MIMO Multiway Relaying With Clustered Full Data Exchange: Signal Space Alignment and Degrees of Freedom

Recently, much research interest has been focused on the design of efficient communication mechanisms for multiple-input-multiple-output (MIMO) multiway relay channels (mRCs). In this paper, we investigate achievable degrees of freedom (DoFs) of the MIMO mRC with L clusters and K users per cluster, where each user is equipped with M antennas and the relay with N antennas. Our analysis is focused on a new data exchange model, termed clustered full data exchange, i.e., each user in a cluster wants to learn the messages of all the other users in the same cluster. Novel signal alignment techniques are developed to jointly and systematically construct the beamforming matrices at the users and the relay for efficient implementation of physical-layer network coding. Based on this, we derive an achievable DoF of the MIMO mRC with an arbitrary network configuration of L and K, as well as with an arbitrary antenna configuration of M and N. We show that our proposed scheme achieves the DoF capacity when M/N ≤ 1/(LK - 1) and M/N ≥ ((K - 1)L + 1)/KL. The DoF results derived in this paper can serve as fundamental benchmarks in evaluating the performance of practical communication systems over MIMO mRCs and provide guidance and insights into the design of wireless relay networks.