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37
Topological interference management through index coding
, 2013
"... While much recent progress on interference networks has come about under the assumption of abundant channel state information at the transmitters (CSIT), a complementary perspective is sought in this work through the study of interference networks with no CSIT except a coarse knowledge of the topolo ..."
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Cited by 30 (14 self)
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While much recent progress on interference networks has come about under the assumption of abundant channel state information at the transmitters (CSIT), a complementary perspective is sought in this work through the study of interference networks with no CSIT except a coarse knowledge of the topology of the network that only allows a distinction between weak and significant channels and no further knowledge of the channel coefficients ’ realizations. Modeled as a degreesoffreedom (DoF) study of a partially connected interference network with no CSIT, the problem is found to have a counterpart in the capacity analysis of wired networks with arbitrary linear network coding at intermediate nodes, under the assumption that the sources are aware only of the end to end topology of the network. The wireless (wired) network DoF (capacity) region, expressed in dimensionless units as a multiple of the DoF (capacity) of a single point to point channel (link), is found to be bounded above by the capacity of an index coding problem where the antidotes graph is the complement of the interference graph of the original network and the bottleneck link capacity is normalized to unity. The problems are shown to be equivalent under linear solutions over the same field. An interference alignment
Degrees of freedom of MIMO cellular networks: Twocell threeuserpercell case
 in IEEE Global Commun. Conf
, 2013
"... Abstract—This paper characterizes the spatiallynormalized degrees of freedom of a 2cell, 2user/cell MIMO cellular networks with M antennas at each user and N antennas at each basestation. We show that the optimal DoF is a piecewise linear function, with either M or N being the bottleneck. Denot ..."
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Cited by 12 (2 self)
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Abstract—This paper characterizes the spatiallynormalized degrees of freedom of a 2cell, 2user/cell MIMO cellular networks with M antennas at each user and N antennas at each basestation. We show that the optimal DoF is a piecewise linear function, with either M or N being the bottleneck. Denoting the ratio M/N as γ, we show that the network has redundant dimensions in both M and N when γ ∈ {1/2, 1} and that the network has no redundancy when γ ∈ {1/4, 2/3, 3/2}. We also show that not all proper systems are feasible and that the only set of feasible proper systems that lie on the properimproper boundary are those with γ ∈ {1/4, 2/3, 3/2}. We make comparisons between the DoF achievable using strategies such as time sharing between users or cells and discuss their implications on user scheduling in such networks. I.
Geometry of the 3User MIMO interference channel
 in Proc. Allerton Conference on Communication, Control, and Computing (Allerton
, 2011
"... Abstract—This paper studies vector space interference alignment for the threeuser MIMO interference channel with no time or frequency diversity. The main result is a characterization of the feasibility of interference alignment in the symmetric case where all transmitters have M antennas and all ..."
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Abstract—This paper studies vector space interference alignment for the threeuser MIMO interference channel with no time or frequency diversity. The main result is a characterization of the feasibility of interference alignment in the symmetric case where all transmitters have M antennas and all receivers have N antennas. If N ≥M and all users desire d transmit dimensions, then alignment is feasible if and only if (2r+1)d ≤ max(rN, (r+1)M) for all nonnegative integers r. The analogous result holds with M and N switched if M ≥ N. It turns out that, just as for the 3user parallel interference channel [1], the length of alignment paths captures the essence of the problem. In fact, for each feasible value of M and N the maximum alignment path length dictates both the converse and achievability arguments. One of the implications of our feasibility criterion is that simply counting equations and comparing to the number of variables does not predict feasibility. Instead, a more careful investigation of the geometry of the alignment problem is required. The necessary condition obtained by counting equations is implied by our new feasibility criterion. I.
MIMO multiway relaying with clustered full data exchange: Signal space alignment and degrees of freedom
 IEEE Trans. Wireless Commun
, 2014
"... Abstract—Recently, much research interest has been attracted towards the design of efficient communication mechanisms for multipleinput multipleoutput (MIMO) multiway relay channels (mRCs). In this paper, we investigate achievable degrees of freedom (DoF) of the MIMO mRC with L clusters and K user ..."
