CNN-Based End-to-End CPU-AP-UE Power Allocation for Spectral Efficiency Enhancement in Cell-Free Massive MIMO Networks

Abstract

Cell-free massive multiple-input multiple-output (MIMO) networks eliminate cell boundaries and enhance uniform quality of service by enabling cooperative transmission among access points (APs). In conventional cellular networks, user equipment located at the cell edge experiences severe interference and unbalanced resource allocation. However, in cell-free massive MIMO networks, multiple access points cooperatively serve user equipment (UEs), effectively mitigating these issues. Beamforming and cooperative transmission among APs are essential in massive MIMO environments, making efficient power allocation a critical factor in determining overall network performance. In particular, considering power allocation from the central processing unit (CPU) to the APs enables optimal power utilization across the entire network. Traditional power allocation methods such as equal power allocation and max–min power allocation fail to fully exploit the cooperative characteristics of APs, leading to suboptimal network performance. To address this limitation, in this study we propose a convolutional neural network (CNN)-based power allocation model that optimizes both CPU-to-AP power allocation and AP-to-UE power distribution. The proposed model learns the optimal power allocation strategy by utilizing the channel state information, AP-UE distance, interference levels, and signal-to-interference-plus-noise ratio as input features. Simulation results demonstrate that the proposed CNN-based power allocation method significantly improves spectral efficiency compared to conventional power allocation techniques while also enhancing energy efficiency. This confirms that deep learning-based power allocation can effectively enhance network performance in cell-free massive MIMO environments.

1. Introduction

Wireless networks demand ultra-high data rates, ultra-low latency, and massive simultaneous user connectivity [1], necessitating the development of cell-free massive multiple-input multiple-output (MIMO) technology. Traditional cellular networks suffer from performance degradation at the cell edges, where user equipment (UE) experiences high interference and unbalanced resource allocation, leading to poor communication quality. To overcome these limitations, cell-free massive MIMO replaces cell boundaries with a cooperative architecture, allowing multiple access points (APs) to jointly serve user equipment across the network. This structure improves uniform quality of service and mitigates performance degradation at the cell edges. The APs are connected to a central processing unit (CPU) by a wired backhaul, enabling centralized coordination and effective interference mitigation [2].

However, the practical deployment of cell-free massive MIMO systems requires efficient power allocation strategies. In particular, power should be allocated both from the CPU to the APs and from the APs to the UEs [3]; both of these stages significantly influence the spectral efficiency (SE) and energy efficiency (EE) [4]. The amount of power assigned by the CPU determines the maximum transmission power of each AP and affects overall interference and power usage. Similarly, the way in which APs distribute power among UEs directly impacts each user’s signal quality and data throughput. Therefore, holistic optimization of CPU-AP-UE power allocation is crucial for achieving high system performance with minimal energy wastage. Traditional power allocation methods such as equal power allocation and max–min power allocation rely on heuristic approaches [3]. While computationally simple, these techniques fail to adapt to dynamic network conditions [5]. Equal power allocation ignores spatial variations in channel quality, leading to inefficient resource usage. Max–min power allocation improves fairness by supporting the weakest UEs, but often sacrifices total throughput by underutilizing stronger links [6].

Recently, deep learning-based power control strategies have gained attention thanks to their ability to generalize across complex nonlinear environments. In particular, convolutional neural networks (CNNs) are well suited for capturing spatial features from network topology and channel data. CNNs can process inputs such as channel state information (CSI), AP-UE distance, interference levels, and signal-to-interference-plus-noise ratio (SINR) to learn spatially adaptive power allocation strategies. Based on these inputs, the model learns how to assign power differently depending on user location, channel quality, and interference conditions [7]. This enables flexible and context-aware power control that adapts to dynamic network scenarios instead of relying on fixed allocation rules. This study proposes a CNN-based power allocation model that jointly optimizes both CPU-to-AP and AP-to-UE power distribution. The model is trained end-to-end via supervised learning using data generated from conventional max–min optimization. Simulation results demonstrate that the proposed method significantly improves per-user SE while maintaining EE under realistic network conditions. By integrating both allocation stages into a unified deep learning framework, this work represents a novel approach to hierarchical power control in cell-free networks.

