A New DoF Upper Bound and Its Achievability for KK-User MIMO Y Channels

This work is to study the degrees of freedom (DoF) for the $K$-user MIMO Y channel. Previously, two transmission frameworks have been proposed for the DoF analysis when $N \geq 2M$, where $M$ and $N$ denote the number of antennas at each source node and the relay node respectively. The first method is named as signal group based alignment proposed by Hua et al. in [1]. The second is named as signal pattern approach introduced by Wang et al. in [2]. But both of them only studied certain antenna configurations. The maximum achievable DoF in the general case still remains unknown. In this work, we first derive a new upper bound of the DoF using the genie-aided approach. Then, we propose a more general transmission framework, generalized signal alignment (GSA), and show that the previous two methods are both special cases of GSA. With GSA, we prove that the new DoF upper bound is achievable when $\frac{N}{M} \in \left(0,2+\frac{4}{K(K-1)}\right] \cup \left[K-2, +\infty\right)$. The DoF analysis in this paper provides a major step forward towards the fundamental capacity limit of the $K$-user MIMO Y channel. It also offers a new approach of integrating interference alignment with physical layer network coding.Comment: 6 pages, 3 figures, submitted to IEEE ICC 2015. arXiv admin note: text overlap with arXiv:1405.071

Degrees of Freedom of the 3-User Rank-Deficient MIMO Interference Channel

We provide the degrees of freedom (DoF) characterization for the $3$-user $M_T\times M_R$ multiple-input multiple-output (MIMO) interference channel (IC) with \emph{rank-deficient} channel matrices, where each transmitter is equipped with $M_T$ antennas and each receiver with $M_R$ antennas, and the interfering channel matrices from each transmitter to the other two receivers are of ranks $D_1$ and $D_2$, respectively. One important intermediate step for both the converse and achievability arguments is to convert the fully-connected rank-deficient channel into an equivalent partially-connected full-rank MIMO-IC by invertible linear transformations. As such, existing techniques developed for full-rank MIMO-IC can be incorporated to derive the DoF outer and inner bounds for the rank-deficient case. Our result shows that when the interfering links are weak in terms of the channel ranks, i.e., $D_1+D_2\leq \min(M_T, M_R)$, zero forcing is sufficient to achieve the optimal DoF. On the other hand, when $D_1+D_2> \min(M_T, M_R)$, a combination of zero forcing and interference alignment is in general required for DoF optimality. The DoF characterization obtained in this paper unifies several existing results in the literature.Comment: 28 pages, 7 figures. To appear in IEEE transactions on wireless communication

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

Sub-Stream Fairness and Numerical Correctness in MIMO Interference Channels

Signal-to-interference plus noise ratio (SINR) and rate fairness in a system are substantial quality-of-service (QoS) metrics. The acclaimed SINR maximization (max-SINR) algorithm does not achieve fairness between user's streams, i.e., sub-stream fairness is not achieved. To this end, we propose a distributed power control algorithm to render sub-stream fairness in the system. Sub-stream fairness is a less restrictive design metric than stream fairness (i.e., fairness between all streams) thus sum-rate degradation is milder. Algorithmic parameters can significantly differentiate the results of numerical algorithms. A complete picture for comparison of algorithms can only be depicted by varying these parameters. For example, a predetermined iteration number or a negligible increment in the sum-rate can be the stopping criteria of an algorithm. While the distributed interference alignment (DIA) can reasonably achieve sub-stream fairness for the later, the imbalance between sub-streams increases as the preset iteration number decreases. Thus comparison of max-SINR and DIA with a low preset iteration number can only depict a part of the picture. We analyze such important parameters and their effects on SINR and rate metrics to exhibit numerical correctness in executing the benchmarks. Finally, we propose group filtering schemes that jointly design the streams of a user in contrast to max-SINR scheme that designs each stream of a user separately.Comment: To be presented at IEEE ISWTA'1