## 4 PSO Techniques for Adaptive Equalization
### Performance Analysis
Table 6 shows the results of 30D particle convergence. Table 7 shows the convergence performance using 60D particles. The findings suggested that HPSO is a robust and effective optimization algorithm, which can outperform other PSO variants in various applications. Its ability to strike a balance between exploration and exploitation, along with the integration of local search techniques provide HPSO a competitive advantage. The superior performance of HPSO makes it a promising choice for optimization tasks where fast convergence and high-quality solutions are desired, such as channel adaptive equalization in communication systems, where accurate estimation and compensation of channel distortion are crucial for reliable data transmission. The evaluated dimensions ranged from 10 to 100. Lower mean function values indicate better optimization performance. The experiment involved applying these PSO variants to the sphere function, a well-known optimization benchmark. The sphere function computes the sum of squared differences between a candidate solution and the optimal solution. This experiment aimed to compare the effectiveness of the PSO techniques in achieving optimal solutions within different dimensional spaces. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**f(x)** & \multicolumn{2}{c}{**fi**} & \multicolumn{3}{c}{**f2**} \\ \hline
**Value** & **Mean** & **Iterations** & **Comp** & **Mean** & **Iterations** & **Comp** \\ \hline PSO & 7.1e\(-\)2 & 500 & 100\% & 55.44 & 500 & 100\% \\ PSO-D & 5.706e\(-\)53 & 500 & 100\% & 0 & 264 & 100\% \\ PSO-DE & 6.35e\(-\)20 & 412 & 70.3\% & 293 & 66.90\% & \\ \hline DMS & 0.71 (2\%) & 500 & 100\% & 37.97 & 500 & 100\% \\ DIMS-D & 3.646e\(-\)54 & 500 & 100\% & 0 & 273 & 100\% \\ DAIS-DE & 3.85e\(-\)20 & 392 & 69.88\% & 0 & 320 & 66.48\% \\ \hline CL & 1.056e\(-\)47 & 500 & 60\% & 0 & 312 & 60\% \\ CL-D & 3.486e\(-\)51 & 500 & 60\% & 0 & 279 & 60\% \\ CEDE & 7.19e\(-\)19 & 319 & 39.2\% & 0 & 258 & 37.63\% \\ \hline HP & 1.0486e\(-\)5 & 50 & 80\% & 29.56 & 500 & 80\% \\ HP-D & 4.906e\(-\)111 & 500 & 80\% & 0 & 87 & 80\% \\ HP-DE2 & 5.216e\(-\)15 & 55 & 3.99\% & 1.18e\(-\)13 & 227 & 12.80\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The 30D particles’ convergence comparison. Table 8 shows the mean function value (MFV) of different PSO algorithms. The simulation results consistently demonstrated the robustness and effectiveness of HPSO across various domains and problem types. Whether applied to engineering design optimization, function optimization, or other complex tasks, HPSO consistently outperformed the competing algorithms. These findings establish HPSO as a promising optimization approach that can provide significant benefits in terms of convergence speed and solution quality, making it an attractive choice for numerous real-world optimization problems. The simulation results consistently demonstrated the robustness and effectiveness of HPSO across various domains and problem types. Whether applied to engineering design optimization, function optimization, or other complex tasks, HPSO consistently outperformed the competing algorithms. Tables 9 and 10 present the MSE values under different signal-to-noise ratio (SNR) levels, which indicate the quality of the channel's output signal. Lower MSE values signify better performance, indicating a closer approximation to the desired output. A negative MSE value can be an artifact of data representation or computation.