1.1. Related Works

Optimizing power allocation is a key challenge in wireless networks, particularly in terms of balancing SE and EE. In cell-free massive MIMO environments, a CPU coordinates power control for multiple distributed APs, which subsequently allocate power to UEs. This hierarchical structure highlights the importance of efficient CPU-to-AP and AP-to-UE power management in achieving system-wide performance and fairness. Prior research has investigated various power allocation schemes, with heuristic-based and AI-based approaches being most commonly explored for practical implementation. While heuristic methods offer simplicity, they often lack adaptability. In contrast, deep learning-based approaches demonstrate promising flexibility and spatial awareness, particularly in complex and dynamic network environments. Recent deep learning-based studies have applied hybrid architectures combining CNNs with long short-term memory (LSTM) networks to address power control and beamforming in massive and ultra-massive MIMO systems [8,9,10]. These works leverage temporal dependencies via LSTM and spatial features via CNN; however, they typically target only AP-to-UE power allocation or beamforming, and do not perform full-chain hierarchical optimization. In contrast, our proposed method performs joint end-to-end CPU-to-AP and AP-to-UE power allocation using a lightweight CNN structure designed for real-time inference and system-wide optimization.

Table 1. Comparison with recent deep learning-based power control methods.

Feature	CNN–LSTM [8]	CNN–LSTM [9]	CNN–LSTM [10]	Proposed CNN
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

summarizes the architectural and functional differences between our model and recent deep learning-based methods.

1.2. Heuristic-Based Power Allocation Methods

Equal power allocation and max–min power allocation are representative heuristic power control methods frequently used as baseline comparisons in cell-free network studies. The equal power allocation strategy assigns the same amount of power to all APs, which then uniformly distribute it among their served UEs. Although this method is simple and computationally efficient, it fails to account for spatial variations in channel quality and user distribution, resulting in inefficient resource utilization and reduced SE. The max–min power allocation method enhances fairness by maximizing the minimum SINR across users, ensuring that even the weakest UEs maintain basic service quality; however, this fairness-driven approach can limit overall SE by underutilizing UEs with stronger channels. While max–min allocation is mathematically formulated as an optimization problem, it is often used as a practical benchmark due to its interpretability and fairness-centric allocation. Overall, heuristic-based methods are easy to implement but cannot dynamically adapt to channel conditions or user density, motivating the development of more flexible data-driven strategies.

1.3. 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.

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.

2. System Model

2.1. Network Architecture

This study considers a downlink power allocation model based on a cell-free massive MIMO network. In conventional cellular networks, each base station (BS) independently transmits signals and serves its own user equipment within a fixed coverage area. However, UEs located near the cell edge often experience poor communication quality due to strong inter-cell interference and imbalanced resource allocation. To address these issues, cell-free massive MIMO eliminates the concept of fixed cells and allows multiple distributed access points to cooperatively serve all UEs. Each AP is connected to a CPU by a wired backhaul, enabling centralized coordination and efficient signal processing (Figure 1).

The network model considered in this study consists of M APs and K UEs, with all APs operating under the control of the CPU. Unlike cellular systems, in which each BS serves its own UEs independently, cell-free massive MIMO adopts a cooperative downlink transmission strategy in which multiple APs jointly serve each UE. This coordination enhances signal quality while mitigating interference. Instead of independent transmission, APs follow centrally optimized transmission parameters determined by the CPU, improving the overall SINR and resulting in better system performance. Unlike idealized models that assume a uniform UE distribution, this study considers a more realistic scenario in which UEs are densely clustered in certain regions. In practice, UEs are often concentrated in urban centers, stadiums, or business districts, creating localized traffic hotspots. Within these clusters, the UEs are randomly distributed to reflect the stochastic nature of user mobility and spatial behavior. These nonuniform yet random user distributions significantly impact network load, and should be considered when designing power allocation strategies. The CNN-based model proposed in this paper explicitly accounts for such spatial patterns in order to ensure efficient power utilization under real-world deployment conditions [15].

