MIMO multiway relaying with pairwise data exchange: A degrees of freedom perspective

Abstract—In this paper, we study achievable degrees of freedom (DoF) of a multiple-input multiple-output (MIMO) multiway relay channel (mRC) where users, each equipped with antennas, exchange messages in a pairwise manner via a common-antenna relay node. A novel and systematic way of joint beamforming design at the users and at the relay is proposed to align signals for efficient implementation of physical-layer network coding (PNC). It is shown that, when the user number, the proposed beamforming design can achieve the DoF capacity of the considered mRC for any setups. For the scenarios with, we show that the proposed signaling scheme can be improved by disabling a portion of relay antennas so as to align signals more efficiently. Our analysis reveals that the obtained achievable DoF is always piecewise linear, and is bounded either by the number of user antennas or by the number of relay antennas. Further, we show that the DoF capacity can be achieved for and, which provides a broader range of the DoF capacity than the existing results. Asymptotic DoF as is also derived based on the proposed signaling scheme. Index Terms—Multiple-input multiple-output (MIMO), mul-tiway relay channel (mRC), physical-layer network coding (PNC), signal space alignment. I