## 6 Conclusions  
Effective ways to boost the performance of a WSN include smooth data aggregation and the proper choice of CHs. The difficulties related to selecting a randomly deployed distant sensor node as a CH in data transmission are addressed by selecting appropriate CHs based on node energy. To select an adequate CH in the network for data aggregation, TLC strategies were proposed that solved existing LEACH boundary issues. In first-level clustering, the node density problem in a particular network region, which can lead to the draining of node energy, was solved by creating a uniform energy region. In the second-level clustering, angular distance estimation was introduced to overcome the heterogeneous characteristics of nodes and support the CHs selection. The energy level in each node remains higher while working with TLC, and thus, dead nodes within the network were significantly reduced. As a result, the simulation results demonstrated that WSN efficiency was considerably enhanced and distant BS issues were remarkably minimized. Hence, the proposed TLC method for CH selection in randomly deployed WSN is effective for distant BS problems and efficient data transmission.  
In this paper, we used a fixed clustering approach that may not perfectly cover dynamic network changes, potential energy imbalance among frequently acting CHs, and scalability challenges in large networks. Additionally, issues related to interference, collisions, and the environmental impact on performance are not thoroughly addressed, and the algorithm assumes static nodes, limiting its applicability in mobile scenarios. Future research should focus on developing dynamic clustering algorithms, integrating energy harvesting techniques, and enhancing scalability to ensure efficient operation in larger networks. Further exploration into interference management, environmental adaptability, and support for mobile nodes will broaden the algorithm's applicability. Incorporating multi-hop routing within the TLC framework and conducting real-world implementation and testing will provide valuable insights and validate the algorithm's practical effectiveness, ultimately leading to a more robust and efficient solution for wireless sensor network applications.  
Conceptualization, S.S. and S.L.; methodology, S.S. and S.K.A.; software, S.S.; formal analysis, S.S. and S.K.A.; investigation, S.L.; resources, S.S. and S.K.A.; data curation, J.L. and S.L.; writing--original draft preparation, S.S.; writing--review and editing, S.K.A.; visualization, S.S. and S.K.A.; supervision, S.L.; project administration, J.L.; funding acquisition, J.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2021R1C1C1012408).  
The data presented this study are available on request from corresponding author. The data are not publicly available due to we will conduct further research on some of the data in this article.  
The simulation software MATLAB R2021a was supported by the Department of Electronics and Information Engineering, Mokpo National University, Republic of Korea.  
The authors declare no conflicts of interest.