## 4 Results and Discussion
Figure 3: Bit Error Rate Comparison of a log likelihood ratio (LLR) based relay selection scheme for different values of Transition Probability for **(a)** Binary Phase Shift Keying (BPSK) Modulation and **(b)** Quadrature Phase Shift Keying (QPSK) Modulation. Without Source to Destination Link. best BER performance is achieved when the transition probability matrix representing only Nakagami fading is selected, where BER of the order of approx. \(3\times 10^{-5}\) is achieved at 10 dB SNR value. While in the case of QPSK modulation, the best achieved BER is approximately \(4\times 10^{-5}\) and is achieved at the 12 dB SNR value. Figure 4c presents a channel capacity comparison for LLR based relay selection scheme under different transition probabilities. It can be observed that the maximum achievable channel capacity is provided under only the Rician fading environment, which is found to be approx. 6.5 Bits/s/Hz at 20 dB SNR. Figure 5 presents (a) LLR based single relay selection scheme (LLR-1 Relay) with source to destination link and (b) LLR based on two relay selection schemes (LLR-2 Relay), with no source to destination link for transition probability and only Nakagami fading environment. The BER comparison of the LLR based relay selection scheme with a source to destination link and without a source to destination link is presented in Figure 5a. An outage comparison for the given scenario is presented in Figure 5b. The threshold of the outage analysis is set to be at an error value greater than \(10^{-4}\). It can be seen that the addition of a source to destination link improves the BER of a proposed scheme as a zero-error point with direct link is found to be at 10 dB SNR, 6 dB better as compared to a system without a direct link, which is found at 16 dB SNR for the considered case with transition matrix presenting equal probability for all considered fading scenarios. Clearly the system with a direct link provides better outage behavior when compared to a system without direct link. Finally, the channel capacity comparison for the considered scenario is presented in Figure 5c. The channel capacity performance of system with direct link is comparably better too. Figure 4: Comparison of LLR based relay selection scheme for different values of Transition Probability with Source to Destination Link. Table 2 presents a BER comparison for a LLR based relay selection considering a source to destination link and relay to destination link with transition probability of a Nakagami fading environment (Figure 4a) and LLR based on two relay selection schemes (LLR-2 Relay), with no source to destination link for transition probability with only a Nakagami fading environment (Figure 5a). Figure 5: Comparison of LLR based relay selection scheme with Direct and Indirect Links. \begin{table}
\begin{tabular}{c c c} \hline
**SNR** & **Figure 5a** & **Figure 4a** \\ \hline
0 & 0.231033203125000 & 0.231768750000000 \\
2 & 0.132341406250000 & 0.133731640625000 \\
4 & 0.050177343750000 & 0.050139453125000 \\
6 & 0.009687500000000 & 0.008972265652000 \\
8 & 0.007076758125000 & 0.00750000000000 \\
10 & 0.000024609375000 & 0.000039843750000 \\
12 & 0 & 0.000000390625000 \\
14 & 0 & 0 \\
16 & 0 & 0 \\
18 & 0 & 0 \\
20 & 0 & 0 \\ \hline \end{tabular}
\end{table} 
Table 2: Bit Error Rate (BER) comparison for scenarios presented in Figures 4a and 5a.