Outage and Local Throughput and Capacity of Random Wireless Networks

TL;DR

This paper introduces the uncertainty cube framework and the spatial contention parameter to systematically analyze outage probabilities and throughput in diverse wireless networks, enabling better comparison across different network geometries and randomness levels.

Contribution

It proposes a novel systematic approach using the uncertainty cube and spatial contention to unify and extend performance analysis of wireless networks.

Findings

Spatial contention characterizes outage and throughput across network classes.

The framework unifies existing results and derives new performance bounds.

Ergodic capacity is compared with fixed-rate throughput in the analysis.

Abstract

Outage probabilities and single-hop throughput are two important performance metrics that have been evaluated for certain specific types of wireless networks. However, there is a lack of comprehensive results for larger classes of networks, and there is no systematic approach that permits the convenient comparison of the performance of networks with different geometries and levels of randomness. The uncertainty cube is introduced to categorize the uncertainty present in a network. The three axes of the cube represent the three main potential sources of uncertainty in interference-limited networks: the node distribution, the channel gains (fading), and the channel access (set of transmitting nodes). For the performance analysis, a new parameter, the so-called {\em spatial contention}, is defined. It measures the slope of the outage probability in an ALOHA network as a function of the transmit probability $p$ at $p=0$. Outage is defined as the event that the signal-to-interference ratio (SIR) is below a certain threshold in a given time slot. It is shown that the spatial contention is sufficient to characterize outage and throughput in large classes of wireless networks, corresponding to different positions on the uncertainty cube. Existing results are placed in this framework, and new ones are derived. Further, interpreting the outage probability as the SIR distribution, the ergodic capacity of unit-distance links is determined and compared to the throughput achievable for fixed (yet optimized) transmission rates.