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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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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.
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.
On the Capacity of the Finite Field Counterparts of Wireless Interference Networks
, 2013
"... This work explores how degrees of freedom (DoF) results from wireless networks can be translated into capacity or linear capacity results for their finite field counterparts that arise in network coding applications. The main insight is that scalar (SISO) finite field channels over Fpn are analogous ..."
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Cited by 5 (3 self)
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This work explores how degrees of freedom (DoF) results from wireless networks can be translated into capacity or linear capacity results for their finite field counterparts that arise in network coding applications. The main insight is that scalar (SISO) finite field channels over Fpn are analogous to n × n vector (MIMO) channels in the wireless setting, but with an important distinction – there is additional structure due to finite field arithmetic which enforces commutativity of matrix multiplication and limits the channel diversity to n, making these channels similar to diagonal channels in the wireless setting. Within the limits imposed by the channel structure, the DoF optimal precoding solutions for wireless networks can be translated into capacity or linear capacity optimal solutions for their finite field counterparts. This is shown through the study of capacity of the 2user X channel and linear capacity of the 3user interference channel. Besides bringing the insights from wireless networks into network coding applications, the study of finite field networks over Fpn also touches upon important open problems in wireless networks (finite SNR, finite diversity scenarios) through interesting parallels between p and SNR, and n and diversity.
Robust transceiver design for Kpairs quasistatic MIMO interference channels via semidefinite relaxation
 IEEE Trans. Wireless Commun
, 2010
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Multipleantenna interference channels with real interference alignment and receive antenna joint processing
 ArXiv
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ADAPTIVE BEAM TRACKING FOR INTERFERENCE ALIGNMENT IN TIMEVARYING MIMO INTERFERENCE CHANNELS: CONJUGATE GRADIENT APPROACH
"... Based on a linear formulation to interference alignment, an adaptive algorithm for interferencealigning beam tracking in timevarying MIMO interference channels is proposed. It is shown that obtaining the interferencealigning beam vector is equivalent to minimizing a certain Rayleigh quotient, ..."
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Based on a linear formulation to interference alignment, an adaptive algorithm for interferencealigning beam tracking in timevarying MIMO interference channels is proposed. It is shown that obtaining the interferencealigning beam vector is equivalent to minimizing a certain Rayleigh quotient, and the conjugate gradient approach is adopted to construct an adaptive algorithm. The convergence and stability of the proposed algorithm are established in static channel case, and numerical results show that the proposed algorithm performs well compared with other existing methods with much less complexity. Index Terms Interference alignment, adaptive algorithm, conjugate gradient, least squares 1.
On the generalized degrees of freedom of the Kuser symmetric MIMO Gaussian interference channels,” Arxiv preprint arXIV: 1105.5306
, 2011
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Beam tracking for interference alignment in slowly fading MIMO interference channels: A perturbations approach under a linear framework
 IEEE Trans. Signal Process
, 2012
"... Abstract—In this paper, the beam design for signalspace interference alignment in slowly fading multiuser multipleinput multipleoutput (MIMO) interference channels is considered. Based on a linear formulation for interference alignment, a predictive beam tracking algorithm is proposed using mat ..."
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Abstract—In this paper, the beam design for signalspace interference alignment in slowly fading multiuser multipleinput multipleoutput (MIMO) interference channels is considered. Based on a linear formulation for interference alignment, a predictive beam tracking algorithm is proposed using matrix perturbation theory. The proposed algorithm, based on a mixture of iteration and update, computes interferencealigning beamforming vectors at the current time by updating the previous beam vectors based on the channel difference between the two time steps during the predictively updating phase, and yields significant reduction in computational complexity compared with existing methods recalculating beams at each time step. The tracking performance of the algorithm is analyzed in terms of mean square error and sum rate loss between the predictively updating approach and the recalculating approach, and the impact of imperfect channel knowledge is also investigated under the statespace channel model. Numerical results show that the proposed algorithm has almost the same performance as nonpredictive methods in sum rate. Thus, the proposed algorithm provides a very efficient way to realize interference alignment in a realistic slowly fading MIMO channel environment. Index Terms—Interference alignment, least squares, null space tracking, perturbation theory, predictive algorithm, slowly fading channels. I.
The DoF of the Asymmetric MIMO Interference Channel with Square Direct Link Channel Matrices
"... with square direct link channel matrices, that is, the uth transmitter and its intended receiver have Mu 2 N antennas each, where Mu need not be the same for all u 2 [1: K]. Starting from a 3user example, it is shown that existing cooperationbased outer bounds are insufficient to characterize the ..."
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with square direct link channel matrices, that is, the uth transmitter and its intended receiver have Mu 2 N antennas each, where Mu need not be the same for all u 2 [1: K]. Starting from a 3user example, it is shown that existing cooperationbased outer bounds are insufficient to characterize the DoF. Moreover, it is shown that two distinct operating regimes exist. With a dominant user, i.e., a user that has more antennas than the other two users combined, it is DoF optimal to let that user transmit alone on the IC. Otherwise, it is DoF optimal to decompose and operate the 3user MIMO IC as an (M1 + M2 + M3)user SISO IC. This indicates that MIMO operations are useless from a DoF perspective in systems without a dominant user. The main contribution of the paper is the derivation of a novel outer bound for the general Kuser case that is tight in the regime where a dominant user is not present; this is done by generalizing the insights from the 3user example to an arbitrary number of users. I.