Degrees of freedom for the MIMO multi-way relay channel

Tian, Ye; Yener, Aylin

doi:10.1109/isit.2013.6620492

Cited by 46 publications

(93 citation statements)

References 24 publications

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“…Remark 3: (Comparison to the existing work [18]): The authors in [18] study the sum DoF for the asymmetric L-cluster K-user MIMO multi-way relay channel. In the special case when L = K = 2, the channel in [18] reduces to our considered two-pair MIMO TWRC.…”

Section: Remark 2: (Connection To Symmetric Two-pair Mimo Twrc)mentioning

confidence: 99%

“…In the special case when L = K = 2, the channel in [18] reduces to our considered two-pair MIMO TWRC. However, the maximum sum DoF results in [18] are neither optimal nor complete, while our sum DoF results in Corollary 1 are optimal and complete.…”

Section: Remark 2: (Connection To Symmetric Two-pair Mimo Twrc)mentioning

confidence: 99%

“…It includes several special cases: K-user MIMO Y channel [12], multi-pair MIMO two-way relay channel [13]- [17], and L-cluster K-user MIMO multiway relay channel [18], [19]. However, the exact capacity analysis for these channels is extremely challenging, only constant-gap capacity is known in the simplest scenario [20], [21].…”

Section: Introductionmentioning

confidence: 99%

“…The DoF analysis for various MU-MIMO TWRC has attracted much attention in the literature [11], [18], [19], [23]- [31]. Such analysis is tractable mainly due to signal alignment proposed in [23] as an integration of PLNC and interference alignment (IA) [32], [33].…”

Section: Introductionmentioning

confidence: 99%

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Optimal DoF Region for the Asymmetric Two-Pair MIMO Two-Way Relay Channel

Liu

Tao

Yuan

2017

IEEE Trans. Signal Process.

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In this paper, we study the optimal degrees of freedom (DoF) region for the two-pair MIMO two-way relay channel (TWRC) with asymmetric antenna setting, where two pairs of users exchange information with the help of a common relay. Each user i is equipped with M i antennas, for i = 1, 2, 3, 4, and the relay is equipped with N antennas. First, we derive an outer bound of the DoF region by using the cutset theorem and the genie-message approach. Then, we propose a new transmission scheme to achieve the outer bound of the DoF region. Due to the asymmetric data exchange, where the two users in each pair can communicate a different number of data streams, we not only need to form the network-coded symbols but also need to process the additional asymmetric data streams at the relay. This is realized through the joint design of relay compression matrix and source precoding matrices. After obtaining the optimal DoF region, we study the optimal sum DoF by solving a linear programming problem. From the optimal DoF region of this channel, we show that in the asymmetric antenna setting, some antennas at certain source nodes are redundant and cannot contribute to enlarge the DoF region. We also show that there is no loss of optimality in terms of the sum DoF by enforcing symmetric data exchange, where the two users in each pair are restricted to communicate the same number of data streams. Index TermsMultiple-input multiple-output, two-way relay channel, interference alignment, physical-layer network coding, signal alignment, degrees of freedom.

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Section: Remark 2: (Connection To Symmetric Two-pair Mimo Twrc)mentioning

confidence: 99%

Section: Remark 2: (Connection To Symmetric Two-pair Mimo Twrc)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal DoF Region for the Asymmetric Two-Pair MIMO Two-Way Relay Channel

Liu

Tao

Yuan

2017

IEEE Trans. Signal Process.

