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：一种主动可重构智能面（RIS）已被证明可提高等同于每个发射机和接收机上的天线数量的两个用户多输入多输出（MIMO）干扰信道（IC）的自由度之和（DoF）。然而，对于任何接收和发送天线的数量，主动RIS何时以及如何帮助提高DoF仍不清楚。本文研究了具有任意天线配置的主动RIS辅助的两个用户MIMO IC的总DoF。特别地，集成了RIS波束成形、发送零强制和干扰解码以解决干扰问题。为了最大化可实现的总DoF，形成了一个整数优化问题，通过RIS波束成形最优化消除干扰链的数量。因此，得到的可实现总DoF可以高于两个用户MIMO IC的总DoF，从而导致RIS增益。此外，给出了RIS增益的一个充分条件，即RIS元素数量和天线配置之间的关系。
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