MIMO Multiway Relaying with Pairwise Data Exchange: A Degrees of Freedom Perspective

In this paper, we study achievable degrees of freedom (DoF) of a multiple-input multiple-output (MIMO) multiway relay channel (mRC) where $K$ users, each equipped with $M$ antennas, exchange messages in a pairwise manner via a common $N$-antenna relay node. % A novel and systematic way of joint beamforming design at the users and at the relay is proposed to align signals for efficient implementation of physical-layer network coding (PNC). It is shown that, when the user number $K=3$, the proposed beamforming design can achieve the DoF capacity of the considered mRC for any $(M,N)$ setups. % For the scenarios with $K>3$, we show that the proposed signaling scheme can be improved by disabling a portion of relay antennas so as to align signals more efficiently. Our analysis reveals that the obtained achievable DoF is always piecewise linear, and is bounded either by the number of user antennas $M$ or by the number of relay antennas $N$. Further, we show that the DoF capacity can be achieved for $\frac{M}{N} \in \left(0,\frac{K-1}{K(K-2)} \right]$ and $\frac{M}{N} \in \left[\frac{1}{K(K-1)}+\frac{1}{2},\infty \right)$, which provides a broader range of the DoF capacity than the existing results. Asymptotic DoF as $K\rightarrow \infty$ is also derived based on the proposed signaling scheme.Comment: 13 pages, 7 figure

The Multi-way Relay Channel

The multiuser communication channel, in which multiple users exchange information with the help of a relay terminal, termed the multi-way relay channel (mRC), is introduced. In this model, multiple interfering clusters of users communicate simultaneously, where the users within the same cluster wish to exchange messages among themselves. It is assumed that the users cannot receive each other's signals directly, and hence the relay terminal in this model is the enabler of communication. In particular, restricted encoders, which ignore the received channel output and use only the corresponding messages for generating the channel input, are considered. Achievable rate regions and an outer bound are characterized for the Gaussian mRC, and their comparison is presented in terms of exchange rates in a symmetric Gaussian network scenario. It is shown that the compress-and-forward (CF) protocol achieves exchange rates within a constant bit offset of the exchange capacity independent of the power constraints of the terminals in the network. A finite bit gap between the exchange rates achieved by the CF and the amplify-and-forward (AF) protocols is also shown. The two special cases of the mRC, the full data exchange model, in which every user wants to receive messages of all other users, and the pairwise data exchange model which consists of multiple two-way relay channels, are investigated in detail. In particular for the pairwise data exchange model, in addition to the proposed random coding based achievable schemes, a nested lattice coding based scheme is also presented and is shown to achieve exchange rates within a constant bit gap of the exchange capacity.Comment: Revised version of our submission to the Transactions on Information Theor

Degrees of Freedom for the MIMO Multi-way Relay Channel

This paper investigates the degrees of freedom (DoF) of the L-cluster, K-user MIMO multi-way relay channel, where users in each cluster wish to exchange messages within the cluster, and they can only communicate through the relay. A novel DoF upper bound is derived by providing users with carefully designed genie information. Achievable DoF is identified using signal space alignment and multiple-access transmission. For the two-cluster MIMO multi-way relay channel with two users in each cluster, DoF is established for the general case when users and the relay have arbitrary number of antennas, and it is shown that the DoF upper bound can be achieved using signal space alignment or multiple-access transmission, or a combination of both. The result is then generalized to the three user case. For the L-cluster K-user MIMO multi-way relay channel in the symmetric setting, conditions under which the DoF upper bound can be achieved are established. In addition to being shown to be tight in a variety of scenarios of interests of the multi-way relay channel, the newly derived upperbound also establishes the optimality of several previously established achievable DoF results for multiuser relay channels that are special cases of the multi-way relay channel.Comment: submitted to IEEE Transactions on Information Theor