# Relay Selection Scheme for Multi-Hop Transmission of MU-MIMO System
## 6 Conclusions  
This paper proposes a method to select an appropriate relay in DF-based multi-hop transmission of MU-MIMO system. The DF-based multi-hop transmission system can degrade the system performance due to the error propagation. In order to improve the system performance by mitigating the error propagation problem, the DF-based multi-hop transmission system requires selection schemes. Therefore, there are many studies related to the relay selection. Among the various relay selection schemes, the BHM scheme is the optimal relay selection scheme [13]. In the BHM scheme, the BS must know both the channel information between the BS and relays and between the relays and UE in order to select an appropriate relay. Therefore, the BHM scheme has very high BER performance, but it is complicated. The proposed relay selection scheme selects one relay using only singular value of the channel matrix between the BS and relays. In the proposed relay selection scheme, the singular values are obtained through the SVD of the channel matrix between the BS and relays. Then, the relay having the largest sum of the singular values is selected. Therefore, in the proposed relay selection scheme, the BS can select an appropriate relay even if the BS only knows the channel information between the BS and relays. In addition, the proposed relay selection scheme provides a method to select an appropriate relay for multi-hop transmission in a 3D channel environment as well as the conventional 2D channel environment. The conventional and proposed relay selection scheme can mitigate the error propagation problem of the DF-based multi-hop transmission system, but the problem still remains. Therefore, we plan to study one that can select an appropriate relay through AOA-based localization estimation and beamforming in a system using a linear and array antenna, and reliably mitigate the error propagation by increasing the SNR of the received signal. The simulation results show that the proposed relay selection scheme has higher BER performance than the random relay selection scheme and similar to the BHM scheme. As a result, the proposed relay selection scheme can select an appropriate relay more easily than the conventional relay selection scheme using only channel information between the BS and relays.  
Figure 8: The BER performance of the proposed and conventional schemes in 3D channel environment (Array antenna).  
**Author Contributions:** [PERSON] proposed a relay selection scheme for MU-MIMO based multi-hop transmission system and performed computational simulations; [PERSON] performed simulation of the conventional system and schemes; [PERSON] gave feedbacks about modified algorithm and all simulation results. Also, [PERSON] provided the experimental materials for better computational simulations and revised critical errors of the manuscript.  
**Acknowledgments:** This work was supported by the MSIT(Ministry of Science and ICT), Korea, under the ITRC(Information Technology Research Center) support program(IITP-2018-0-01423) supervised by the IITP(Institute for Information & communications Technology Promotion) and was supported by Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government(MSIT) (No.2017-0-00217, Development of Immersive Signage Based on Variable Transparency and Multiple Layers).  
**Conflicts of Interest:** The authors declare no conflict of interest.