In a cell-free massive MIMO network, AP cooperation plays a vital role in minimizing interference and enhancing both SE and EE. Unlike conventional systems where each BS handles power control independently, the CPU in cell-free networks can coordinate global power allocation across all APs. Moreover, UEs benefit from constructive signal combination from multiple APs through joint downlink beamforming, which improves the effective SINR and data rate. To address the challenge of downlink power allocation under this cooperative architecture, a CNN-based model is proposed that jointly optimizes CPU-to-AP and AP-to-UE power distribution. By enabling centralized power control, the proposed method can flexibly distribute power budgets across APs depending on their spatial demand and channel conditions. This joint optimization of CPU-to-AP and AP-to-UE stages enhances power efficiency and overall system performance compared to traditional rule-based schemes such as equal power allocation and max–min power allocation [16].

2.2. Channel Model

In the proposed cell-free massive MIMO system, the downlink wireless channel between APs and UEs is modeled as a Rayleigh fading channel. Each AP is equipped with a single antenna, and all APs are coordinated by a CPU responsible for power allocation. The small-scale fading component of the AP–UE channel follows a Rayleigh distribution, which is commonly used in rich scattering environments. The complex baseband channel coefficient between AP i and UE j is modeled as follows:

$$h_{i,j}\sim \mathcal{CN}(0,{\beta }_{i,j})$$

(1)

where ${\beta }_{i,j}$ is the large-scale fading coefficient that accounts for path loss and shadowing. This coefficient is defined using a distance-dependent path loss model, as follows:

$${\beta }_{i,j}={\displaystyle \frac{1}{1+d_{i,j}^{\alpha }}}$$

(2)

where $d_{i,j}$ is the distance between AP i and UE j and where $\alpha$ is the path loss exponent. Each AP transmits with an individual power level, and each UE receives the superposition of signals from multiple APs. The received signal at UE j can be expressed as follows:

$$y_j=\sum _{i=1}^M{h}_{i,j}\sqrt{p_{i,j}}{x}_i+n_j$$

(3)

where $p_{i,j}$ denotes the transmit power from AP i to UE j, $x_i$ is the signal transmitted by AP i, and $n_j$ represents additive white Gaussian noise (AWGN) at UE j, modeled as $n_j\sim \mathcal{CN}(0,{\sigma }^2)$. The downlink SINR at UE j is provided by [3]

$${\mathrm{SINR}}_j={\displaystyle \frac{{\sum }_{i=1}^M{\left|h_{i,j}\right|}^2{p}_{i,j}}{{\sum }_{k\ne j}^K{\sum }_{i=1}^M{\left|h_{i,k}\right|}^2{p}_{i,k}+{\sigma }^2}}.$$

(4)

Using the SINR, the achievable rate for UE j is calculated based on the Shannon capacity formula as follows [17]:

$$R_j=B{log}_2(1+{\mathrm{SINR}}_j)$$

(5)

where B denotes the available system bandwidth. As a system-level performance indicator, the average downlink SE is obtained by averaging the achievable rates across all UEs as follows:

$$R_{\mathrm{avg}}={\displaystyle \frac{1}{K}}\sum _{j=1}^K{R}_j.$$

(6)

While cellular networks can improve the summed SE by allocating more power to users with favorable channel conditions, this often results in unfair resource distribution and degraded performance for users at the cell edges. In contrast, cell-free massive MIMO systems aim to provide uniformly good service to all users through cooperative transmission and centralized power coordination. Therefore, the average SE serves as a more appropriate and fair metric for evaluating the overall performance of cell-free architectures.

