  In this paper, using the stochastic geometry theory, we present a framework
for analyzing the performance of device-to-device (D2D) communications
underlaid uplink (UL) cellular networks. In our analysis, we consider a D2D
mode selection criterion based on an energy threshold for each user equipment
(UE). Specifically, a UE will operate in a cellular mode, if its received
signal strength from the strongest base station (BS) is large than a threshold
\beta. Otherwise, it will operate in a D2D mode. Furthermore, we consider a
generalized log-normal shadowing in our analysis. The coverage probability and
the area spectral efficiency (ASE) are derived for both the cellular network
and the D2D one. Through our theoretical and numerical analyses, we quantify
the performance gains brought by D2D communications and provide guidelines of
selecting the parameters for network operations.
