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.

翻译：主动可重构智能表面（RIS）已被证明能够增强每对收发端天线数相等的两用户多输入多输出（MIMO）干扰信道（IC）的总和自由度（DoF）。然而，对于任意数量的收发天线，主动RIS何时以及如何提升总和DoF仍不明确。本文研究了任意天线配置下主动RIS辅助两用户MIMO IC的总和DoF。特别地，我们将RIS波束成形、发射迫零和干扰解码相结合以对抗干扰问题。为最大化可实现的总和DoF，我们建立了一个整数优化问题，通过RIS波束成形优化消除干扰链路的数量。由此导出的可实现总和DoF能够高于两用户MIMO IC的基准总和DoF，从而产生RIS增益。此外，我们给出了RIS增益的充分条件，即RIS单元数量与天线配置之间的关系表达式。