Achievable degrees of freedom of the four-user MIMO y channel

In this letter, we investigate the achievable degrees of freedom (DoF) of four-user MIMO Y channel where four users each with M antennas intend to exchange messages via a relay of N antennas. By adopting the signal space alignment and a new transmission scheme which jointly align the subspace of unpaired signals from three different users among all the four users, we derive that the DoF per user of max{min(M,\tfrac{{3}{8}N},min(\tfrac{6}{7}M,\tfrac{N} {2}}} can be achieved for this channel. Since signal space alignment relies on the dimensions of intersection space of two users, we show that the signal space is utilized efficiently without the restriction of two-user intersection space in the proposed scheme.