## 2 SIR-Based Performance Analysis
### The Channel Capacity  
Channel capacity has great importance as a system performance measure of wireless systems. The CC is defined as the maximal rate at which information can be transmitted through a wireless channel with arbitrarily small BEP, without delay or complexity limits [26]:  
\[\frac{CC}{B}=\frac{1}{\ln(2)}\int\limits_{0}^{\infty}\ln(1+z)p_{z}(z)dz \tag{16}\]  
where \(CC\) is a label for Shannon capacity expressed in bits/s, and \(B\) marks transmission bandwidth expressed in Hz.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Pout** & \(z=-10\)**dB** & \(z=0\)**dB** & \(z=10\)**dB** \\ \hline \(\kappa_{\rm x}=1,m=1\) & 5 & 8 & 9 \\ \hline \(\kappa_{\rm x}=1.5,m=1\) & 5 & 7 & 10 \\ \hline \(\kappa_{\rm x}=2,m=1\) & 5 & 7 & 12 \\ \hline \(\kappa_{\rm x}=2.5,m=1\) & 5 & 7 & 12 \\ \hline \(\kappa_{\rm x}=3,m=1\) & 5 & 7 & 14 \\ \hline \(\kappa_{\rm x}=4,m=1\) & 5 & 8 & 16 \\ \hline \(\kappa_{\rm x}=1,m=1.5\) & 5 & 8 & 10 \\ \hline \(\kappa_{\rm x}=1,m=2\) & 5 & 8 & 11 \\ \hline \(\kappa_{\rm x}=1,m=2.5\) & 5 & 9 & 13 \\ \hline \(\kappa_{\rm x}=1,m=3\) & 5 & 10 & 14 \\ \hline \(\kappa_{\rm x}=1,m=4\) & 5 & 12 & 16 \\ \hline \end{tabular}
\end{table}
Table 1: Number of terms to be added in expression (15) for Pout to achieve accuracy at the 5 th significant digit when changing parameters \(\kappa_{\rm x}\) and \(m\), and \(\kappa_{y}=1\), \(\mu=1\), \(\Omega=1\), \(\rm s=1\), \(L=2\).  
\begin{table}
\begin{tabular}{c c c c} \hline
**Pout** & \(z=-10\)**dB** & \(z=0\)**dB** & \(z=10\)**dB** \\ \hline \(\kappa_{\rm y}=1,\mu=1,L=2\) & 5 & 8 & 9 \\ \hline \(\kappa_{\rm y}=2,\mu=1,L=2\) & 5 & 10 & 12 \\ \hline \(\kappa_{\rm y}=3,\mu=1,L=2\) & 5 & 13 & 13 \\ \hline \(\kappa_{\rm y}=4,\mu=1,L=2\) & 5 & 15 & 16 \\ \hline \(\kappa_{\rm y}=1,\mu=2,L=2\) & 5 & 11 & 12 \\ \hline \(\kappa_{\rm y}=1,\mu=3,L=2\) & 5 & 13 & 13 \\ \hline \(\kappa_{\rm y}=1,\mu=4,L=2\) & 5 & 15 & 16 \\ \hline \(\kappa_{\rm y}=1,\mu=1,L=3\) & 5 & 7 & 9 \\ \hline \(\kappa_{\rm y}=1,\mu=1,L=5\) & 5 & 6 & 9 \\ \hline \(\kappa_{\rm y}=1,\mu=1,L=2\) & 5 & 8 & 9 \\ \hline \end{tabular}
\end{table}
Table 2: Number of terms to be added in the expression for Pout (15) to achieve precision to the 5 th significant digit for variables \(\kappa_{\rm y}\), \(\mu\), and \(L\). Other parameters are: \(\kappa_{\rm x}=1\), \(m=1\), \(\Omega=1\), \(s=1\).  
Table 3 shows that when the parameters \(\kappa_{x}\) and \(m\) increase, the number of elements that need to be added in order to achieve convergence to the fifth decimal increases, and the series converges more slowly. It is necessary to add between 8 and 17 additions for all values of fading and CCI parameters, as well as powers.  
Figure 6: Normalized channel capacity for different values of BX fading parameters \(\kappa_{x}\) and \(m\).  
Figure 7: Normalized channel capacity for different values of CCI parameters \(\kappa_{y}\) and \(\mu\) and number of branches \(L\).  
As Table 4 shows, as parameters \(\kappa_{y}\) and \(\mu\) grow, the number of elements that need to be added in order to achieve convergence to the fifth decimal increases, and the series does not converge as quickly. When parameter \(L\) increases, the number of elements for convergence tends to 10 for all values of \(w_{i}\) [dB]. This is also possible to see from Table 4.