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.