## 4 Simulation Results
### Numerical Simulation and Discussion  
Table 7 shows the increase of secrecy capacity after one iteration for SISO under perfect channel estimation. The base value of the iteration step is \(\beta=0.5\). The imperfect channel estimation is not considered here. The secrecy capacity increases the most after one iteration of ISQP, followed closely by SQP. The secrecy capacity of the BPA algorithm has the least increase. The COCOA algorithm, another typical iterative algorithm, is also compared in Tables 7 and 8. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of Transmitting Antennas & 2 \\ Number of Receiving Antennas & 2 \\ Number of Eavesdropping Antennas & 2 \\ Transmission Power & 10 \\ Mean of Channel \(\mathbf{H}\) and \(\mathbf{G}\) & 0 \\ Variance of Channel \(\mathbf{H}\) and \(\mathbf{G}\) & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Simulation Parameters for MIMO. \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Complexity for Each Iteration** \\ \hline ISQP & \(16(N_{H1}+N_{H2})+N_{f1}+167\) \\ SQP & \(142+16(N_{H1}+N_{H2})+N_{f1}+N_{f2}\) \\ BPA & \(36\;N_{f2}+166\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Complexity Analysis for MIMO under Perfect Channel Estimation. \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Complexity for Each Iteration** \\ \hline ISQP & \(16(N_{H1}+N_{H2})+N_{f1}+167\) \\ SQP & \(142+16(N_{H1}+N_{H2})+N_{f1}+N_{f2}\) \\ BPA & \(36\;N_{f2}+166\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Complexity Analysis for MIMO under Imperfect Channel Estimation. Table 8 shows the complexity comparison of algorithms for SISO under the perfect channel estimation. BPA leads to the largest calculated amount of computation and the worst optimization result. Such poor performance is owing to the lack of clear search directions for BPA. On the contrary, ISQP has the smallest calculated amount of computation and the best optimization result due to the simplicity of the initial matrix. According to Tables 7 and 8, the optimization performance of ISQP is similar to that of SQP. However, ISQP requires much less computation. Therefore, we conclude that ISQP is a more effective and thus more desirable algorithm. ISQP and SQP requires fewer iterations than COCOA when \(\varepsilon=1\times 10^{-6}\). The expression \(\varepsilon=1\times 10^{-6}\) refers to the two-norm of the gradient rate for BPA and COCOA. Again, BPA requires the most iterations. Tables 9-11 show the influence of the initial point on the optimization of secrecy capacity. The results are similar across different algorithms. The even distribution of transmission between information-bearing and SCO\(-\)AN seems to be the optimal distribution scheme. This result paves the way to an exciting field for future research. Figure 4 shows the performance comparison of different algorithms. Figure 4 contains four subfigures, each showing a similar trend in the results. Subfigure (a) shows the optimization performance of SISO under perfect channel estimation versus different SNR. Subfigure (b) shows the optimization performance of SISO under imperfect channel estimation versus different SNR. Subfigure (c) shows the optimization performance of MIMO under perfect channel estimation versus different SNR. Subfigure (d) shows the optimization performance of MIMO under perfect channel estimation versus different SNR. Subfigure (d) shows the optimization performance of MIMO under imperfect channel estimation versus different SNR. According to Section 3, BPA requires the most computation and has the worst optimization performance. While SQP and ISQP have similar performance, SQP requires 15% more calculated amounts than ISQP. The optimization performance of COCOA is slightly better than that of BPA, but COCOA is not an excellent iterative algorithm due to the lack of efficacy. Figure 5 shows SCO\(-\)AN's secrecy capacity with and without allocation versus different SNR.