### CNN-Based Power Allocation  
Convolutional neural networks have recently emerged as an effective alternative for wireless power control. Unlike traditional fully connected neural networks, CNNs are capable of extracting spatial dependencies among APs and UEs. By leveraging input features such as channel state information, AP-UE distance, interference level, and SINR, CNNs can learn context-aware and fine-grained power allocation strategies that adapt to real-time network conditions. However, most existing CNN-based models focus solely on AP-to-UE power allocation and assume fixed or uniform CPU-to-AP power distribution [11; 12]. In these stage-wise architectures, the CPU allocates power equally to all APs regardless of their spatial location or connectivity to UEs, and only the AP-to-UE power split is learned by the model. This decoupled approach limits the ability to perform holistic optimization, especially in scenarios where certain APs require more power due to user density or channel conditions. Consequently, network performance may be suboptimal due to misaligned resource allocation at the AP level.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Feature** & **CNN–LSTM [8]** & **CNN–LSTM [9]** & **CNN–LSTM [10]** & **Proposed CNN** \\ \hline Target Application & CF-mMIMO IoT & Massive MIMO & UM-MIMO Beamforming & CF-mMIMO \\ CPU-to-AP Optimization & No & No & No & Yes \\ AP-to-UE Optimization & Yes & Yes & No & Yes \\ Temporal Modeling & Yes (LSTM) & Yes (LSTM) & Yes (LSTM) & No \\ Input Features & CSI, SE/EE, time series & Location, CSI & CSI sequences & CSI, distance, SINR, interference \\ Model Complexity & High & Moderate & High & Low \\ Real-Time Suitability & No & No & No & Yes \\ End-to-End Control & Partial & Partial & – & Yes \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison with recent deep learning-based power control methods.  
In contrast, our proposed CNN-based model performs end-to-end learning that jointly optimizes both CPU-to-AP and AP-to-UE power allocation within a unified framework. This allows the model to dynamically adjust the total transmit power at each AP as well as its distribution across UEs in a spatially adaptive manner. The proposed joint learning strategy captures global spatial correlations and enables system-wide optimization based on both topological and signal conditions. In addition to CNN-based methods, other learning-based approaches such as deep reinforcement learning (DRL) and graph neural networks have also been investigated. DRL methods such as deep q-networks and deep deterministic policy gradient offer long-term optimization under time-varying conditions, but require complex reward design and extensive training [13]. Graph neural network-based models are suitable for distributed scenarios and can represent AP-UE connectivity as graphs, but often decouple the hierarchical power control stages and may not be suitable for centralized architectures [14]. In comparison, our proposed CNN model provides an efficient and interpretable solution for centrally coordinated systems, achieving a strong balance between throughput, fairness, and energy efficiency while offering significantly lower complexity than alternatives such as GNNs that are better suited to decentralized architectures. In contrast to GNNs, CNNs excel in capturing spatial locality in centralized cell-free MIMO systems.  
This study evaluates the proposed method against traditional heuristic schemes such as equal power allocation and max-min power allocation as well as against stage-wise CNN models. Simulation results demonstrate that the integrated CNN architecture consistently improves per-user SE while enhancing EE, confirming the effectiveness of joint spatially-aware learning in cell-free massive MIMO environments.