Degrees of Freedom of MIMO Multiway Relay Channel With Clustered Pairwise Exchange

In this paper, we consider a symmetric multiple-input-multiple-output (MIMO) multiway relay channel (mRC) with L clusters and K users per cluster operating in clustered pairwise data exchange. Each user is equipped with M antennas, and the relay is equipped with N antennas. The degrees of freedom (DoF) of the MIMO mRC has recently attracted much research interest. The DoF results under certain configurations of (L,K,M,N) have been reported. However, the DoF capacity of the MIMO mRC with an arbitrary network configuration is, in general, far from being well understood. In this regard, the main contribution of this paper is to propose a systematic signal alignment approach to jointly design the beamforming matrices at the users and the relay. Based on that, an achievable DoF is derived for the MIMO mRC with an arbitrary network configuration of (L,K,M,N). Our analysis revealed that the derived achievable DoF is piecewise linear in M and N alternately. Moreover, we showed that the DoF capacity can be achieved for M/N ∈ [1/LK(K-1) + 1/2, ∞) and M/N ∈ (0, Lq/LK(Lq-1)], where q = 2 ⌈K/2⌉.We further derived the asymptotic DoF as K or L → ∞. The DoF analysis in this paper can provide insights on the practical design of efficient communication mechanisms over multiterminal MIMO relay networks.