2.3. Problem Formulation

In cell-free massive MIMO networks, efficient downlink power allocation plays a crucial role in achieving high SE and EE. The power control process involves two stages: power allocation from a CPU to each of the M APs, followed by power distribution from each AP to the K UEs that it serves. Let $P_{\text{CPU-AP}}=[p_1,p_2,\dots ,p_M]$ denote the CPU-to-AP power allocation vector and let $P_{\text{AP-UE}}=\left[p_{i,j}\right]\in {\mathbb{R}}^{M\times K}$ represent the AP-to-UE power allocation matrix, where $p_{i,j}$ is the power allocated from AP i to UE j. Max–min power allocation has traditionally been used as a fairness-oriented benchmark, aiming to maximize the minimum SINR across all UEs. However, this approach may limit performance for UEs with favorable channels. To overcome this limitation, a CNN-based power allocation framework is proposed which learns from max–min optimized data while incorporating additional spatial and contextual information such as channel state information, AP–UE distance, and interference conditions [18]. While trained on fairness-centric max–min results, the model learns to generalize beyond static optimization by inferring context-aware patterns. This allows it to adaptively allocate power in ways that improve both fairness and efficiency under realistic dynamic network conditions.

During training, the CNN minimizes the error between its predicted power allocations and the optimal values obtained from max–min optimization [11]. The loss function is defined as follows:

$$\underset{\theta }{min}{\displaystyle \frac{1}{N}}\sum _{i=1}^N\left(\parallel P_{\text{CPU-AP},i}^{\mathrm{CNN}}-P_{\text{CPU-AP},i}^{\mathrm{opt}}{\parallel }^2+\hspace{0.17em}{\parallel P_{\text{AP-UE},i}^{\mathrm{CNN}}-P_{\text{AP-UE},i}^{\mathrm{opt}}\parallel }^2\right)$$

(7)

where $P_{\text{CPU-AP},i}^{\mathrm{CNN}}$ and $P_{\text{AP-UE},i}^{\mathrm{CNN}}$ are the CNN-predicted values and $P_{\text{CPU-AP},i}^{\mathrm{opt}}$, $P_{\text{AP-UE},i}^{\mathrm{opt}}$ are the max–min optimized references [3,7]. To generate predictions, the trained CNN takes as input a tensor consisting of spatial and signal features such as large-scale fading coefficients, AP–UE distances, channel gain magnitudes, and estimated interference levels. These features are stacked into a multi-channel matrix of size $C\times M\times K$, where C denotes the number of input feature types, M is the number of APs, and K is the number of UEs. The network outputs the CPU–AP and AP–UE power allocation values through two separate fully connected branches.

The optimization is subject to practical constraints. The power allocated from the CPU to each AP must lie within a valid range:

$$0\le p_i\le P_{\text{CPU-AP},max},\forall i\in \{1,\dots ,M\}.$$

(8)

In addition, the total transmit power from each AP to its served UEs should not exceed the power it receives from the CPU:

$$\sum _{j=1}^K{p}_{i,j}\le p_i,\forall i\in \{1,\dots ,M\}.$$

(9)

To ensure reliable communication quality, each UE should also satisfy a minimum SINR requirement as follows:

$${\mathrm{SINR}}_j\ge {\gamma }_{min},\forall j\in \{1,\dots ,K\}$$

(10)

where ${\gamma }_{min}$ denotes the minimum SINR threshold to guarantee acceptable service quality. In this study, ${\gamma }_{min}$ is set as a design parameter based on typical quality of service requirements in downlink communication. This formulation establishes the power allocation problem as a constrained optimization task. In the next section, a learning-based solution using a CNN is presented to approximate this solution in a data-driven and scalable manner.

3. Proposed CNN-Based Power Allocation Method

This study proposes a CNN-based power allocation framework that jointly optimizes both CPU-to-AP and AP-to-UE power distribution in cell-free massive MIMO networks. Unlike conventional methods that allocate power in two disjoint stages, the proposed model performs end-to-end learning to dynamically assign power based on real-time network conditions and spatial context.

