On the Broadcast Capacity of Large Wireless Networks at Low SNR

TL;DR

This paper introduces a novel broadcast scheme for large low-SNR wireless networks that achieves asymptotic capacity through successive beamforming, with a detailed analysis of the underlying mathematical properties.

Contribution

A new broadcast method utilizing successive beamforming is proposed, achieving asymptotic capacity in large low-SNR networks, supported by mathematical analysis of the network's singular value behavior.

Findings

Scheme achieves asymptotic broadcast capacity

Capacity expressed via largest singular value of fading matrix

Mathematical analysis of singular value behavior provided

Abstract

The present paper focuses on the problem of broadcasting information in the most efficient manner in a large two-dimensional ad hoc wireless network at low SNR and under line-of-sight propagation. A new communication scheme is proposed, where source nodes first broadcast their data to the entire network, despite the lack of sufficient available power. The signal's power is then reinforced via successive back-and-forth beamforming transmissions between different groups of nodes in the network, so that all nodes are able to decode the transmitted information at the end. This scheme is shown to achieve asymptotically the broadcast capacity of the network, which is expressed in terms of the largest singular value of the matrix of fading coefficients between the nodes in the network. A detailed mathematical analysis is then presented to evaluate the asymptotic behavior of this largest singular value.