# Relay Selection Scheme for Multi-Hop Transmission of MU-MIMO System
## 1 Introduction  
Recently, the multi user-multiple input multiple output (MU-MIMO) scheme plays an important role in increasing the average throughput of the cell and the throughput of the cell edge user in the long term evolution-advanced (LTE-A) [1]. The MU-MIMO scheme can increase the channel capacity without additional bandwidth allocation by transmitting signals to multiple user equipment (UEs) at the same time [2,3]. In addition, since one base station (BS) simultaneously transmits signal to multiple UEs, the cell average throughput of the LTE-A communication system can be increased [4]. There are many MU-MIMO schemes. Typical MU-MIMO schemes include channel inversion scheme and block diagonalization (BD) scheme. In the channel inversion scheme, the BS multiplies the transmission signal by the inverse matrix of the MIMO channel matrix between the BS and UE. Therefore, when the BS transmits the pre-coded signal, the UE receives the desired signal in which the interference signal is removed and only the noise is added. In the BD scheme, a pre-coding matrix is generated using the MIMO channel matrix between the BS and UE, and the BS transmits the signal multiplied by the pre-coding matrix. When the UE receives the pre-coding signal of the BD scheme, the UE receives the desired signal with the interference cancellation and only the noise is added, similar to the channel inversion scheme. Therefore, the MU-MIMO scheme is essential for increasing the cell average throughput of the LTE-A communication system. The sum capacity of the MU-MIMO channel is proved to be achieved by the dirty paper coding (DPC) which perfectly pre-subtracts the inter user interference (IUI). However, the DPC is difficult to apply to MU-MIMO system in practice, since the DPC requires additional complexity at the BS and UE. The BD scheme has been proposed to solve thehigh implementation complexity and nonlinear characteristic of DPC. Unlike the DPC, the BD scheme is a linear precoding scheme and its implementation complexity is very low. In addition, when there is no IUI, it is possible to approximately achieve the sum capacity that can be achieved by the DPC [5]. Therefore, this paper adopts the BD scheme with low implementation complexity. In order to obtain an appropriate performance evaluation of MIMO schemes, the usage of wireless channel model reflecting spatial channel characteristic is required [6; 7]. Therefore, the 3 rd generation partnership project (3 GPP) proposed a 3-dimensional (3D) channel model through TR36.873 document. The 3D channel model proposed by 3 GPP has additional parameters unlike the conventional 2-dimensional (2D) channel model. The large-scale parameters of the 3D channel model are shadow fading, delay spread, and angular spread. The small-scale parameters include delays, cluster power, angle-of-arrival (AOA), and angle-of-departure (AOD) [8]. Among these parameters, the AOA can be used to estimate the localization of the UEs. There is a study related to AOA-based localization estimation using MIMO-OFDM channel state information (CSI) [9]. In addition, the 3D channel model includes parameters related to polarization and antenna configuration (linear antenna, array antenna) [10]. The proposed relay selection scheme can select appropriate relay in 3D channel as well as 2D channel. The cell coverage is very important in wireless communication system such as LTE or LTE-A. As the distance between the BS and UE increases, the power of the transmitted signal is attenuated by the path loss. Thereby the received signal-to-noise ratio (SNR) is reduced. The reduction of the SNR of the received signal degrades the reliability of wireless communication systems such as the LTE or LTE-A. The multi-hop transmission system can overcome the above problem. The multi-hop transmission system can mitigate the power attenuation of the transmitted signal due to the path loss by using the relay between the BS and UE. As a result, the cell coverage of the wireless communication system can be expanded.