In this paper, the original Multiple Input Multiple Output (MIMO) Y channel is extended into a more generalized circumstance, called a generalized MIMO Y channel with general signal demands. The model consists of K(K≥2) nodes each equipped with $M_k$ antennas and an intermediate relay equipped with $N$ antennas. There is no direct link between the nodes. Therefore, supposing that node $i$ and node $j$ $(ineq jin{1,2,cdots,K})$ exchange $n_{ij}$ signals, each node has to transmit $m_k(m_k=sum_{ineq k}^Kn_{ki},m_kleq M_k)$ signals for other nodes in the MAC phase, and then receive $m_k$ signals in the BC phase, via the relay. Then, it's proved that $sum_{k=1}^{K} m_k$ degrees of freedom (DoF) can be achieved by making use of signal space alignment (SSA) and interference nulling beamforming in this model, when $N geq 1/2(sum_{k=1}^{K} m_k)$ and $(M_i+M_j) geq (N+n_{ij})$.
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