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Cited by 6 (3 self)
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Abstract—Recently, much research interest has been attracted towards the design of efficient communication mechanisms for multipleinput multipleoutput (MIMO) multiway relay channels (mRCs). In this paper, we investigate achievable degrees of freedom (DoF) of the MIMO mRC with L clusters and K users per cluster, where each user is equipped with M antennas and the relay with N antennas. Our analysis is focused on a new data exchange model, termed 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 jointly and systematically construct the beamforming matrices at the users and the relay for efficient implementation of physicallayer 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 M
Beyond oneway communication: Degrees of freedom of multiway relay MIMO interference networks,” arXiv:1401.5582
, 2014
"... We characterize the degrees of freedom (DoF) of multiway relay MIMO interference networks. In particular, we consider a wireless network consisting of 4 user nodes, each with M antennas, and one Nantenna relay node. In this network, each user node sends one independent message to each of the othe ..."
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We characterize the degrees of freedom (DoF) of multiway relay MIMO interference networks. In particular, we consider a wireless network consisting of 4 user nodes, each with M antennas, and one Nantenna relay node. In this network, each user node sends one independent message to each of the other user nodes, and there are no direct links between any two user nodes, i.e., all communication must pass through the relay node. For this network, we show that the symmetric DoF value per message is given by max(min(M3, N
On the achievable degrees of freedom for the 3user rankdeficient MIMO interference channel,” [Online]. Available: http://arxiv.org/abs/1211.4198
, 2012
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MIMO multiway relaying with pairwise data exchange: A degrees of freedom perspective
 IEEE TRANS. ON SIGNAL PROCESS
, 2014
"... In this paper, we study achievable degrees of freedom (DoF) of a multipleinput multipleoutput (MIMO) multiway relay channel (mRC) where users, each equipped with antennas, exchange messages in a pairwise manner via a commonantenna relay node. A novel and systematic way of joint beamforming design ..."
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Cited by 5 (1 self)
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In this paper, we study achievable degrees of freedom (DoF) of a multipleinput multipleoutput (MIMO) multiway relay channel (mRC) where users, each equipped with antennas, exchange messages in a pairwise manner via a commonantenna 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 physicallayer network coding (PNC). It is shown that, when the user number, the proposed beamforming design can achieve the DoF capacity of the considered mRC for any setups. For the scenarios with, 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 or by the number of relay antennas. Further, we show that the DoF capacity can be achieved for and, which provides a broader range of the DoF capacity than the existing results. Asymptotic DoF as is also derived based on the proposed signaling scheme.
Degrees of Freedom of RankDeficient MIMO Interference Channels
"... Abstract — We characterize the degrees of freedom (DoF) of multipleinput and multipleoutput (MIMO) interference channels with rankdeficient channel matrices. For the twouser rankdeficient MIMO interference channel, we provide a tight outer bound to show that the previously known achievable DoF ..."
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Cited by 5 (4 self)
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Abstract — We characterize the degrees of freedom (DoF) of multipleinput and multipleoutput (MIMO) interference channels with rankdeficient channel matrices. For the twouser rankdeficient MIMO interference channel, we provide a tight outer bound to show that the previously known achievable DoF in the symmetric case is optimal and generalize the result to fully asymmetric settings. For the Kuser rankdeficient interference channel, we improve the previously known achievable DoF and provide a tight outer bound to establish optimality in symmetric settings. In particular, we show that for the Kuser rankdeficient interference channel, when all nodes have M antennas, all direct channels have rank D0, all cross channels are of rank D, and the channels are otherwise generic, the optimal DoF value per user is min(D0, M − (min(M, (K − 1)D)/2)). Notably for interference channels, the rankdeficiency of direct channels does not help and the rank deficiency of crosschannels does not hurt. The main technical challenge is to account for the spatial dependences introduced by rank deficiencies in the interference alignment schemes that typically rely on the independence of channel coefficients. Index Terms — Channel capacity, degrees of freedom, interference channel, multipleinput multipleoutput (MIMO), rank deficient channels, interference alignment I.