Abstract-We consider a multi-way massive multiple-input multiple-output relay network with zero-forcing processing at the relay. By taking into account the time-division duplex protocol with channel estimation, we derive an analytical approximation of the spectral efficiency. This approximation is very tight and simple which enables us to analyze the system performance, as well as, to compare the spectral efficiency with zero-forcing and maximum-ratio processing. Our results show that by using a very large number of relay antennas and with zero-forcing technique, we can simultaneously serve many active users in the same timefrequency resource, each with high spectral efficiency.
I. INTRODUCTIONMulti-way relay networks are relevant for many applications, such as data transfer in multimedia teleconference and data exchange between sensor nodes and data fusion centers in wireless communications [1]. Due to the multiplexing gain, the spectral efficiency of multi-way relay networks is much larger than that of two-way or one-way relay networks. Therefore, during the past years, multi-way relay networks have attracted considerable research interest [2]. On a parallel avenue, massive multiple-input multiple-output (MIMO) has also attracted a significant amount of research interest from both academia and industry [3]. In massive MIMO, hundreds of antennas are deployed at the base station to serve simultaneously tens of users. With simple linear processing techniques, such as maximum-ratio (MR) or zero-forcing (ZF) processing, massive MIMO can offer huge spectral and energy efficiency [4]. Thus, massive MIMO combined with multi-way relaying technique is a strong candidate for the next-generation wireless communication systems.Recently, there have been some works in multi-way massive MIMO relay systems [5], [6]. These systems can offer all benefits of both massive MIMO and multi-way relaying technologies, and hence, are expected to offer very high spectral efficiency. In particular, in [5], the authors show that by using very large antenna arrays at the relay together with ZF processing, the system performance can improve significantly. Furthermore, [6] shows that the transmit power of each user and/or the relay can be made inversely proportional to the number of relay antennas, while maintaining a required quality of service. However, these works assume perfect channel state information (CSI) at the relay and users. In practice, especially in massive MIMO systems, the impact of channel estimation should be taken into consideration. In [7], the authors analyze