  Previous studies of connectivity in wireless networks have focused on
undirected geometric graphs. More sophisticated models such as
Signal-to-Interference-and-Noise-Ratio (SINR) model, however, usually leads to
directed graphs. In this paper, we study percolation processes in wireless
networks modelled by directed SINR graphs. We first investigate
interference-free networks, where we define four types of phase transitions and
show that they take place at the same time. By coupling the directed SINR graph
with two other undirected SINR graphs, we further obtain analytical upper and
lower bounds on the critical density. Then, we show that with interference,
percolation in directed SINR graphs depends not only on the density but also on
the inverse system processing gain. We also provide bounds on the critical
value of the inverse system processing gain.