3.1. Motivation for Using CNN

Traditional power allocation schemes such as equal power allocation and max–min power allocation either lack adaptability or sacrifice efficiency. Heuristic methods do not account for spatial variations and channel diversity, while fairness-oriented strategies such as max–min improve service guarantees for weak users at the cost of degrading high-quality links. Moreover, many learning-based approaches focus only on AP-to-UE power allocation, treating CPU-to-AP power as fixed or uniform. This simplification neglects the reality that AP-UE link quality, distance, and interference vary significantly across the network. Consequently, uniform CPU-to-AP allocation can result in resource misalignment, as some APs may require more power to maintain reliable communication but be under-provisioned due to their static assignment.

To validate the design choice of using a CNN-only architecture, a CNN–LSTM variant was constructed by appending a recurrent layer to the convolutional feature extractor. Although the CNN–LSTM model has a smaller parameter count, it incurs significantly higher inference latency due to the sequential nature of LSTM operations [19].

Figure 2 presents a radar chart that compares the two models in terms of five normalized criteria, namely, inverse latency, inverse parameter count, real-time suitability, training stability, and architectural simplicity. To enable fair comparison, all scores are normalized to the range [0, 1]. The inference times for the CNN and CNN–LSTM models were measured as 9.68 ms and 18.29 ms, respectively, and the corresponding parameter counts were 34.7 million and 9.8 million. These values were normalized using inverse scaling, with each score computed as follows: $\mathrm{Score}\left(x\right)=min\left(x\right)/x$. The qualitative metrics were scored based on architectural depth, convergence behavior, and observed inference consistency. The CNN model demonstrates strong advantages in four out of five dimensions, particularly in inference latency and deployment efficiency, while the CNN–LSTM model benefits from a smaller parameter count.

Table 2. Comparison of parameter count and inference time.

Model	Parameter Count	Inference Time (ms)
CNN	34.7M	9.68
CNN–LSTM	9.8M	18.29

provides the corresponding numerical results.

These results indicate that the CNN model achieves a superior tradeoff between architectural simplicity and inference speed, making it more appropriate for real-time power allocation in per-snapshot cell-free massive MIMO systems.

CNNs are particularly well suited to wireless network applications due to their ability to extract local spatial correlations through shared weights and small receptive fields. In cell-free massive MIMO systems, where the spatial arrangement of APs and UEs directly impacts interference and link performance, CNNs can learn how geometry and environmental conditions affect power demand. This enables flexible and adaptive power allocation tailored to network topology. Building on these strengths, this study proposes a CNN model that simultaneously learns both stages of power allocation, i.e., CPU-to-AP and AP-to-UE, within a unified framework. By learning spatial relationships and channel patterns, the model determines power allocations based not only on instantaneous channel gain but also on the level of power that each UE requires to meet its SINR target under adverse conditions.

3.2. CNN Model Architecture and Feature Definition

The proposed CNN maps input network features to hierarchical power allocation outputs as follows:

$$[P_{\text{CPU-AP}},P_{\text{AP-UE}}]=f_{\theta }\left(\mathbf{X}\right)$$

(11)

where $\mathbf{X}\in {\mathbb{R}}^{C\times M\times K}$ is the input tensor, $\theta$ denotes the CNN parameters, $P_{\text{CPU-AP}}\in {\mathbb{R}}^M$ is the CPU-to-AP power vector, and $P_{\text{AP-UE}}\in {\mathbb{R}}^{M\times K}$ is the AP-to-UE power matrix. The input tensor $\mathbf{X}$ consists of $C=4$ feature channels, capturing spatial and contextual characteristics of the wireless environment. Each channel corresponds to a specific feature describing the AP–UE relationship, including the channel gain $|h_{i,j}{|}^2$, distance $d_{i,j}$, estimated interference at each link, and initial SINR estimated under uniform power allocation. These four feature maps are stacked into a three-dimensional tensor of size $4\times M\times K$, enabling the CNN to process spatially correlated patterns across all AP–UE pairs. By feeding this structured input to the network, the model is able to capture both local channel conditions and global interference characteristics, which are essential for making informed power allocation decisions.

