# Adaptive Relay Selection Scheme by Using Compound Channel
## 5 Simulation Results  
The simulation parameters are shown in Table 1. The number of symbols is 64 and the channel is a Rayleigh fading channel. The simulations iterate 100,000 times to sufficient for convergence of the Monte Carlo. To compare performance according to outage, modulation scheme uses both QPSK and 16-QAM. The detection scheme uses the zero-forcing (ZF) scheme to reduce the complexity of detection. Two distance ranges are used to compare the performance effect of distance. One of distance rate is divided into \(S\) to \(R_{k}\) and \(R_{k}\) to \(D_{u}\) based on 0.5. The other distance rate is divided into \(S\) to \(R_{k}\) and \(R_{k}\) to \(D_{u}\) based on 1. The distance rate 1 has a greater channel variation than the 0.5 distance rate. The maximum total distance of both two ranges is normalized to 1, and each relay has a random distribution within the range. The number of users is two and each user is detected by single user detection. The number of \(R_{k}\) and the antenna of the relay are simulated for four and eight to compare the performance according to the number of antennas and relays. For simplicity of simulation, \(N_{l}\) and \(N_{m}\) are fixed. The proposed scheme is compared to the two schemes mentioned in Section 3. This is because above cited researches and proposed scheme are based on the capacity and Frobenius norm. For the equality of simulations, the capacity and Frobenius norm-based selection schemes use the same compound channel as the proposed scheme and select a relay with the largest capacity. The simulation graphs show the user-average BER performances of proposed scheme, capacity and Frobenius norm-based selection schemes. Each number of \(N_{t}\) and \(N_{r}\) is four in from Figure 3. Figure 3a,b are shown using a 0.5 distance rate and Figure 3c,d are shown using a 1 distance rate. Figure 3a,c are shown using a 16-QAM modulation scheme and Figure 3b,d are shown using a QPSK modulation scheme. The simulation results show that the proposed scheme has improved BER performance than the capacity and Frobenius norm-based schemes. The capacity-based and Frobenius norm-based schemes have the same performance. In Figure 3a, the proposed scheme shows about 8 dB higher performance than the capacity and Frobenius norm-based schemes at BER of \(10^{-2}\). The overall graph shape of Figure 3b is similar to Figure 3a, but the performance of Figure 3b has higher performance than Figure 3a. The gain of BER performance increases especially at low SNR due to the frequent occurrence of outages. At BER of \(10^{-2}\), the proposed scheme in Figure 3b has about 6 dB higher performance than Figure 3a. The capacity and Frobenius norm-based schemes in Figure 3c has similar performance to Figure 3a. On the other hand, the BER performance of proposed scheme improves as the number of relays increase. The BER performance of the proposed scheme is improved by about 3\(\sim\)7 dB based on BER of \(10^{-2}\). At the low SNR, proposed scheme has a nonlinear BER performance unlike Figure 3b due to the extended channel variation. Based on the six relays, the proposed scheme of Figure 3d has 6 dB performance gain compared to Figure 3c at BER of \(10^{-3}\). At BER of \(10^{-4}\), the proposed scheme of Figure 3d also improves the gain about \(9\sim 14\) dB than Figure 3b. The BER performances of the proposed scheme improve as the number of available relays increases. Figure 3c,d show that the diversity gain of relay gets greater as distance rate increases. Figure 4 show simulation results with \(N_{t}\) and \(N_{r}\) of eight. The composition of Figure 4 is the same Figure 3. The proposed scheme in Figure 4a has 7 dB higher performance than capacity and Frobenius norm-based schemes at BER of \(10^{-2}\). Furthermore, the proposed scheme in Figure 4a has 6 dB performance gain compared to Figure 4b at BER of \(10^{-2}\). Since \(N_{m}\) is fixed, BER performances of Figure 4a,b are greater by 1 dB than the performances of Figure 3a,b with the same number of \(N_{t}\) and \(N_{r}\).