## 6 Conclusions  
This paper proposed a CNN-based power allocation framework for cell-free massive MIMO networks. The proposed method jointly learns CPU-to-AP and AP-to-UE power allocation using spatially distributed input features such as CSI, interference levels, and AP-UE distances. Unlike traditional schemes such as equal power allocation and max-min power allocation, the proposed method performs end-to-end optimization that adapts power allocation dynamically across the entire transmission hierarchy. Simulation results under realistic UE clustering scenarios demonstrate that the CNN integrated model consistently achieves the highest performance in both SE and EE. While the SE performance of the two CNN-based methods is similar, the integrated model provides significantly better EE by avoiding unnecessary power use at underutilized APs. This shows that the proposed method not only improves throughput but also minimizes energy waste through globally coordinated power control.  
Future work may explore the integration of CNN-based power control with user-centric clustering strategies in cell-free massive MIMO systems. As both power control and clustering decisions are centrally managed at the CPU level, their joint optimization can enhance overall system efficiency. Dynamically grouping APs based on user location and channel conditions may reduce unnecessary power consumption while maintaining quality of service, ultimately improving scalability and fairness in dense network deployments.  
Conceptualization, [PERSON]-[PERSON] and [PERSON]; methodology, [PERSON]-[PERSON] and [PERSON]-[PERSON]; software, [PERSON]-[PERSON] and [PERSON]; validation, [PERSON]-J.C. and [PERSON]-[PERSON]; formal analysis, [PERSON]-J.C.; investigation, [PERSON]-[PERSON] and [PERSON]; resources, [PERSON]-[PERSON] and [PERSON]; data curation, [PERSON]-[PERSON] and [PERSON]; writing--original draft preparation, [PERSON]; writing--review and editing, [PERSON] and [PERSON]; visualization, [PERSON] and [PERSON]; supervision, [PERSON] and [PERSON]; project administration, [PERSON] and [PERSON]; funding acquisition, [PERSON]. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2020R1A6A1A03038540). This work was supported by Institute of Information & Communications Technology Planning & Evaluation (IITP) under the metaverse support program to nurture the best talents (IITP-2025-RS-2023-00254529) grant funded by the Korean Government (MSIT). This work was supported by an IITP (Institute of Information & Communications Technology Planning & Evaluation)-ITRC (Information Technology Research Center) grant funded by the Korean Government (Ministry of Science and ICT) (IITP-2025-RS-2021-II211816).  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest; the funders had no role in the design of the paper, in the collection, analysis, or interpretation of the data, in the writing of the manuscript, or in the decision to publish the results.