The Spatial Outage Capacity of Wireless Networks

TL;DR

This paper introduces the concept of spatial outage capacity (SOC) in wireless networks, providing analytical bounds and a closed-form expression, revealing that maximum active link density occurs when all transmitters are always active.

Contribution

It defines and analyzes the SOC for Poisson bipolar networks, deriving bounds and a closed-form expression, and shows that full activity maximizes SOC in high-reliability regimes.

Findings

Exact and approximate expressions for link density under outage constraints.

SOC is maximized when all transmitters are active.

In high-reliability regimes, the optimal transmit probability is 1.

Abstract

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.