  How to manage the interference introduced by the enormous wireless devices is
a crucial issue to address in the prospective sixth-generation (6G)
communications. The treating interference as noise (TIN) optimality conditions
are commonly used for interference management and thus attract significant
interest in existing wireless systems. Cell-free massive multiple-input
multiple-output (CF mMIMO) is a promising technology in 6G that exhibits high
system throughput and excellent interference management by exploiting a large
number of access points (APs) to serve the users collaboratively. In this
paper, we take the first step on studying TIN in CF mMIMO systems from a
stochastic geometry perspective by investigating the probability that the TIN
conditions hold with spatially distributed network nodes. We propose a novel
analytical framework for TIN in a CF mMIMO system with both Binomial Point
Process (BPP) and Poisson Point Process (PPP) approximations. We derive the
probability that the TIN conditions hold in close form using the PPP
approximation. Numerical results validate our derived expressions and
illustrate the impact of various system parameters on the probability that the
TIN conditions hold.
