基于拉丁矩形的MIMO双向中继无线网络编码
Wireless Network Coding for MIMO Two-way Relaying using Latin Rectangles
摘要：
考虑用于物理层网络编码双向MIMO中继场景的调制方案的设计，其中$n_R$天线在中继器R处，$n_A$和$n_B$天线分别在端节点A和B处。我们考虑的噪声和转发（DNF）协议，它采用两个阶段：多址（MA）阶段和广播（BC）阶段。对于网络编码的SISO双向中继已知的是，根据信道条件自适应地改变在中继处使用的联网编码映射（也被称为去噪映射）极大地降低了在MA阶段期间在中继处发生的多址干扰的影响，并且所有这些网络编码映射应当满足称为{ \it排他性定律}的要求。满足互斥律的网络编码图可等价地看作拉丁矩形。本文证明了对于MIMO双向中继，当信道衰落系数矩阵的行空间是$\mathbb{C}^{n_A+n_B}$的有限个向量子空间（称为奇异衰落子空间）的一个子空间时，中继站会发生深度衰落。结果表明，适当选择网络编码映射可以去除大部分奇异衰落子空间，称为可去除奇异衰落子空间。对于$2^λ$ -PSK信号集，证明了不可移除奇异衰落子空间的数目只占奇异衰落子空间总数的一小部分。当端节点使用不同数量的天线的情况下的拉丁矩形被示出为可从拉丁方的情况下，当它们使用相同数量的天线。此外，网络编码映射，删除所有可移动的奇异奇异衰落子空间被证明是可获得的一个小的拉丁方。
英文摘要：
The design of modulation schemes for the physical layer network-coded two-way MIMO relaying scenario is considered, with $n_R$ antennas at the relay R, $n_A$ and $n_B$ antennas respectively at the end nodes A and B. We consider the denoise-and-forward (DNF) protocol which employs two phases: Multiple access (MA) phase and Broadcast (BC) phase. It is known for the network-coded SISO two-way relaying that adaptively changing the networking coding map used at the relay, also known as the denoising map, according to the channel conditions greatly reduces the impact of multiple access interference which occurs at the relay during the MA phase and all these network coding maps should satisfy a requirement called the {\it exclusive law}. The network coding maps which satisfy exclusive law can be viewed equivalently as Latin Rectangles. In this paper, it is shown that for MIMO two-way relaying, deep fade occurs at the relay when the row space of the channel fade coefficient matrix is a subspace of a finite number of vector subspaces of $\mathbb{C}^{n_A+n_B}$ which are referred to as the singular fade subspaces. It is shown that proper choice of network coding map can remove most of the singular fade subspaces, referred to as the removable singular fade subspaces. For $2^λ$-PSK signal set, it is shown that the number of non-removable singular fade subspaces is a small fraction of the total number of singular fade subspaces. The Latin Rectangles for the case when the end nodes use different number of antennas are shown to be obtainable from the Latin Squares for the case when they use the same number of antennas. Also, the network coding maps which remove all the removable singular singular fade subspaces are shown to be obtainable from a small set of Latin Squares.
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