## 4 PSO Techniques for Adaptive Equalization
### Performance Analysis  
The selected PSO variants were utilized to analyze their efficacy for adaptive filtering in this study. The bit error rate (BER) is a measure of the error rate in a digital communication channel. It quantifies the probability of bit errors occurring during transmission. A lower BER indicates better channel performance, as it signifies fewer errors in the received bits. Factors that affect the BER include noise, interference, the modulation scheme, the coding techniques, and the channel characteristics. By analyzing and optimizing the BER, engineers can improve the overall reliability and quality of digital communication systems. A convergence analysis was conducted in an experimental setting, simulating a digital communication channel model. Six key parameters are defined to analyze the convergence of hybrid PSO. Population size \(n\), data window size \(N\), acceleration parameters \(c1\) and \(c2\), maximum velocity range, and the number of taps for the adaptive channel equalizer were selected. This methodical approach ensures the algorithm's effectiveness and adaptability for various scenarios. To observe the behavior of HPSO, a convergence analysis was conducted in an experimental setting simulating a digital communication channel model. The analysis, as depicted in Table 4, demonstrated the stabilization of the convergence rate as the number of iterations (N) increased. This observation underscores HPSO's capability to steadily refine its optimization process, an attribute essential for optimizing digital communication systems. The analysis of the convergence of HPSO over \(N\) iterations is shown in Table 4, which shows that the convergence rate becomes stabilized when \(N\) is large. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Topic** & **Advantages** & **Limitations** \\ \hline Ring Topology & \(\bullet\) & Local information sharing and cooperation [140] & \(\bullet\) & Limited information propagation beyond immediate neighbors [99] \\  & \(\bullet\) & Promotes exploration and exploitation & & \\ \hline Dynamic Multi-Swarm & \(\bullet\) & Efficient exploration of different regions & \(\bullet\) & Increased computational complexity [141] \\  & \(\bullet\) & Balances exploration and exploitation & \(\bullet\) & Requires careful tuning of swarm characteristics [107] \\ \hline Fully Informed & \(\bullet\) & Enhanced global exploration capability & \(\bullet\) & Increased communication and computational overhead \\  & & \(\bullet\) & Sensitivity to parameter settings [112] \\ \hline Dynamic Neighborhood & \(\bullet\) & Adaptability to changing problem conditions [142] & \(\bullet\) & Complexity in managing dynamic neighbor relationships \\  & \(\bullet\) & Improved exploration and exploitation & \(\bullet\) & Additional computational overhead [114] \\ \hline Hybridization & \(\bullet\) & Leveraging strengths of multiple techniques & \(\bullet\) & Increased algorithm complexity \\  & \(\bullet\) & Enhanced performance and solution quality & \(\bullet\) & Requires expertise in multiple algorithms or methods [143] \\ \hline Cooperative Particle Swarm & \(\bullet\) & Knowledge exchange and cooperation among swarms & \(\bullet\) & Increased communication and coordination requirements \\  & \(\bullet\) & Tackling large-scale optimization problems [144] & \(\bullet\) & Complexity in swarm interaction management \\ \hline Self-Organizing Hierarchical & \(\bullet\) & Efficient exploration and coordination across different levels & \(\bullet\) & Complexity in the hierarchical organization and coordination [145] \\ \hline Comprehensive Learning & \(\bullet\) & Adaptation to problem characteristics & \(\bullet\) & Requires problem-specific knowledge or heuristics [146] \\  & \(\bullet\) & Improved convergence and solution quality & \(\bullet\) & Increased algorithm complexity and parameter tuning effort \\ \hline \hline \end{tabular}
\end{table} 
Table 3: PSO variants advantages and limitations for adaptive filtering.