  In this paper, distributed user scheduling schemes are proposed for the
multi-user MIMO-Y channel, where three $N_{T}$-antenna users ($N_{T}=2N,\,3N$)
are selected from three clusters to exchange information via an $N_{R}$-antenna
amplify-and-forward (AF) relay ($N_{R}=3N$), and $N\geq1$ represents the number
of data stream(s) of each unicast transmission within the MIMO-Y channel. The
proposed schemes effectively harvest multi-user diversity (MuD) without the
need of global channel state information (CSI) or centralized computations. In
particular, a novel reference signal space (RSS) is proposed to enable the
distributed scheduling for both cluster-wise (CS) and group-wise (GS) patterns.
The minimum user-antenna (Min-UA) transmission with $N_{T}=2N$ is first
considered. Next, we consider an equal number of relay and user antenna (ER-UA)
transmission with ${N_{T}=3N}$, with the aim of reducing CSI overhead as
compared to Min-UA. For ER-UA transmission, the achievable MuD orders of the
proposed distributed scheduling schemes are analytically derived, which proves
the superiority and optimality of the proposed RSS-based distributed
scheduling. These results reveal some fundamental behaviors of MuD and the
performance-complexity tradeoff of user scheduling schemes in the MIMO-Y
channel.
