A new DoF upper bound and its achievability for K-user MIMO Y channels

This work is to study the degrees of freedom (DoF) of the K-user MIMO Y channel. Previously, two transmission frameworks, in addition to the original signal alignment introduced by Lee et al., have been proposed for the DoF analysis at different antenna configurations. One is signal group based alignment proposed by Hua et al. and the other is a signal pattern approach proposed by Wang et al. Yet, the maximum achievable ( DoF at antenna configuration N/E ∈ (2K
²
-2K/K
²
-K+2, K
²
-3K+k/K-1) still remains unknown, where M and N denote the number of antennas at each source node and the relay node, respectively. In this work, we first derive a new upper bound of the DoF using the genie-aided approach. Then, we propose a more general transmission framework, generalized signal alignment (GSA), to approach the new bound. With GSA, we prove that the new DoF upper bound is tight when N/M ∈ (0, 2 + 4/K(K-1)] ∪ [K - 2, + ∞).