The CNN architecture consists of three convolutional layers, each with 32 filters and a kernel size of $3\times 3$, followed by ReLU activation and batch normalization. This configuration was selected in order to balance computational efficiency and representation capacity. The $3\times 3$ kernel size enables the model to capture fine-grained spatial features while maintaining a low parameter count, and 32 filters provides a practical baseline that offers sufficient expressiveness without incurring excessive complexity [20,21]. Pooling layers are omitted to preserve the spatial resolution of the AP–UE grid, which is critical for fine-grained link-specific power control. The final convolutional output is flattened and passed through two separate fully-connected branches; one branch generates the CPU-to-AP power vector while the other produces the AP-to-UE power matrix, both of which are reshaped to match their target dimensions. This dual-head architecture allows the model to jointly learn global and local power control strategies within a single end-to-end framework. A detailed description of the CNN model architecture and training procedure is provided in Appendix A to support reproducibility (Figure 3).

For comparison, a separate CNN was also trained using a stage-wise configuration in which the CPU-to-AP power is fixed equally across all APs and only the AP-to-UE allocation is learned. While this approach permits partial adaptability, it fails to account for heterogeneous AP conditions and spatial variations in user demand. In contrast, the proposed integrated CNN learns both allocation layers jointly, enabling globally optimized and context-aware power assignment tailored to dynamic network environments.

3.3. CNN Training and Optimization Objective

To train the proposed CNN model, a supervised learning approach was adopted using data generated from traditional max–min power optimization. Specifically, the method introduced in [3] is followed, in which the downlink power control problem is solved under a max–min fairness criterion to maximize the minimum achievable SINR across all UEs under per-AP power constraints. This is achieved by iteratively transforming the problem into a sequence of second-order cone programs (SOCPs), which are globally optimal under convex feasibility. The resulting power allocation matrices provide fairness-centric ground truth for supervised training.

To simulate practical network environments, the dataset included diverse network realizations with user distributions clustered around high-traffic regions such as urban centers or event areas. Each training sample consisted of a spatial layout of APs and UEs, large-scale fading coefficients, and corresponding input features. These features are used to form the input tensor to the CNN, while the optimal power values from the max–min solution form the output supervision targets. The CNN model was trained on 10,000 samples generated under Rayleigh fading channels with a path loss exponent of $\alpha =3.76$. Each sample encodes spatial features such as clustered UE distributions, AP-UE distances, channel gain magnitudes, estimated interference levels, and initial SINR values. Training was conducted for 50 epochs using the Adam optimizer, with a batch size of 32 and a learning rate of ${10}^{-3}$. A validation split of 20% was considered to apply early stopping if necessary.

Figure 4 illustrates the training loss curve of the CNN model. The loss rapidly decreases within the first ten epochs and converges smoothly, remaining stable with minimal fluctuations throughout the remaining training process. This confirms that the model learns efficiently and is not prone to overfitting.

The CNN was trained to minimize the discrepancy between its predicted power allocations and the max–min references while ensuring compliance with power constraints. By learning from optimal yet computationally expensive power control solutions, the CNN generalizes to new scenarios with far lower inference complexity and supports end-to-end hierarchical power control beyond the original optimization formulation. The loss function combines two mean squared error (MSE) terms, corresponding to the CPU-to-AP and AP-to-UE power variables, along with a regularization term used to ensure that the sum of AP-to-UE power does not exceed each AP’s CPU-assigned power [11]:

$$\mathcal{L}\left(\theta \right)={\displaystyle \frac{1}{N}}\sum _{i=1}^N\left(\parallel P_{\text{CPU-AP},i}^{\mathrm{CNN}}-P_{\text{CPU-AP},i}^{\mathrm{opt}}{\parallel }_2^2+\hspace{0.17em}{\parallel P_{\text{AP-UE},i}^{\mathrm{CNN}}-P_{\text{AP-UE},i}^{\mathrm{opt}}\parallel }_F^2\right)+\lambda \sum _{i=1}^{M}max\left(0,\sum _{j=1}^K{\widehat{p}}_{i,j}-{\widehat{p}}_i\right)$$

(12)

where ${\parallel ·\parallel }_F$ is the Frobenius norm and $\lambda$ is a hyperparameter controlling the penalty for violating AP power constraints.

