Average Achievable Rate Analysis of Cell-Free Massive MIMO in the Finite Blocklength Regime with Imperfect CSI

Acquiring perfect channel state information (CSI) introduces substantial challenges in cell-free massive MIMO (CF-mMIMO) systems, primarily due to the large dimensionality of channel parameters, especially under ultra-reliable low-latency communication (uRLLC) constraints. Furthermore, the impact of imperfect CSI on the average achievable rate within the finite blocklength regime remains largely unexplored. Motivated by this gap, this paper proposes a novel analytical framework that provides a closed-form expression for the average achievable rate with imperfect CSI in the Laplace domain. We demonstrate analytically that both the channel dispersion and the expected channel capacity can be expressed explicitly in terms of the Laplace transform of the large-scale fading component. Numerical simulations confirm that the derived expressions match closely with Monte Carlo simulations, verifying their accuracy. Furthermore, we theoretically show that although imperfect CSI degrades performance in the finite blocklength regime, the inherent characteristics of CF-mMIMO architecture effectively mitigates this loss.