Degrees of Freedom for the MIMO Multi-way Relay Channel

TL;DR

This paper derives and verifies the maximum degrees of freedom for the MIMO multi-way relay channel, demonstrating optimality of certain communication strategies and generalizing results across various configurations.

Contribution

It introduces a novel DoF upper bound for the MIMO multi-way relay channel and shows how to achieve it using signal space alignment and multiple-access transmission.

Findings

Derived a new DoF upper bound using genie information.

Achieved the DoF bound with signal space alignment or multiple-access methods.

Generalized results to multiple clusters and users, confirming the bound's tightness.

Abstract

This paper investigates the degrees of freedom (DoF) of the L-cluster, K-user MIMO multi-way relay channel, where users in each cluster wish to exchange messages within the cluster, and they can only communicate through the relay. A novel DoF upper bound is derived by providing users with carefully designed genie information. Achievable DoF is identified using signal space alignment and multiple-access transmission. For the two-cluster MIMO multi-way relay channel with two users in each cluster, DoF is established for the general case when users and the relay have arbitrary number of antennas, and it is shown that the DoF upper bound can be achieved using signal space alignment or multiple-access transmission, or a combination of both. The result is then generalized to the three user case. For the L-cluster K-user MIMO multi-way relay channel in the symmetric setting, conditions under which the DoF upper bound can be achieved are established. In addition to being shown to be tight in a variety of scenarios of interests of the multi-way relay channel, the newly derived upperbound also establishes the optimality of several previously established achievable DoF results for multiuser relay channels that are special cases of the multi-way relay channel.