  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.
