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This paper investigates the achievable total degrees of freedom (DoF) of the MIMO multi-way relay channel that consists of K users, where each user is equipped with M antennas, and a decode-and-forward relay equipped with N antennas. In this channel, each user wants to convey K - 1 private messages to the other users in addition to a common message to all of them. Due to the absence of direct links between the users, communication occurs through the relay in two phases: a multiple access channel (MAC) phase and a broadcast (BC) phase. We derive cut-set bounds on the total DoF of the network, and show that the network has DoF less than or equal to K min {N, M}. Achievability of the upper bound is shown by using signal space alignment for network coding in the MAC phase, and zero- forcing precoding in the BC phase. We show that introducing the common messages besides the private messages leads to achieving higher total DoF than using the private messages only.

Achievable degrees of freedom on K-user MIMO multi-way relay channel with common and private messages