# Energy Efficiency Optimization in Massive MIMO Secure Multicast Transmission
## 1 Introduction  
With the great development of network information technology and the continuous improvement of wireless communication technology, modern society puts forward higher requirements for the current communication transmission. With the extensive amount of research, there are a number of breakthrough technologies, such as the multiple-input multiple-output (MIMO) technology [1]. This technology has great potential to improve both the spectrum efficiency and the energy efficiency of the system, which is the development direction of future 5G/B5G wireless communication systems [2, 3]. In the long-term evolution (LTE) standard, the wireless multicast transmission is also widely studied. In wireless multicast transmission, one base station (BS) sends public information to multiple user terminals (UTs). That is to say, that the BS can effectively transmit group-oriented signals by utilizing an evolved multimedia broadcast multicast service (eMBMS) [4; 5; 6; 7; 8]. As a mature technology, wireless multicast technology has certain advantages in improving the network traffic and reducing the communication cost. The combination of wireless multicast and massive MIMO is widely concerned with improving the quality of service (QoS), owing to its performance of effectively shaping the multicast transmission signals [9; 10; 11; 12]. Due to the openness of the wireless propagation media, security issues are critical indicators in wireless transmissions of all fields. To ensure the security of transmission, many works traditionally use key-based enciphering. However, this method meets its challenge for secure wireless communications with additional control signaling and feedback channel management. Therefore, the security and privacy of physical layer security in wireless channels have a wide range of research [13; 14; 15], thanks to its great ability to work in a keyless scenarios. In previous works, the physical layer security of massive MIMO unicast transmission has been studied [16; 17; 18; 19]. Meanwhile, in some existing works, the physical layer security of multicast transmission is also considered. For example, secure multicast precoding has been investigated [20; 21; 22]. Besides, some works have studied the security by introducing artificial noise into the multicast transmission, e.g., in [23; 24]. Energy efficiency is another important indicator of performance in designing wireless transmission, which has been widely concerned by both academia and industry [25; 26]. About 5% of the energy consumption of the whole world is produced by information and communication technologies, owing to its connected devices and infrastructure constantly being consumed [27]. In the future of 5G/B5G development, energy demand will soon become unmanageable. Therefore, a promising answer to this issue is to find considerable metrics which can limit energy consumptions but meet the needs of secure and reliable communication. However, most of the works on secure multicast transmission are limited to optimizing the secure rate, and almost no energy efficiency issues are considered. Some existing works have investigated the energy efficiency of unicast transmission instead of multicast transmission [28; 29; 30]. In some previous works, the energy efficiency multicast transmission was investigated [31; 32], but the issues of security were not solved well. In some works, it is assumed that the legitimate UTs' instantaneous channel state information (CSI) is known [17; 21; 22; 23; 33]. However, due to CSI's capture/feedback overhead in frequency division duplex MIMO systems, there are some difficulties in obtaining instantaneous CSI at the BS. It is the reason why most of the previous work has assumed this. On the other hand, statistical CSI has enormous advantages over instantaneous CSI for BS to obtain. Because of its slower change, BS can get statistical CSI accurately [34]. Therefore, statistical CSI is more suitable for wireless transmission design in high mobility scenarios.