TY - JOUR
T1 - Joint Detection and Localization of an Unknown Number of Sources Using the Algebraic Structure of the Noise Subspace
AU - Morency, Matthew W.
AU - Vorobyov, Sergiy A.
AU - Leus, Geert
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: King Abdullah University of Science and Technology–Massachusetts Institute of Technology–Delft University of Technology Consortium; Academy of Finland; Natural Sciences and Engineering Research Council of Canada;
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2018/6/18
Y1 - 2018/6/18
N2 - Source localization and spectral estimation are among the most fundamental problems in statistical and array signal processing. Methods that rely on the orthogonality of the signal and noise subspaces, such as Pisarenko's method, MUSIC, and root-MUSIC, are some of the most widely used algorithms to solve these problems. As a common feature, these methods require both a priori knowledge of the number of sources and an estimate of the noise subspace. Both requirements are complicating factors to the practical implementation of the algorithms and, when not satisfied exactly, can potentially lead to severe errors. In this paper, we propose a new localization criterion based on the algebraic structure of the noise subspace that is described for the first time to the best of our knowledge. Using this criterion and the relationship between the source localization problem and the problem of computing the greatest common divisor (GCD), or more practically approximate GCD, for polynomials, we propose two algorithms, which adaptively learn the number of sources and estimate their locations. Simulation results show a significant improvement over root-MUSIC in challenging scenarios such as closely located sources, both in terms of detection of the number of sources and their localization over a broad and practical range of signal-to-noise ratios. Furthermore, no performance sacrifice in simple scenarios is observed.
AB - Source localization and spectral estimation are among the most fundamental problems in statistical and array signal processing. Methods that rely on the orthogonality of the signal and noise subspaces, such as Pisarenko's method, MUSIC, and root-MUSIC, are some of the most widely used algorithms to solve these problems. As a common feature, these methods require both a priori knowledge of the number of sources and an estimate of the noise subspace. Both requirements are complicating factors to the practical implementation of the algorithms and, when not satisfied exactly, can potentially lead to severe errors. In this paper, we propose a new localization criterion based on the algebraic structure of the noise subspace that is described for the first time to the best of our knowledge. Using this criterion and the relationship between the source localization problem and the problem of computing the greatest common divisor (GCD), or more practically approximate GCD, for polynomials, we propose two algorithms, which adaptively learn the number of sources and estimate their locations. Simulation results show a significant improvement over root-MUSIC in challenging scenarios such as closely located sources, both in terms of detection of the number of sources and their localization over a broad and practical range of signal-to-noise ratios. Furthermore, no performance sacrifice in simple scenarios is observed.
UR - http://hdl.handle.net/10754/660343
UR - https://ieeexplore.ieee.org/document/8387523/
UR - http://www.scopus.com/inward/record.url?scp=85048630714&partnerID=8YFLogxK
U2 - 10.1109/tsp.2018.2847692
DO - 10.1109/tsp.2018.2847692
M3 - Article
SN - 1053-587X
VL - 66
SP - 4685
EP - 4700
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 17
ER -