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dc.contributor.authorGonzález Fernández, Óscar 
dc.contributor.authorBeltrán Álvarez, Carlos 
dc.contributor.authorSantamaría Caballero, Luis Ignacio 
dc.contributor.otherUniversidad de Cantabriaes_ES
dc.date.accessioned2016-10-26T15:14:55Z
dc.date.available2016-10-26T15:14:55Z
dc.date.issued2014-03
dc.identifier.issn0018-9448
dc.identifier.issn1557-9654
dc.identifier.otherTEC2010-19545-C04-03es_ES
dc.identifier.otherCSD2008-00010es_ES
dc.identifier.urihttp://hdl.handle.net/10902/9392
dc.description.abstractIn this paper, we consider the feasibility of linear interference alignment (IA) for multiple-input multiple-output (MIMO) channels with constant coefficients for any number of users, antennas and streams per user; and propose a polynomialtime test for this problem. Combining algebraic geometry techniques with differential topology ones, we first prove a result that generalizes those previously published on this topic. Specifically, we consider the input set (complex projective space of MIMO interference channels), the output set (precoder and decoder Grassmannians) and the solution set (channels, decoders and precoders satisfying the IA polynomial equations), not only as algebraic sets but also as smooth compact manifolds. Using this mathematical framework, we prove that the linear alignment problem is feasible when the algebraic dimension of the solution variety is larger than or equal to the dimension of the input space and the linear mapping between the tangent spaces of both smooth manifolds given by the first projection is generically surjective. If that mapping is not surjective, then the solution variety projects into the input space in a singular way and the projection is a zero-measure set. This result naturally yields a simple feasibility test, which amounts to checking the rank of a matrix. We also provide an exact arithmetic version of the test, which proves that testing the feasibility of IA for generic MIMO channels belongs to the bounded-error probabilistic polynomial (BPP) complexity class.es_ES
dc.description.sponsorshipThe work of Ó. González and I. Santamaría was supported by MICINN (Spanish Ministry for Science and Innovation) under grants TEC2010-19545-C04-03 (COSIMA), CONSOLIDER-INGENIO 2010 CSD2008-00010 (COMONSENS) and FPU grant AP2009-1105. Carlos Beltrán was partially supported by the MICINN grant MTM2010-16051.es_ES
dc.format.extent18 p.es_ES
dc.language.isoenges_ES
dc.publisherInstitute of Electrical and Electronics Engineers Inc.es_ES
dc.rights© 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.es_ES
dc.sourceIEEE Transactions on Information Theory, 2014, 60(3), 1840 - 1856es_ES
dc.subject.otherInterference alignmentes_ES
dc.subject.otherMIMO interference channeles_ES
dc.subject.otherPolynomial equationses_ES
dc.subject.otherAlgebraic geometryes_ES
dc.subject.otherDifferential topologyes_ES
dc.titleA feasibility test for linear interference alignment in MIMO channels with constant coefficientses_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.relation.publisherVersionhttps://doi.org/10.1109/TIT.2014.2301440es_ES
dc.rights.accessRightsopenAccesses_ES
dc.identifier.DOI10.1109/TIT.2014.2301440
dc.type.versionacceptedVersiones_ES


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