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）已被证明能在发射端和接收端天线数量相等的两用户多输入多输出（MIMO）干扰信道（IC）中提升总和自由度（DoF）。然而，对于任意数量的接收和发射天线，主动RIS在何时以及如何提升总和自由度仍不明确。本文研究任意天线配置下主动RIS辅助的两用户MIMO IC的总和自由度。具体而言，RIS波束成形、发射端迫零与干扰解码被联合用于解决干扰问题。为最大化可达总和自由度，本文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。结果表明，所得可达总和自由度可高于两用户MIMO IC的总和自由度，从而产生RIS增益。进一步地，本文给出了RIS增益的充分条件，即RIS单元数量与天线配置之间的关系。