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 {Σ
_i=1
⁴
M
_i
, 2 Σ
_i=2
⁴
M
_i
, 2N, 2/7 Σ
_∀i,∀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.