Pilot Contamination Aware Transformer for Downlink Power Control in Cell-Free Massive MIMO Networks

TL;DR

The paper tackles pilot contamination in CFmMIMO downlink power control by introducing the PAPC transformer, which fuses the large-scale fading matrix $ extbf{B}$ with pilot allocation $oldsymbol{ ilde{oldsymbol{oldsymbol{ ilde{oldsymbol{ ilde}}}}}$ through an attention-based masking mechanism. Trained in an unsupervised fashion to maximize a smoothed-minimum spectral efficiency utility, PAPC preserves the structure of $ extbf{B}$, handles varying user counts via padding, and outputs feasible power control coefficients $ extbf{M}$ under per-BS constraints. Empirical results show PAPC achieving performance close to the accelerated proximal gradient (APG) algorithm while offering substantial computational efficiency gains (up to ~1000x faster), and robustly handling pilot contamination across large-scale networks up to $M=100$ APs and $K=80$ users. The work thus provides a scalable, pilot-contamination-aware solution for CFmMIMO downlink control with strong practical implications for real-time network optimization and future large deployments.

Abstract

Learning-based downlink power control in cell-free massive multiple-input multiple-output (CFmMIMO) systems offers a promising alternative to conventional iterative optimization algorithms, which are computationally intensive due to online iterative steps. Existing learning-based methods, however, often fail to exploit the intrinsic structure of channel data and neglect pilot allocation information, leading to suboptimal performance, especially in large-scale networks with many users. This paper introduces the pilot contamination-aware power control (PAPC) transformer neural network, a novel approach that integrates pilot allocation data into the network, effectively handling pilot contamination scenarios. PAPC employs the attention mechanism with a custom masking technique to utilize structural information and pilot data. The architecture includes tailored preprocessing and post-processing stages for efficient feature extraction and adherence to power constraints. Trained in an unsupervised learning framework, PAPC is evaluated against the accelerated proximal gradient (APG) algorithm, showing comparable spectral efficiency fairness performance while significantly improving computational efficiency. Simulations demonstrate PAPC's superior performance over fully connected networks (FCNs) that lack pilot information, its scalability to large-scale CFmMIMO networks, and its computational efficiency improvement over APG. Additionally, by employing padding techniques, PAPC adapts to the dynamically varying number of users without retraining.

Figures (11)

• Figure 1: Illustration of the CFmMIMO system with $M$ distributed BSs, each equipped with $N$ antennas, serving $K$ single-antenna users under the coordination of a CP. The channel between BS $m$ and user $k$ is denoted by $\mathbf{g}_{mk}$.
• Figure 2: Diagram of the unsupervised learning framework for downlink power control in CFmMIMO. The DNN, $F_D(\cdot, \cdot; W)$, takes the large-scale fading coefficient matrix $\mathbf{B}$ and the pilot allocation information $\boldsymbol{\Phi}$ as inputs to generate the power control coefficients. The DNN is trained to generate these coefficients to minimize the average of the utility function, $u(\cdot; \boldsymbol{\Phi}, \mathbf{B})$.
• Figure 3: Preprocessing stage of the CFmMIMO power control model. The input matrix $\mathbf{B}$ is transposed, log-transformed, and mapped to a higher-dimensional representation $\mathbf{Z}^{(0)}$ for use in subsequent transformer blocks.
• Figure 4: MMHA architecture in the PAPC transformer, processing the input through multiple attention heads combined with masking feature to model inter-user relationships and handle pilot contamination.
• Figure 5: The PAPC transformer block processes the input using an MMHA and a feed-forward network, with residual connections and layer normalizations.