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    A feasibility test for linear interference alignment in MIMO channels with constant coefficients

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    Identificadores
    URI: http://hdl.handle.net/10902/9392
    DOI: 10.1109/TIT.2014.2301440
    ISSN: 0018-9448
    ISSN: 1557-9654
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    Author
    González Fernández, ÓscarAutoridad Unican; Beltrán Álvarez, CarlosAutoridad Unican; Santamaría Caballero, Luis IgnacioAutoridad Unican
    Date
    2014-03
    Derechos
    © 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.
    Publicado en
    IEEE Transactions on Information Theory, 2014, 60(3), 1840 - 1856
    Publisher
    Institute of Electrical and Electronics Engineers Inc.
    Enlace a la publicación
    https://doi.org/10.1109/TIT.2014.2301440
    Palabras clave
    Interference alignment
    MIMO interference channel
    Polynomial equations
    Algebraic geometry
    Differential topology
    Abstract:
    In 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.
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    • D12 Artículos [280]
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    UNIVERSIDAD DE CANTABRIA

    Repositorio realizado por la Biblioteca Universitaria utilizando DSpace software
    Contact Us | Send Feedback
    Metadatos sujetos a:licencia de Creative Commons Reconocimiento 3.0 España