Degrees of freedom for the MIMO multi-way relay channel

This paper investigates the degrees of freedom (DoF) of the L-cluster LT-user MIMO multi-way relay channel. A DoF upperbound is derived by providing users with carefully designed genie information, and properly enhancing the received signal of one of the users. For the L-cluster LT-user MIMO multi-way relay channel in the symmetric setting, conditions under which the DoF upperbound can be achieved using either multiple access transmission or signal space alignment are established, demonstrating that the newly derived upperbound is the first tight DoF upperbound for the general MIMO multi-way relay channel. Additionally, this new upperbound proves the optimality of the achievable DoF for several special cases of the MIMO multi-way relay channel obtained in previous works. The results provide the insight that, with fixed spatial dimension at the relay, increasing the number of users and clusters cannot provide any DoF gain. In addition, it is observed that allowing three or more users to share the spatial dimension of the relay cannot provide any DoF gain.