Feasibility Conditions of Signal Space Alignment for Network Coding on K-User MIMO Y Channels

In this paper, we consider K-user MIMO Y channels where K users simultaneously exchange messages with each other via an intermediate relay. Degrees of freedom (DOF) of this channel are not known in general. The investigation of the feasibility conditions of signal space alignment for network coding is an initial step for addressing this open problem. We verify that when user i has Mⁱ antennas (i = 1, ⋯, K) and a relay has N antennas, the DOF of K(K - 1) is achieved if M_i ≥ K - 1, N ≥ (K(K-1)/2) and N <; min{M_i + M_j|∀ i ≠ j}. It is accomplished by adopting the signal space alignment for network coding during both multiple access channel and broadcasting channel phase. The achievability is shown by an amplify-and forward (AF) relaying strategy combined with the signal space alignment for the network coding scheme, which provides a lower bound of the capacity.