Lattice parameter estimation from sparse, noisy measurements

Barry G. Quinn, I. Vaughan L. Clarkson

    Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionResearchpeer-review

    Abstract

    We consider a problem in which noisy measurements are made of the positions of points in a lattice. Some parameters of the lattice are known but others need to be estimated. In particular, it is not known a priori from which lattice point each measurement arises. In previous work [1-5], the authors have considered estimating the parameters of a one-dimensional lattice from measurements on the real Line. The application is period estimation from sparse, noisy measurements of a periodic event, e.g., estimation of baud in telecommunications signal processing. Here, we take a first step in generalising the results to higher-dimensional lattices, starting with two dimensions. We propose a model in which the lattice is square but the unknown parameters are a translation, rotation and scaling. An application is again in telecommunications, to blind detection of QAM. We propose an estimator based on the Bartlett point-process periodogram [6]. We show that, under certain conditions, the estimator is strongly consistent and obeys a central limit theorem. We demonstrate convergence to the limit with numerical simulations.

    LanguageEnglish
    Title of host publicationConference Record of the Fiftieh Asilomar Conference on Signals, Systems and Computers
    EditorsMichael B. Matthews
    Place of PublicationPiscataway, NJ
    PublisherInstitute of Electrical and Electronics Engineers (IEEE)
    Pages1821-1825
    Number of pages5
    ISBN (Electronic)9781538639542
    DOIs
    Publication statusPublished - 2016
    Event50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016 - Pacific Grove, United States
    Duration: 6 Nov 20169 Nov 2016

    Other

    Other50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016
    CountryUnited States
    CityPacific Grove
    Period6/11/169/11/16

    Fingerprint

    Parameter estimation
    Lattice constants
    Telecommunication
    Quadrature amplitude modulation
    Signal processing
    Computer simulation

    Cite this

    Quinn, B. G., & Clarkson, I. V. L. (2016). Lattice parameter estimation from sparse, noisy measurements. In M. B. Matthews (Ed.), Conference Record of the Fiftieh Asilomar Conference on Signals, Systems and Computers (pp. 1821-1825). Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/ACSSC.2016.7869698
    Quinn, Barry G. ; Clarkson, I. Vaughan L. / Lattice parameter estimation from sparse, noisy measurements. Conference Record of the Fiftieh Asilomar Conference on Signals, Systems and Computers. editor / Michael B. Matthews. Piscataway, NJ : Institute of Electrical and Electronics Engineers (IEEE), 2016. pp. 1821-1825
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    Quinn, BG & Clarkson, IVL 2016, Lattice parameter estimation from sparse, noisy measurements. in MB Matthews (ed.), Conference Record of the Fiftieh Asilomar Conference on Signals, Systems and Computers. Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, pp. 1821-1825, 50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016, Pacific Grove, United States, 6/11/16. https://doi.org/10.1109/ACSSC.2016.7869698

    Lattice parameter estimation from sparse, noisy measurements. / Quinn, Barry G.; Clarkson, I. Vaughan L.

    Conference Record of the Fiftieh Asilomar Conference on Signals, Systems and Computers. ed. / Michael B. Matthews. Piscataway, NJ : Institute of Electrical and Electronics Engineers (IEEE), 2016. p. 1821-1825.

    Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionResearchpeer-review

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    N2 - We consider a problem in which noisy measurements are made of the positions of points in a lattice. Some parameters of the lattice are known but others need to be estimated. In particular, it is not known a priori from which lattice point each measurement arises. In previous work [1-5], the authors have considered estimating the parameters of a one-dimensional lattice from measurements on the real Line. The application is period estimation from sparse, noisy measurements of a periodic event, e.g., estimation of baud in telecommunications signal processing. Here, we take a first step in generalising the results to higher-dimensional lattices, starting with two dimensions. We propose a model in which the lattice is square but the unknown parameters are a translation, rotation and scaling. An application is again in telecommunications, to blind detection of QAM. We propose an estimator based on the Bartlett point-process periodogram [6]. We show that, under certain conditions, the estimator is strongly consistent and obeys a central limit theorem. We demonstrate convergence to the limit with numerical simulations.

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    Quinn BG, Clarkson IVL. Lattice parameter estimation from sparse, noisy measurements. In Matthews MB, editor, Conference Record of the Fiftieh Asilomar Conference on Signals, Systems and Computers. Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE). 2016. p. 1821-1825 https://doi.org/10.1109/ACSSC.2016.7869698