Degrees of freedom of the MIMO K-way relay channel with fractional signal space alignment

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.