RF Mismatches and Nonlinear Distortions in Cell-Free Massive MIMO: Impact Analysis and Calibration Performance Analysis
Shu Xu, Jiexin Zhang, Ruming Yang, Chunguo Li, Lüxi Yang
Abstract
Cell-free massive multiple-input multiple-output (MIMO) is known for its potential to enhance overall system performance. Thanks to the principle of channel reciprocity, it becomes possible to implement downlink beamforming by exploiting the estimated uplink channel in time-division duplex (TDD) mode. However, the assumption of perfect hardware conditions, as made in prior studies, is not reflective of practical realities. The involvement of hardware impairments disrupts this reciprocity, resulting in performance degradation. This paper investigates the impact of hardware impairments in downlink data transmission, where a novel model is established by jointly considering the radio frequency (RF) mismatches and nonlinear distortions. We first derive closed-form achievable user rate expressions and prove that the impact of RF mismatches vanishes as the number of access points (APs) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M \to \infty $ </tex-math></inline-formula> in certain distributions of RF gains. Then, we study the scenarios when the number of user equipments (UEs) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K \to \infty $ </tex-math></inline-formula>, as well as various degrees of hardware impairments’ severity scaling M. Finally, we introduce a channel calibration process and theoretically derive its performance, observing that in certain scenarios, the need for calibration becomes redundant as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M \to \infty $ </tex-math></inline-formula>. These findings are further validated through numerical results, confirming the scaling laws derived in our study.