EMF-Compliant Power Control in Cell-Free Massive MIMO: Model-Based and Data-Driven Approaches

TL;DR

The paper addresses EMF exposure constraints in user-centric CF-mMIMO by formulating max-min QoS power-control problems for downlink and uplink under IPD/SAR limits. It develops model-based solutions: SCO for the DL with a log-sum-exp surrogate and convex optimization for the UL, and introduces data-driven alternatives including end-to-end DNNs and deep unfolding to reduce real-time complexity. Extensive simulations show that model-based methods reliably satisfy EMF constraints while delivering strong fairness, and that data-driven approaches closely approximate this performance with much lighter computation, especially the unfolded DL scheme. The work demonstrates the practicality of integrating EMF-awareness into CF-mMIMO design and highlights deep unfolding as a promising avenue for efficient, interpretable power-control in future 6G systems.

Abstract

The impressive growth of wireless data networks has recently led to increased attention to the issue of electromagnetic pollution and the fulfillment of electromagnetic field (EMF) exposure limits. This paper tackles the problem of power control in user-centric cell-free massive multiple-input-multiple-output (CF-mMIMO) systems under EMF constraints. Specifically, the power allocation maximizing the minimum data rate across users is derived for both the uplink and the downlink. To solve such optimization problems, two approaches are proposed, i.e., model-based and data-driven. The proposed model-based solutions for the downlink utilize successive convex optimization and the log-sum-exp approximation for the minimum of a discrete set, whereas ordinary techniques are employed for the uplink. With regard to data-driven solutions, solutions based on both end-to-end architectures and deep unfolding techniques are explored. Extensive numerical results confirm that the proposed model-based solutions effectively fulfill the EMF constraints while ensuring very good performance; moreover, the results show that the proposed data-driven approaches can tightly approximate the performance of model-based solutions but with much lower computational complexity.

Figures (14)

• Figure 1: CF-mMIMO deployment where $K = 18$ UEs are connected to $N = 2$ APs, out of a total of $M = 9$, each with $L = 3$ antennas.
• Figure 2: General end-to-end training scheme. The inputs $\mathcal{X}$ are directly mapped onto the outputs $\hat{\mathcal{Y}}$ based on the labels $\mathcal{Y}$.
• Figure 3: General deep unfolding scheme. The inputs $\mathcal{X}$ are mapped onto the outputs $\hat{\mathcal{Y}} \equiv \hat{\mathcal{Y}}^{(n)}$ via $n$ DNNs (each modeling an SCO iteration).
• Figure 4: Deep unfolding scheme without side information. The initial estimate $\hat{\mathcal{Y}}^{(0)}$ is sequentially updated until the final output $\hat{\mathcal{Y}}^{(n)}$.
• Figure 5: CDF of the DL user rate under CB processing with UPC, fair FPC, opportunistic (opp). FPC, OPC (maximin), and E2E-DNN.