Degrees of Freedom of Signal Alignment for Generalized MIMO Y Channel with General Signal Demands

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 (i ≠ j∈{1,2,···, K}) exchange n_ij signals, each node has to transmit m_k(m_k =Σ_{i ≠ k}^k n_ki, m_k≤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 Σ_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 ≥ 1/2(Σ_k=1^K m_k) and (M_i+M_j) ≥ (N+n_ij).