Diversity and Degrees of Freedom of Cooperative Wireless Networks

TL;DR

This paper develops max-flow min-cut theorems to compute diversity and degrees of freedom in multi-antenna wireless networks, demonstrating that simple protocols suffice to achieve optimal performance.

Contribution

It introduces a unified framework for calculating diversity and DOF in arbitrary wireless networks using max-flow min-cut theorems and deterministic network conversions.

Findings

Max-flow min-cut theorems for diversity and DOF

Amplify-and-forward protocols achieve optimality

DOF characterization extends to multi-source multi-sink networks

Abstract

Wireless fading networks with multiple antennas are typically studied information-theoretically from two different perspectives - the outage characterization and the ergodic capacity characterization. A key parameter in the outage characterization of a network is the diversity, whereas a first-order indicator for the ergodic capacity is the degrees of freedom (DOF), which is the pre-log coefficient in the capacity expression. In this paper, we present max-flow min-cut type theorems for computing both the diversity and the degrees of freedom of arbitrary single-source single-sink multi-antenna networks. We also show that an amplify-and-forward protocol is sufficient to achieve this. The degrees of freedom characterization is obtained using a conversion to a deterministic wireless network for which the capacity was recently found. We show that the diversity result easily extends to multi-source multi-sink networks and evaluate the DOF for multi-casting in single-source multi-sink networks.