An algebraic geometry perspective for the estimation of the directions of arrival

被引：0

作者：

Compagnoni M. ^{[1
]}

Notari R. ^{[2
]}

Marcon M. ^{[1
]}

Spagnolini U. ^{[1
]}

机构：

[1] Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Piazza L. Da Vinci 32, Milano

[2] Dipartimento di Matematica, Politecnico di Milano, Piazza L. Da Vinci 32, Milano

来源：

Journal of the Franklin Institute | 2023年 / 360卷 / 01期

关键词：

Algebra - Geometry - Multiple signal classification - Signal to noise ratio;

D O I：

10.1016/j.jfranklin.2022.11.020

中图分类号：

学科分类号：

摘要：

Directions of Arrival for Uniform Linear Arrays represent a widely studied topic in many fields of signal processing, with large attention on computational complexity, estimation accuracy and noise rejection. In this article we study the mathematical model behind Directions of Arrival from the point of view of algebraic geometry, focusing on its relation with the rational normal curve. On this basis, we give a novel interpretation for the root-MUSIC algorithm, that is a widely adopted estimation approach in signal processing. Furthermore, we propose some novel estimation techniques. The first one is based on the computation of the points on the rational normal curve that minimize the distance from the linear subspace defined by the measured Directions of Arrival. The others require the study of the secant varieties of the rational normal curve and the minimization of the distance between the point of the Grassmannian defined by the signal subspace and a certain secant variety. The results obtained from simulations in a noisy scenario show that our estimators are statistically consistent. One algorithm outperforms root-MUSIC over a wide range of scenarios, especially in presence of few snapshots and low Signal to Noise Ratio. © 2022 The Franklin Institute

引用

页码：38 / 64

页数：26

共 24 条

[1]

Abdelbari A., Bilgehan B., A novel doa estimation method of several sources for 5g networks, 2020 International Conference on Electrical, Communication, and Computer Engineering (ICECCE), pp. 1-6, (2020)

[2]

Hu Y., Abhayapala T.D., Samarasinghe P., Multiple source direction of arrival estimations using relative sound pressure based music, IEEE/ACM Trans. Audio Speech Lang. Process., (2020)

[3]

Li J., Stoica P., Mimo radar with colocated antennas, IEEE Signal Process. Mag., 24, 5, pp. 106-114, (2007)

[4]

Jaafer Z., Goli S., Elameer A., Best performance analysis of doa estimation algorithms, pp. 235-239, (2018)

[5]

Gerstoft P., Xenaki A., Mecklenbrauker C.F., Multiple and single snapshot compressive beamforming, J. Acoust. Soc. Am., 138, 4, pp. 2003-2014, (2015)

[6]

Van Trees H., Optimum array processing – Part IV of detection, estimation, and modulation therory, (2002)

[7]

Cohen L., Time-Frequency analysis: Theory and applications, (1995)

[8]

Manikas A., Differential geometry in array processing, (2004)

[9]

Jie S., Fu-cheng Y., Fu-qing C., Yi-wei Y., Complex envelope estimation of direct-path pulse signal based on real data, International Conference on Radar Systems (Radar 2017), pp. 1-5, (2017)

[10]

Kleene H., Schulz D., Concept of a complex envelope faber polynomial approach for the solution of maxwells equations, 2018 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), pp. 1-3, (2018)

← 1 2 3 →