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.
In this paper we consider a network where the nodes locations are modeled by a realization of a Poisson point process and remains fixed or changes very slowly over time. Most of the literature focuses on the spatial average of the link outage probabilities. But each link in the network has an associated link-outage probability that depends on the fading, path loss, and the relative locations of the interfering nodes. Since the node locations are random, the outage probability of each link is a random variable and in this paper we obtain its distribution, instead of just the spatial average. This work supplements the existing results which focus mainly on the average outage probability averaged over space. We propose a new notion of transmission capacity (TC) based on the outage distribution, and provide asymptotically tight bounds for the TC.