In this paper, we study the degrees of freedom (DoF) of the frequency-selective K-user interference channel in the presence of an instantaneous relay (IR) with multiple receive and transmit antennas. We investigate two scenarios based on the IR antennas' cooperation ability. First, we assume that the IR receive and transmit antennas can coordinate with each other, where the transmitted signal of each transmit antenna can depend on the received signals of all receive antennas, and we derive an achievable DoF for this model. In our interference alignment scheme, we divide receivers into two groups, called clean and dirty receivers. We design our scheme such that a part of the message of clean receivers can be demultiplexed at the IR. Thus, the IR can use these message streams for interference cancelation at the clean receivers. Next, we consider an IR, whose antennas do not have coordination with each other, where the transmitted signal of each transmit antenna only depends on the received signal of its corresponding receive antenna, and we derive an achievable DoF for it. We show that the achievable DoF decreases considerably compared with the coordinated case. In both of these models, our schemes achieve the maximum K DoFs, if the number of transmit and receive antennas is more than a finite threshold.

翻译：在本文中,我们研究了在瞬时中继器(IR)存在多接收和传输天线的情况下,选择频率的K用户干扰通道的自由度。我们根据IR天线的合作能力,对两种情景进行调查。首先,我们假设IR接收和传输天线可以相互协调,每个传输天线的传输信号取决于所有接收天线的接收信号,我们为这一模型获得一个可实现的DoF。在我们的干扰调整方案中,我们将接收器分为两个组,称为清洁和脏的接收器。我们设计了我们的计划,使清洁接收器的部分信息可以在IR上解开。因此,IR可以使用这些信息流在清洁接收器上取消干扰。接下来,我们考虑一个IR,每个传输天线的传输信号可以取决于所有接收天线的接收信号,我们为该天线找到一个可实现的DF。我们发现,与经过协调的案件相比,可实现的DOF数量大大下降。在这两种模型中,如果接收的天线达到极限,那么“DOF”是最大的标准。