Achievable Degrees of Freedom Region of the MIMO Relay Networks using the Detour Schemes

TL;DR

This paper characterizes the achievable degrees of freedom region in MIMO relay networks, introducing new schemes like Signal Space Alignment and Detour Schemes to improve understanding of network capacity.

Contribution

It extends the analysis of DoF from total capacity to the entire DoF region in MIMO relay networks using novel alignment and detour schemes.

Findings

Achieves the outer bound on DoF region under certain antenna configurations.

Develops a new outer bound based on the one-sided genie concept.

Introduces the Signal Space Alignment and Detour Schemes for improved DoF characterization.

Abstract

In this paper, we study the degrees of freedom (DoF) of the MIMO relay networks. We start with a general Y channel, where each user has $M_i$ antennas and aims to exchange messages with the other two users via a relay equipped with $N$ antennas. Then, we extend our work to a general 4-user MIMO relay network. Unlike most previous work which focused on the total DoF of the network, our aim here is to characterize the achievable DoF region as well. We develop an outer bound on the DoF region based on the notion of one sided genie. Then, we define a new achievable region using the Signal Space Alignment (SSA) and the Detour Schemes. Our achievable scheme achieves the upper bound for certain conditions relating $M_i$'s and $N$.