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.
| Language | English |
|---|---|
| Title of host publication | Conference Record of the Fiftieh Asilomar Conference on Signals, Systems and Computers |
| Editors | Michael B. Matthews |
| Place of Publication | Piscataway, NJ |
| Publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| Pages | 1821-1825 |
| Number of pages | 5 |
| ISBN (Electronic) | 9781538639542 |
| DOIs | |
| Publication status | Published - 2016 |
| Event | 50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016 - Pacific Grove, United States Duration: 6 Nov 2016 → 9 Nov 2016 |
Other
| Other | 50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016 |
|---|---|
| Country | United States |
| City | Pacific Grove |
| Period | 6/11/16 → 9/11/16 |
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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 proceeding › Conference proceeding contribution › Research › peer-review
TY - GEN
T1 - Lattice parameter estimation from sparse, noisy measurements
AU - Quinn, Barry G.
AU - Clarkson, I. Vaughan L.
PY - 2016
Y1 - 2016
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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85016310232&partnerID=8YFLogxK
U2 - 10.1109/ACSSC.2016.7869698
DO - 10.1109/ACSSC.2016.7869698
M3 - Conference proceeding contribution
SP - 1821
EP - 1825
BT - Conference Record of the Fiftieh Asilomar Conference on Signals, Systems and Computers
A2 - Matthews, Michael B.
PB - Institute of Electrical and Electronics Engineers (IEEE)
CY - Piscataway, NJ
ER -