  Using stochastic geometry tools, we develop a comprehensive framework to
analyze the downlink coverage probability, ergodic capacity, and energy
efficiency (EE) of various types of users (e.g., users served by direct base
station (BS) transmissions and indirect intelligent reflecting surface
(IRS)-assisted transmissions) in a cellular network with multiple BSs and IRSs.
The proposed stochastic geometry framework can capture the impact of channel
fading, locations of BSs and IRSs, arbitrary phase-shifts and interference
experienced by a typical user supported by direct transmission and/or
IRS-assisted transmission. For IRS-assisted transmissions, we first model the
desired signal power from the nearest IRS as a sum of scaled generalized gamma
(GG) random variables whose parameters are functions of the IRS phase shifts.
Then, we derive the Laplace Transform (LT) of the received signal power in a
closed form. Also, we model the aggregate interference from multiple IRSs as
the sum of normal random variables. Then, we derive the LT of the aggregate
interference from all IRSs and BSs. The derived LT expressions are used to
calculate coverage probability, ergodic capacity, and EE for users served by
direct BS transmissions as well as users served by IRS-assisted transmissions.
Finally, we derive the overall network coverage probability, ergodic capacity,
and EE based on the fraction of direct and IRS-assisted users, which is defined
as a function of the deployment intensity of IRSs, as well as blockage
probability of direct transmission links. Numerical results validate the
derived analytical expressions and extract useful insights related to the
number of IRS elements, large-scale deployment of IRSs and BSs, and the impact
of IRS interference on direct transmissions.
