Using matrix norms to estimate the direction of arrival of planar waves on an ULA

• Published in: Journal of the Franklin Institute 2019-04, Vol.356 (6), p.3781-3796
• Main Authors: Lemos, Rodrigo P., Kunzler, Jonas A., Burgos B., Diego F., Souza, Mário J. de, Silva, Hugo V. L. e, Ferreira, Yroá R., Flôres, Edna L., Sander, Oliver
• Format: Article
• Language: English
• Subjects: Angle of arrival; Covariance matrix; Direction of arrival; Estimating techniques; Mathematical analysis; Matrix; Matrix algebra; Matrix methods; Norms; Plane waves; Singular value decomposition; Spectrum analysis
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2018.11.036

•A new approach to the DOA estimation based on matrix norms.•The spectrum indicates the source position.•A mathematical formulation for the relationship between the DOA angles is presented.•It generally improves the performance and the runtime compared to the previous method. SEAD method estimates the direction-of-arrival angles on an uniformly linear array based on the difference between the two largest singular values, what is called differential spectrum. Although it presented an outstanding performance, the ability to indicate the source positions was not elucidated yet. Inspired by the differential spectrum formulation we derived a total differential spectrum and found out that the matrix norm induced by the vector 2-norm of a modified spatial covariance matrix can be used to estimate the direction-of-arrival of multiple plane waves. Indeed we show that matrix norms are estimators and we propose their use instead of the singular value decomposition in SEAD-based methods. We present a general mathematical expression in order to explicit the operating principles of the proposed methods. Consequently, we were able to explain how the relation between the arriving and the search angles produces the larger peaks on the differential spectrum. To evaluate the important role played by matrix norms, a thousand experiments were carried out. They showed that the proposed approach proved to be as accurate as the previous SEAD-based methods, while providing a significant reduction on runtime. It also outperformed well-established methods like MODEX regarding the estimation error.