On the Degree of Freedom for Multi-Source Multi-Destination Wireless Network with Multi-layer Relays

TL;DR

This paper analyzes the degrees of freedom and sum DoF in multi-hop layered relay wireless networks with arbitrary nodes, revealing capacity limitations due to network structure and proposing a simplified, CSIT-based achievable scheme.

Contribution

It provides a comprehensive DoF analysis for multi-hop relay networks with arbitrary configurations, highlighting capacity limitations and introducing a simplified transmission scheme.

Findings

Capacity of multi-hop networks is strictly less than single-hop networks.

Linear DoF scaling law holds when the number of hops is fixed.

Achievable scheme avoids routing and simplifies scheduling with CSIT.

Abstract

Degree of freedom (DoF) region provides an approximation of capacity region in high signal-to-noise ratio (SNR) regime, while sum DoF gives the scaling factor. In this correspondence, we analyse the DoF region and sum DoF for unicast layered multi-hop relay wireless networks with arbitrary number of source/destination/relay nodes, arbitrary number of hops and arbitrary number of antennas at each node. The result is valid for quite a few message topologies. We reveal the limitation on capacity of multi-hop network due to the concatenation structure and show the similarity with capacitor network. From the analysis on bound gap and optimality condition, the ultimate capacity of multi-hop network is shown to be strictly inferior to that of single-hop network. Linear scaling law can be established when the number of hops is fixed. At cost of channel state information at transmitters (CSIT) for each component single-hop network, our achievable scheme avoids routing and simplifies scheduling.