Generalized Signal Alignment For MIMO Two-Way X Relay Channels

We study the degrees of freedom (DoF) of MIMO two-way X relay channels. Previous work studied the case $N < 2M$, where $N$ and $M$ denote the number of antennas at the relay and each source, respectively, and showed that the maximum DoF of $2N$ is achievable when $N \leq \lfloor\frac{8M}{5}\rfloor$ by applying signal alignment (SA) for network coding and interference cancelation. This work considers the case $N>2M$ where the performance is limited by the number of antennas at each source node and conventional SA is not feasible. We propose a \textit{generalized signal alignment} (GSA) based transmission scheme. The key is to let the signals to be exchanged between every source node align in a transformed subspace, rather than the direct subspace, at the relay so as to form network-coded signals. This is realized by jointly designing the precoding matrices at all source nodes and the processing matrix at the relay. Moreover, the aligned subspaces are orthogonal to each other. By applying the GSA, we show that the DoF upper bound $4M$ is achievable when $M \leq \lfloor\frac{2N}{5}\rfloor$ ($M$ is even) or $M \leq \lfloor\frac{2N-1}{5}\rfloor$ ($M$ is odd). Numerical results also demonstrate that our proposed transmission scheme is feasible and effective.Comment: 6 pages, 6 figures, to appear in IEEE ICC 201

MIMO Multiway Relaying with Clustered Full Data Exchange: Signal Space Alignment and Degrees of Freedom

We investigate achievable degrees of freedom (DoF) for a multiple-input multiple-output (MIMO) multiway relay channel (mRC) with $L$ clusters and $K$ users per cluster. Each user is equipped with $M$ antennas and the relay with $N$ antennas. We assume a new data exchange model, termed \emph{clustered full data exchange}, i.e., each user in a cluster wants to learn the messages of all the other users in the same cluster. Novel signal alignment techniques are developed to systematically construct the beamforming matrices at the users and the relay for efficient physical-layer network coding. Based on that, we derive an achievable DoF of the MIMO mRC with an arbitrary network configuration of $L$ and $K$, as well as with an arbitrary antenna configuration of $M$ and $N$. We show that our proposed scheme achieves the DoF capacity when $\frac{M}{N} \leq \frac{1}{LK-1}$ and $\frac{M}{N} \geq \frac{(K-1)L+1}{KL}$.Comment: 13 pages, 4 figure