The multiple-input-multiple-output (MIMO) Gaussian wireless network with
K users and an intermediate relay is investigated. In this network, each user with available local channel state information (CSI) intends to convey a multicast message to all other users while receiving all messages from other users via the relay. This model is termed the MIMO
K-way relay channel with distributed CSI. For this channel, the sum capacity is shown as
MK/(
K-1)log(
SNR)+
o(
SNR) where each user and the relay is equipped with
M antennas. Achievability is based on the signal space alignment strategy with a
K-1 time slot extension. A most general case is then considered, in which each user intends to recover all messages required within
T time slots. We provide an improved scheme called fractional signal space alignment which achieves
MK/(
K-1) degrees of freedom in the general case and the feasibility condition is also explored.
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