High-SIR Transmission Capacity of Wireless Networks with General Fading and Node Distribution

TL;DR

This paper analyzes the success probability and transmission capacity of wireless networks with general fading and node distributions, especially in the low-interference regime, providing new theoretical insights beyond Poisson models.

Contribution

It introduces an asymptotic analysis framework for success probability in networks with general node distributions and fading, extending beyond traditional Poisson assumptions.

Findings

Success probability scales as 1 - gamma * eta^kappa for small eta.

Bounds on the exponent kappa depend on path loss and fading.

Framework characterizes transmission capacity under general conditions.

Abstract

In many wireless systems, interference is the main performance-limiting factor, and is primarily dictated by the locations of concurrent transmitters. In many earlier works, the locations of the transmitters is often modeled as a Poisson point process for analytical tractability. While analytically convenient, the PPP only accurately models networks whose nodes are placed independently and use ALOHA as the channel access protocol, which preserves the independence. Correlations between transmitter locations in non-Poisson networks, which model intelligent access protocols, makes the outage analysis extremely difficult. In this paper, we take an alternative approach and focus on an asymptotic regime where the density of interferers $\eta$ goes to 0. We prove for general node distributions and fading statistics that the success probability $\p \sim 1-\gamma \eta^{\kappa}$ for $\eta \rightarrow 0$, and provide values of $\gamma$ and $\kappa$ for a number of important special cases. We show that $\kappa$ is lower bounded by 1 and upper bounded by a value that depends on the path loss exponent and the fading. This new analytical framework is then used to characterize the transmission capacity of a very general class of networks, defined as the maximum spatial density of active links given an outage constraint.