Degrees of freedom of MIMO Y channel with multiple relays

We study the degrees of freedom (DoF) of a symmetric multi-relay multiple-input multiple-output (MIMO) Y channel, where three users, each equipped with M antennas, exchange messages via multiple geographically separated relay nodes, each with N antennas. We formulate a general DoF achievability problem assuming the use of linear precoding and post-processing. To solve this problem, we present a new uplink-downlink asymmetric strategy where the user precoders are designed for signal alignment and the user post-processors are used for interference neutralization. Based on that, we derive an achievable DoF of the considered model for an arbitrary antenna setup. The optimality of the derived DoF is established under certain antenna configurations. Also, we show that our design considerably outperforms the conventional uplink-downlink symmetric design.