On the DoF of two-user interference channel with an instantaneous relay

This paper studies the degrees of freedom (DoF) of the two-user multi-antenna Gaussian interference channel with an instantaneous relay, or relay without delay, where the relay transmitted signal in channel use t can depend on all received signals up to and including that at channel use t. It is assumed that the two transmitters and the two receivers have M antennas, while the relay receives through N antennas and transmits through L antennas. An achievable DoF is derived for all possible values of (M;N;L), based on a linear transmission strategy at the relay that aims to neutralize as much interference as possible at each destination. The proposed scheme is shown to attain the largest DoF among all linear transmission strategies at the relay and to actually be the optimal DoF for certain values of (M;N;L).