We consider the degrees of freedom (DoF) of the $\textrm {2}\times \textrm {2}\times \textrm {2}$ multiple-input multiple-output (MIMO) interference network with arbitrary antenna configuration and practical rank-deficiency. Different from existing researches on the $\textrm {2}\times \textrm {2}\times \textrm {2}$ MIMO interference model, the antenna number can be arbitrarily different at the transmitters, relays and receivers simultaneously, and the ranks of the channel matrices can be arbitrarily different. The exact DoF sum of this scenario is obtained. For different configurations of antennas and ranks, the outer bound is proved mainly by the min-cut outer bound and the achievability is presented with effective schemes, which combine zero-forcing (ZF) scheme, ZF over broadcast channel, interference alignment in X channel, and aligned interference neutralization (AIN) to match the outer bound. The traditional AIN scheme is modified in this paper to maximize the utilization of signal space overlap. Some related earlier works can be seen as special cases of our research.

中文翻译：

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秩亏 2 × 2 × 2 MIMO 干扰网络的自由度

我们考虑的自由度 (DoF) $\textrm {2}\times \textrm {2}\times \textrm {2}$ 具有任意天线配置和实际秩缺陷的多输入多输出 (MIMO) 干扰网络。与现有的研究不同 $\textrm {2}\times \textrm {2}\times \textrm {2}$ MIMO干扰模型，同时在发射端、中继端和接收端的天线数可以任意不同，信道矩阵的秩可以任意不同。获得此场景的确切 DoF 总和。对于不同的天线和秩配置，外界主要由最小割外界证明，并提出了有效方案的可实现性，其中结合了迫零（ZF）方案，广播信道上的ZF，X信道中的干扰对齐, 并对齐干扰中和 (AIN) 以匹配外边界。本文对传统的 AIN 方案进行了修改，以最大限度地利用信号空间重叠。一些相关的早期工作可以看作是我们研究的特例。