays for each RF link of the architecture is only connected to a portion of the transmit antenna.