Abstract
Ultra-Reliable and Low-Latency Communications (URLLC) is essential for sixth generation communications, with Cell-Free massive Multiple-input-Multiple-Output (CF mMIMO) being a promising architecture to support these demands. This paper addresses the challenge of optimizing energy efficiency in CF mMIMO systems for URLLC, focusing on the probabilistic delay bounds and finite blocklength communications. We propose a theoretical framework that considers tail distributions to evaluate extreme reliability and latency requirements, instead of relying on asymptotic analysis. In particular, a closed-form expression for the signal-to-interference-plus-noise ratio (SINR) distribution is derived, accommodating imperfections in channel state information caused by pilot contamination. Then, the paper also presents a comprehensive reliability analysis, incorporating both delay violation probability and average decoding error probability, utilizing stochastic network calculus for accurate statistical modeling. Finally, an innovative power control algorithm is proposed to maximize effective energy efficiency (EEE), the ratio of the effective data rate to total power consumption, while meeting stringent Quality-of-Service (QoS) constraints and power limits. Extensive simulations validate the theoretical framework and the efficacy of the proposed algorithm, demonstrating its ability to enhance EEE in various scenarios and providing insights into the interplay between EEE, delay, and reliability metrics.