The degrees of freedom of the K-pair-user full-duplex two-way interference channel with a MIMO relay

In a K-pair-user two-way interference channel (TWIC), 2K messages and 2K transmitters/receivers form a K-user IC in the forward direction (K messages) and another K-user IC in the backward direction which operate in full-duplex. All nodes may interact, or adapt inputs to past received signals. The optimal degrees of freedom (DoF, also known as the multiplexing gain) is known to be K [1]: full-duplex operation doubles the DoF, but interaction does not further increase the DoF. In this paper, we characterize the DoF of the K-pair-user TWIC with a MIMO, full-duplex relay. If the relay is noncausal/ instantaneous (at time k forwards a function of its received signals up to time k) and has 2K antennas, we demonstrate a one-shot scheme where the relay mitigates all interference to achieve the interference-free 2K DoF. In contrast, if the relay is causal (at time k forwards a function of its received signals up to time k - 1), we show that a full-duplex MIMO relay cannot increase the DoF of the K-pair-user TWIC beyond K, as if no relay or interaction is present.