3.4. Context-Aware Power Inference via CNN

The proposed CNN enables spatially adaptive power inference by interpreting complex network features in real time. Instead of simply reinforcing strong links, the model learns to identify UEs that require greater power due to unfavorable conditions such as weak channels, far distances from APs, or high interference levels. This behavior emerges as a result of supervised training based on max–min optimized power allocations, which inherently prioritize fairness by allocating more power to disadvantaged users. During training, the CNN receives input tensors representing spatial and signal features and minimizes the discrepancy between its predicted allocations and the max–min references. Through this process, the model implicitly learns the relationship between environmental conditions and required power levels to meet fairness-driven SINR targets. After the AP-to-UE power matrix is determined, the required CPU-to-AP power is derived by aggregating the per-AP transmission demands. This hierarchical inference allows the network to flexibly and efficiently allocate power while respecting hardware limitations and service constraints. In this way, the proposed design ensures improved user-level performance and EE through globally optimized and context-aware decision making.

4. Simulation Setup

To evaluate the effectiveness of the proposed CNN-based power allocation method, we conducted simulations in a downlink cell-free massive MIMO network under realistic deployment conditions. UEs were densely clustered in localized high-traffic regions, creating spatial imbalance and heterogeneous interference. The goal of the simulation was to verify how well the proposed method handles per-user performance in terms of SE and EE while minimizing power wastage and improving fairness. To emulate realistic network dynamics, each simulation snapshot assumed fixed user positions within a coherence time, with UE locations randomly redrawn across samples based on clustered spatial distributions. This structure reflects pseudo-mobility and variable load conditions, as is commonly observed in urban deployments, while also preserving quasi-static channel assumptions at the per-snapshot level.

Performance was evaluated using per-user metrics and visualized through cumulative distribution functions (CDF). These plots highlight not only the average performance but also how power allocation affects users at different percentiles. The per-user average SE and EE serve as key performance indicators, as the proposed model aims to improve not only total system throughput but also user-level quality of service under nonuniform and interference-limited conditions [4]. These metrics provide more meaningful insights into spatially adaptive power allocation behavior across the entire network.

4.1. Simulation Parameters

The simulated network consists of multiple APs connected to a CPU, serving multiple UEs distributed across the coverage area. The simulation parameters are summarized in

Table 3. Simulation parameters.

Parameter	Value
Number of APs (M)	64
Number of UEs (K)	20
System Bandwidth (B)	10 KHz
Noise Power Density ($N_0$)	−174 dBm/Hz
Path Loss Model	${\beta }_{i,j}={\displaystyle \frac{1}{1+d_{i,j}^{\alpha }}}$, where $\alpha =3.76$
Channel Model	Rayleigh fading
UE Distribution	Clustered in high-density regions
AP Transmission Power ($P_{\mathrm{AP},max}$)	200 mW
CPU Transmission Power ($P_{\mathrm{CPU},max}$)	10 W
Minimum SINR Threshold (${\gamma }_{min}$)	0 dB
CNN Training Epochs	1000
CNN Learning Rate	$1\times {10}^{-3}$

[3,6,16].

The CNN model was trained using the Adam optimizer with a batch size of 64 and a learning rate of $1\times {10}^{-3}$. A validation set comprising 20% of the training data was used for early stopping, and training was continued for up to 1000 epochs. All training samples were generated under random user distributions with nonuniform clustering to enhance generalization.

4.2. Comparison Methods

The performance of the proposed CNN-based method was compared with three baseline schemes: equal power allocation (EPA) assigns uniform power from the CPU to all APs and from APs to UEs regardless of their spatial or channel conditions; max–min power allocation is a fairness-oriented approach that allocates power to maximize the minimum SINR among all users; finally, the third method, referred to as “CPU–AP Equal + AP–UE CNN”, applies equal power from the CPU to each AP while using a CNN to determine the AP-to-UE power distribution.

