  Cell-free (CF) massive multiple-input-multiple-output (MIMO) has emerged as
an alternative deployment for conventional cellular massive MIMO networks.
Prior works relied on the strong assumption (quite idealized) that the APs are
uniformly distributed, and actually, this randomness was considered during the
simulation and not in the analysis. However, in practice, ongoing and future
networks become denser and increasingly irregular. Having this in mind, we
consider that the AP locations are modeled by means of a Poisson point process
(PPP) which is a more realistic model for the spatial randomness than a grid or
uniform deployment. In particular, by virtue of stochastic geometry tools, we
derive both the downlink coverage probability and achievable rate. Notably,
this is the only work providing the coverage probability and shedding light on
this aspect of CF massive MIMO systems. Focusing on the extraction of
interesting insights, we consider small-cells (SCs) as a benchmark for
comparison. Among the findings, CF massive MIMO systems achieve both higher
coverage and rate with comparison to SCs due to the properties of favorable
propagation, channel hardening, and interference suppression. Especially, we
showed for both architectures that increasing the AP density results in a
higher coverage which saturates after a certain value and increasing the number
of users decreases the achievable rate but CF massive MIMO systems take
advantage of the aforementioned properties, and thus, outperform SCs. In
general, the performance gap between CF massive MIMO systems and SCs is
enhanced by increasing the AP density. Another interesting observation concerns
that a higher path-loss exponent decreases the rate while the users closer to
the APs affect more the performance in terms of the rate.
