Degrees of freedom of completely-connected multi-way interference networks

This paper considers a fully-connected interference network with a relay in which multiple users equipped with a single antenna want to exchange multiple unicast messages with other users in the network by sharing the relay equipped with multiple antennas. For such a network, the optimal degrees of freedom (DoF) are derived by providing both converse and achievability. Further, considering single-antenna relays in the three-user fully-connected interference network, it is shown that three distributed relays with a single antenna is sufficient to achieve the optimal DoF. A major implication of the derived DoF results is that a relay with multiple antennas or distributed relays employing a single antenna increases the capacity scaling law of the multi-user interference network when multiple directional information flows are considered, even if the networks are fully-connected and all nodes operate in half-duplex. These results verify the intuition that the relay is useful in increasing DoF for the multi-way the interference network.