Degrees of Freedom of the MIMO Y Channel: Signal Space Alignment for Network Coding

In this paper, we study a network information flow problem for a multiple-input-multiple-output (MIMO) Gaussian wireless network with three users each equipped with M antennas and a single intermediate relay equipped with N antennas. In this network, each user intends to convey independent messages for two different users via the intermediate relay while receiving two independent messages from the other two users. This is a generalized version of the two-way relay channel for the three-user case. We will call it a "MIMO Y channel." For this MIMO Y channel, we show that the capacity is 3M log(SNR) + o(log(SNR)) if N >= [3M/2] by using two novel signaling techniques, which are signal space alignment for network coding, and network-coding-aware interference nulling beamforming.