Information Theoretic Cut-set Bounds on the Capacity of Poisson Wireless Networks

TL;DR

This paper develops a comprehensive information theoretic bound for Poisson wireless networks using stochastic geometry, identifying different operating regimes and extending existing scaling laws with new bounds.

Contribution

It introduces a unified multi-parameter cut-set bound applicable to arbitrary Poisson networks, extending previous results with detailed numerical examples.

Findings

Identifies four operating regimes based on SNR levels.

Confirms and extends known scaling laws in wireless networks.

Provides numerical bounds illustrating theoretical limits.

Abstract

This paper presents a stochastic geometry model for the investigation of fundamental information theoretic limitations in wireless networks. We derive a new unified multi-parameter cut-set bound on the capacity of networks of arbitrary Poisson node density, size, power and bandwidth, under fast fading in a rich scattering environment. In other words, we upper-bound the optimal performance in terms of total communication rate, under any scheme, that can be achieved between a subset of network nodes (defined by the cut) with all the remaining nodes. Additionally, we identify four different operating regimes, depending on the magnitude of the long-range and short-range signal to noise ratios. Thus, we confirm previously known scaling laws (e.g., in bandwidth and/or power limited wireless networks), and we extend them with specific bounds. Finally, we use our results to provide specific numerical examples.