###### Abstract  
Adaptive equalization is crucial in mitigating distortions and compensating for frequency response variations in communication systems. It aims to enhance signal quality by adjusting the characteristics of the received signal. Particle swarm optimization (PSO) algorithms have shown promise in optimizing the tap weights of the equalizer. However, there is a need to enhance the optimization capabilities of PSO further to improve the equalization performance. This paper provides a comprehensive study of the issues and challenges of adaptive filtering by comparing different variants of PSO and analyzing the performance by combining PSO with other optimization algorithms to achieve better convergence, accuracy, and adaptability. Traditional PSO algorithms often suffer from high computational complexity and slow convergence rates, limiting their effectiveness in solving complex optimization problems. To address these limitations, this paper proposes a set of techniques aimed at reducing the complexity and accelerating the convergence of PSO.  
adaptive filtering; particle swarm optimization; bit error rate; signal quality  
approach, and the dynamic neighborhood topology [6]. The primary research question driving this study is how to improve PSO for adaptive filters in terms of convergence, accuracy, and adaptability. By answering this question, the research provides valuable insights and recommendations to optimize the tap weights of adaptive filters, thereby enhancing signal quality and mitigating distortions in communication systems. The primary research questions driving this study are as follows:  
* RQ1: How can the optimization capabilities of PSO be further enhanced for adaptive filters in the context of equalization?
* RQ2: How does the resemblance of PSO with algorithms such as the the least mean squares (LMS) and recursive least squares (RLS) contribute to the understanding and development of adaptive filters?
* RQ3: What are the recent advancements in PSO algorithms, such as ring topology, dynamic multi-swarm PSO, and fully informed PSO, and how do they improve the performance of adaptive filtering?
* RQ4: How does the dynamic neighborhood concept in PSO contribute to better exploration and exploitation of the search space?
* RQ5: What are the benefits and challenges of hybridization techniques, such as hybrid PSO and cooperative PSO, in improving the optimization capabilities of PSO?
* RQ6: What are the time and space complexity considerations of PSO algorithms, and how do they impact the scalability and efficiency of the optimization process?
* RQ7: What are the limitations and challenges of PSO to achieve a better convergence rate?  
The study sought to explore and propose various techniques to improve the convergence, accuracy, and adaptability of PSO algorithms. The research investigated the combination of PSO with other optimization algorithms, the introduction of adaptive mechanisms, the application of multi-objective optimization, and the utilization of the constriction factor approach and dynamic neighborhood topology. By answering these research questions, the study aimed to provide insights and recommendations for optimizing the tap weights of adaptive filters using PSO in communication systems.  
This review is further divided into six parts. Section 2 elaborates on the techniques used for adaptive equalization. PSO, its time complexity, and its resemblance to other optimization algorithms are discussed in Section 3. Section 4 provides a comprehensive overview of PSO approaches used for adaptive filtering including the comparative analysis of PSO variants. Hybrid PSO, the best-fit PSO solution for adaptive filtering, is discussed in Section 5 concerning its advantages and disadvantages. In the end, the conclusion and future directions are given in Section 6.  
Section 2 is dedicated to addressing RQ1 and RQ2. The answers to RQ3 and RQ4 can be found in Section 3. Section 4 presents the discussions regarding RQ5. Lastly, Section 5 delves into the responses to RQ6 and RQ7.