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“…In [31], functional-decode-and-forward is shown to achieve the cut-set upper bound on the capacity region of the multi-way relay channel where the channel inputs and outputs lie in a finite field. Reference [32] studies the degrees of freedom of the multi-way relay channel with three users in each cluster and then states conditions under which the results can be generalized. An interesting special case of the multi-way relay channel is the multi-pair relay channel which is studied in [33] where the capacity region is first investigated in a deterministic setting, and then, the resulting insights are used for the Gaussian setting.…”

Section: Introductionmentioning

confidence: 99%

The energy harvesting multi-way relay channel with intermittent data: the impact of buffer sizes

Varan

Yener

2015

J Wireless Com Network

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In this paper, a multi-way relay channel is considered with energy harvesting nodes. The harvested energy at each node can be stored in a battery of finite capacity. Additionally, each node employs a data buffer of limited size to store data prior to transmission. Data packets to be exchanged between the nodes arrive at the source nodes in an intermittent fashion. In this setup, the offline sum throughput maximization problem, which turns out to be a convex optimization problem, is solved. The corresponding online problem is formulated, and a backward induction-based optimal solution is proposed. In addition, a near-optimum low complexity solution is presented. It is noted that the solutions for the offline and online throughput maximization problems for the multi-way relay channel also provide solutions for its special cases, e.g., the multi-pair two-way relay channel, the two-way channel, and others. Numerical results are presented to demonstrate the resulting optimal transmission policies for various channel setups, comparing the sum throughput to upper and lower bounds, and demonstrating the impact of buffer sizes at the relay.

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Using network coding to achieve the capacity of deterministic relay networks with relay messages

Zewail

Mohasseb

Nafie

et al. 2016

Wireless Communications

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In this paper, we derive the capacity of the deterministic relay networks with relay messages. We consider a network that consists of five nodes, four of which can only communicate via the fifth one. However, the fifth node is not merely a relay as it may exchange private messages with the other network nodes. First, we develop an upper bound on the capacity region based on the notion of a single-sided genie. In the course of the achievability proof, we also derive the deterministic capacity of a four-user relay network (without private messages at the relay). The capacity achieving schemes use a combination of two network coding techniques: the simple ordering scheme and detour scheme. In the simple ordering scheme, we order the transmitted bits at each user such that the bi-directional messages will be received at the same channel level at the relay, while the basic idea behind the detour scheme is that some parts of the message follow an indirect paths to their respective destinations. This paper, therefore, serves to show that user cooperation and network coding can enhance throughput, even when the users are not directly connected to each other. Finally, we make a conjecture about the capacity region of the general K-node relay network with relay messages.A. Zewail et al.The capacity of deterministic relay networks with relay messages the relay just re-orders the received equations created from the superposition of the transmitted signals on the wireless medium and forwards them. We call this scheme the simple ordering scheme (SOS). Then, from the insights of this work, the authors of [7] used a combination of lattice codes and random Gaussian codes at the source nodes to propose a coding scheme that achieves to within 2 bits per user of the cut-set upper bound on the capacity of the two-pair two-way relay network.Reference [8] studied the two-way X-Channel. First, a new upper bound based on the notion of a single-sided genie was developed, then it was used to characterize the deterministic multicast capacity of their network. To prove the achievability, the authors proposed the idea of Detour Schemes that route some bits intended for a certain receiver via alternative paths when they cannot be accommodated on direct routes. Thereafter, the capacity of the deterministic Y-channel was defined in [9]. Building on this result, the authors investigated the capacity of the Gaussian Ychannel in [10]. Then, we extended these works in [11], by considering a four-user relay network with no direct link, where each user wishes to exchange a number of private messages with the other three users via the relay node. Achievability of the capacity region was demonstrated via two detour schemes (DS), which are different from the ones used in [8] because of the different nature of the multicast network. After that, in [12], we studied the capacity of a three-user relay network where the relay node is interested in exchanging some private messages with the other network users. It was shown that, if all messages emanating from ...

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Degrees of freedom for the MIMO multi-way relay channel

Cited by 46 publications

References 24 publications

Optimal DoF Region for the Asymmetric Two-Pair MIMO Two-Way Relay Channel

Optimal DoF Region for the Asymmetric Two-Pair MIMO Two-Way Relay Channel

The energy harvesting multi-way relay channel with intermittent data: the impact of buffer sizes

Using network coding to achieve the capacity of deterministic relay networks with relay messages

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