On DoF of Active RIS-Assisted MIMO Interference Channel with Arbitrary Antenna Configurations: when Will RIS Help?

An active reconfigurable intelligent surface (RIS) has been shown to be able to enhance the sum-of-degrees-of-freedom (DoF) of a two-user multiple-input multiple-output (MIMO) interference channel (IC) with equal number of antennas at each transmitter and receiver. However, for any number of receive and transmit antennas, when and how an active RIS can help to improve the sum-DoF are still unclear. This paper studies the sum-DoF of an active RIS-assisted two-user MIMO IC with arbitrary antenna configurations. In particular, RIS beamforming, transmit zero-forcing, and interference decoding are integrated together to combat the interference problem. In order to maximize the achievable sum-DoF, an integer optimization problem is formulated to optimize the number of eliminating interference links by RIS beamforming. As a result, the derived achievable sum-DoF can be higher than the sum-DoF of two-user MIMO IC, leading to a RIS gain. Furthermore, a sufficient condition of the RIS gain is given as the relationship between the number of RIS elements and the antenna configuration.