On The Sum Dof Of The Asymmetric Four-User Mimo Y Channel

This work studies the sum degrees of freedom (DoF) of the asymmetric four-user MIMO Y channel, where each user i, for 1 <= i <= 4, is equipped with Mi antennas, and the relay is equipped with N antennas. By using the genie message approach, we derive that the sum DoF is upper bounded by min {Sigma(4)(i= 1) Mi(,) 2 Sigma(4)(i= 2) M-i, 2N, 2/7 Sigma(for all i for all j> i) max{N, M-i + M-j}, where M-1 >= M-2 >= M-3 >= M-4. Then, we show that the bound is tight under certain antenna constraints using signal alignment, generalized signal alignment, and antenna deactivation techniques.