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. PAPC is further validated through ablation studies and evaluated across several representative CFmMIMO scenarios, demonstrating robustness to pilot contamination, scalability, and adaptability to varying user counts without retraining.

This paper studies the impact of additional pilot overhead for covariance matrix estimation in a time-division duplexed (TDD) massive multiple-input multiple-output (MIMO) system. We choose average uplink (UL) and downlink (DL) spectral efficiencies (SEs) as performance metrics for the massive MIMO system, and derive closed form expressions for them in terms of the additional pilot overhead. The expressions are derived by considering linear minimum mean squared error (LMMSE)-type and element-wise LMMSE-type channel estimates that represent LMMSE and element-wise LMMSE with estimated covariance matrices, respectively. Using these expressions, a detailed theoretical analysis of SE behavior as a function of pilot overhead for both LMMSE-type and element-wise LMMSE-type channel estimation are presented, followed by simulations, which also demonstrate and validate theoretical results.

An analytical lower bound on uplink channel capacity of a user in a massive multiple-input multiple-output system where the channel vector and the covariance matrices of the users in that cell are unknown is derived in this paper. This analytical bound enables us to choose appropriate sample size for covariance matrix estimation to meet the spectral efficiency requirements. The accurate agreement between the derived bound and the simulated bound based on random samples of channel vectors and covariance matrices is shown.