Capacity of Multiple Unicast in Wireless Networks: A Polymatroidal Approach

TL;DR

This paper demonstrates that in wireless networks, a simple layered approach combining local physical schemes with global routing can achieve near-optimal performance, extending classical wireline results to the wireless context.

Contribution

It introduces a polymatroidal network model for wireless networks and proves a max-flow min-cut approximation, highlighting the effectiveness of layered architectures with physical-layer schemes.

Findings

Layered architectures can be near-optimal with proper local scheme design.

Reciprocity of wireless channels is critical for the main result.

Feedback enables separation of physical and network layers.

Abstract

A classical result in undirected wireline networks is the near optimality of routing (flow) for multiple-unicast traffic (multiple sources communicating independent messages to multiple destinations): the min cut upper bound is within a logarithmic factor of the number of sources of the max flow. In this paper we "extend" the wireline result to the wireless context. Our main result is the approximate optimality of a simple layering principle: {\em local physical-layer schemes combined with global routing}. We use the {\em reciprocity} of the wireless channel critically in this result. Our formal result is in the context of channel models for which "good" local schemes, that achieve the cut-set bound, exist (such as Gaussian MAC and broadcast channels, broadcast erasure networks, fast fading Gaussian networks). Layered architectures, common in the engineering-design of wireless networks, can have near-optimal performance if the {\em locality} over which physical-layer schemes should operate is carefully designed. Feedback is shown to play a critical role in enabling the separation between the physical and the network layers. The key technical idea is the modeling of a wireless network by an undirected "polymatroidal" network, for which we establish a max-flow min-cut approximation theorem.