# Relay Selection Scheme for Multi-Hop Transmission of MU-MIMO System
## 5 Simulation Results  
This section compares the BER performance of the proposed scheme with the conventional schemes through the BER performance graph according to the SNR. This simulation is based on the OFDM transmission scheme adopted in the LTE and LTE-A. The BER performance of the OFDM transmission scheme can be changed by time and frequency synchronization and channel coding. The BER performance sensitivity of OFDM transmission scheme according to time and frequency synchronization was studied in [18; 19], and the performance changes according to channel coding was studied in [20]. In addition, the analysis of OFDM performance for noise effects was studied in [21]. The simulation parameters are as follows. The number of sub-carriers is 128, and the length of the cyclic prefix (CP) is 32. The modulation order is the quadrature phase shift keying (QPSK) and 16-quadrature amplitude modulation (16-QAM). It is assumed that the number of relay candidates is 20. In this simulation, two kinds of channel models are used. Since the conventional 2D channel model is assumed to be the non line-of-sight (NLOS) environment with seven-multi paths, this paper uses the Rayleigh fading channel with seven-multi paths [22]. The 3D channel model is the 3D spatial channel model (3D SCM) proposed by the 3 GPP. Figures 5 and 6 show that the BER performance of the conventional schemes and proposed scheme in the 2D channel environment (7-multi paths Rayleigh fading channel). In Figures 5 and 6, the [2; 2; 1] and [4; 4; 2] refer to the [BS antenna, relay antenna, UE antenna]. In case of the random relay, it has lowest BER performance because it selects one relay randomly among 20 relay candidates. Because each relay has different channel condition due to the distance of obstacles between the BS and relays, a relay having poor channel conditions can be selected in random relay selection scheme. The proposed relay selection scheme has the BER performance similar to that of the optimal relay selection scheme (BHM scheme). In the BHM scheme, the relay is selected by using both the channel information between the BS and relays and channel information between the relays and UEs, but the proposed relay selection scheme selects the relay using only the channel information between the BS and relays. In other words, the proposed relay selection scheme can select the appropriate relay more simply than the optimal relay selection scheme (BHM scheme). As can be seen in Figure 5, the BHM scheme in BER \(10^{-2}\) has about 5 dB higher performance than the random relay selection scheme. The proposed scheme has similar BER performance with the BHM scheme in all SNR environments. As shown in Figure 6, even if the number of antennas of the BS, relays, and UEs is increased, the BHM scheme has approximately 5 dB higher BER performance than the random relay selection scheme and the proposed relay selection scheme has similar BER performance with the BHM scheme in all SNR environments. As shown in Figures 5 and 6, the proposed relay selection scheme has similar BER performance with the optimal relay selection scheme (BHM scheme) and has better BER performance than the random relay selection scheme. Figures 7 and 8 show the BER performance of the conventional schemes and the proposed scheme in the 3D channel (3D SCM) environment. In Figure 7, the [4; 4; 2] refers to the [BS antenna, relay antenna, UE antenna], and 'Linear' means that the antennas of the BS and relays are linearly arranged (\(4\times 1\)). As shown in Figure 7, the random relay has the lowest BER performance because it selects one relay among 20 relays candidates. The proposed relay selection scheme has similar BER performance to the BHM scheme. In other words, the proposed relay selection scheme can select the appropriate relay using only the channel information between the BS and relays in the 3D channel environment. In Figure 8, the 'Array' means that the antennas of the BS and relays are arranged in an array (\(2\times 2\)).