4.3. Evaluation Metrics

Per-user SE is defined as follows:

$${\mathrm{SE}}_j={log}_2(1+{\mathrm{SINR}}_j).$$

SE is measured in bits per second per Hertz (bps/Hz), based on the Shannon capacity formula; accordingly, the achievable data rate for user j is provided as follows:

$$R_j=B·{\mathrm{SE}}_j$$

where B is the system bandwidth. This metric quantifies how efficiently each user’s channel can carry information under the given SINR conditions.

EE is calculated for each user as follows:

$${\mathrm{EE}}_j={\displaystyle \frac{R_j}{P_{\mathrm{total},j}}}$$

where $P_{\mathrm{total},j}$ represents the total power consumed to serve user j, including both the CPU-to-AP and AP-to-UE power contributions [4]. This metric reflects how effectively power is used to support communication performance on a per-user basis. All metrics are evaluated at the per-user level and averaged across multiple randomized UE distributions to ensure statistically meaningful comparisons.

5. Performance Analysis

This section presents simulation results comparing the proposed CNN-based power allocation method with three baselines: EPA, max–min power allocation, and a stage-wise CNN approach in which the CPU-to-AP power is fixed equally and only the AP-to-UE power allocation is learned. Performance is evaluated in terms of per-user SE and EE and visualized using CDF plots. These CDFs illustrate both average performance and distribution across users, allowing for a detailed evaluation of fairness, adaptivity, and energy usage.

Figure 5 shows the CDF plot of the per-user SE. The CNN integrated method achieves the best overall performance, with a right-shifted curve compared to the other methods. A larger portion of users attain higher SE values, and the per-user average SE is also higher. However, the difference in SE between the two CNN-based methods is relatively small, as both effectively learn user-specific allocation patterns. The EPA method performs the worst, as it does not account for spatial or channel variability. The max–min method improves fairness but sacrifices overall throughput. The stage-wise CNN approach provides notable improvement over traditional baselines but is limited by its fixed CPU-to-AP allocation, which restricts full spatial optimization.

Figure 6 illustrates the CDF plot of the per-user EE. While SE and EE often trade off against each other, the CNN integrated model shows strong performance on both fronts. It achieves the most right-shifted EE curve, demonstrating that users can maintain high data rates with reduced power consumption. This is because the model learns to avoid unnecessary transmission by APs with poor link conditions, and allocates more power only where it is most effective. The stage-wise CNN model achieves similar SE but lower EE, as it cannot control how much total power is delivered to each AP. Even when some APs are underutilized, they still consume fixed power, reducing the overall EE. In contrast, the integrated model dynamically adjusts both AP-to-UE and CPU-to-AP allocations, enabling global energy savings without sacrificing throughput. EPA has the worst EE performance due to its indiscriminate power usage. Max–min guarantees minimum service levels, but is not energy-aware and often allocates excessive power to weak links.

Table 4. Per-user average and standard deviation of SE and EE.

Method	Avg SE (bps/Hz)	Std SE	Avg EE (bits/J)	Std EE
Equal Power	2.93	0.67	0.042	0.009
Max-Min	3.58	0.54	0.050	0.007
Stage-wise CNN	4.06	0.49	0.061	0.005
Proposed CNN	4.28	0.46	0.075	0.004

summarizes the per-user average and standard deviation for SE and EE across all methods. The proposed CNN model outperforms all baselines in terms of average SE and EE while also achieving the lowest standard deviation, indicating improved fairness and consistency across users.

These results clearly demonstrate that although both CNN-based methods perform similarly in terms of SE, the CNN integrated model offers a clear advantage in terms of EE. By jointly learning both levels of power allocation, it avoids wasteful power assignments and adapts better to user and channel conditions across the network. The ability to optimize energy usage without degrading throughput confirms the effectiveness of the integrated approach, particularly in scenarios where EE is critical.

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.