  We address a fundamental question in wireless networks that, surprisingly,
has not been studied before: what is the maximum density of concurrently active
links that satisfy a certain outage constraint? We call this quantity the
spatial outage capacity (SOC), give a rigorous definition, and analyze it for
Poisson bipolar networks with ALOHA. Specifically, we provide exact analytical
and approximate expressions for the density of links satisfying an outage
constraint and give simple upper and lower bounds on the SOC. In the
high-reliability regime where the target outage probability is close to zero,
we obtain an exact closed-form expression of the SOC, which reveals the
interesting and perhaps counter-intuitive result that all transmitters need to
be always active to achieve the SOC, i.e., the transmit probability needs to be
set to 1 to achieve the SOC.
