Feasibility Conditions for Interference Alignment

Yetis, Cenk M.; Gou, Tiangao; Jafar, Syed A.; Kayran, A.H.

doi:10.1109/glocom.2009.5425326

Cited by 128 publications

(113 citation statements)

References 3 publications

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“…X K . We denote this K-user MIMO interference channel as an (M r × M t , d) K system, in the same manner as in [10], where all signal spaces span all available dimensions. For all the cases considered we assume…”

Section: System Modelmentioning

confidence: 99%

Interference Alignment as a Rank Constrained Rank Minimization

Papailiopoulos

Dimakis

2010

2010 IEEE Global Telecommunications Conference GLOBECOM 2010

143

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We show that the maximization of the sum degrees-of-freedom for the static flat-fading multipleinput multiple-output (MIMO) interference channel is equivalent to a rank constrained rank minimization problem (RCRM), when the signal spaces span all available dimensions. The rank minimization corresponds to maximizing interference alignment (IA) so that interference spans the lowest dimensional subspace possible. The rank constraints account for the useful signal spaces spanning all available spatial dimensions. That way, we reformulate all IA requirements to requirements involving ranks. Then, we present a convex relaxation of the RCRM problem inspired by recent results in compressed sensing and low-rank matrix completion theory that rely on approximating rank with the nuclear norm. We show that the convex envelope of the sum of ranks of the interference matrices is the normalized sum of their corresponding nuclear norms and introduce tractable constraints that are asymptotically equivalent to the rank constraints for the initial problem. We also show that our heuristic relaxation can be tuned for the multi-cell interference channel. Furthermore, we experimentally show that in many cases the proposed algorithm attains perfect interference alignment and in some cases outperforms previous approaches for finding precoding and zero-forcing matrices for interference alignment.

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Section: System Modelmentioning

confidence: 99%

Interference Alignment as a Rank Constrained Rank Minimization

Papailiopoulos

Dimakis

2010

2010 IEEE Global Telecommunications Conference GLOBECOM 2010

143

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“…Following the previous works on IA for K-pairs MIMO interference networks [12]- [15], [18], in this work, we focus on the feasibility issue of the following problem:…”

Section: System Model and Problem Formulationmentioning

confidence: 99%

The feasibility conditions of interference alignment for MIMO interference networks

Ruan

Lau

Win

2012

2012 IEEE International Symposium on Information Theory Proceedings

108

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Abstract-Interference alignment (IA) has attracted great attention in the last few years for its breakthrough performance in interference networks. However, despite the numerous works dedicated to IA, the feasibility conditions of IA remains unclear for most network topologies. The IA feasibility analysis is challenging as the IA constraints are sets of high-degree polynomials, for which no systematic tool to analyze the solvability conditions exists. In this work, by developing a new mathematical framework that maps the solvability of sets of polynomial equations to the linear independence of their first-order terms, we propose a sufficient condition that applies to MIMO interference networks with general configurations. We have further proved that this sufficient condition matches with the necessary conditions under a wide range of configurations. These results further consolidate the theoretical basis of IA.

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“…. , K}) with high probability as long as K ≤ 2N −1 [6]. Let us examine the "fully loaded" case K = 2N − 1.…”

Section: A Interference Alignmentmentioning

confidence: 99%

Minimum Mean Squared Error interference alignment

Schmidt

Shi

Berry

et al. 2009

2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers

193

165

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Abstract-To achieve the full multiplexing gain of MIMO interference networks at high SNRs, the interference from different transmitters must be aligned in lower-dimensional subspaces at the receivers. Recently a distributed "max-SINR" algorithm for precoder optimization has been proposed that achieves interference alignment for sufficiently high SNRs. We show that this algorithm can be interpreted as a variation of an algorithm that minimizes the sum Mean Squared Error (MSE). To maximize sum utility, where the utility depends on rate or SINR, a weighted sum MSE objective is used to compute the beams, where the weights are updated according to the sum utility objective. We specify a class of utility functions for which convergence of the sum utility to a local optimum is guaranteed with asynchronous updates of beams, receiver filters, and utility weights. Numerical results are presented, which show that this method achieves interference alignment at high SNRs, and can achieve different points on the boundary of the achievable rate region by adjusting the MSE weights.

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Feasibility Conditions for Interference Alignment

Abstract: Abstract-

Cited by 128 publications

References 3 publications

Interference Alignment as a Rank Constrained Rank Minimization

Interference Alignment as a Rank Constrained Rank Minimization

The feasibility conditions of interference alignment for MIMO interference networks

Minimum Mean Squared Error interference alignment

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