This article presents a joint two-dimensional dynamic mode decomposition (JTDDMD) approach to estimate the azimuth angle, elevation angle, and frequency for multiple narrowband sources using the L-shaped array. According to the placement position of different coordinate axes of the receiving antenna in the array, i.e., x- or z-axis, the received signal is divided into two datasets. Two-dimensional dynamic mode decomposition (TDDMD), the sub algorithm of JTDDMD, is used twice to deal with these two datasets separately. Through the analysis of the x-axis subarray received signal using TDDMD, the electrical angle in the x-direction and frequency are obtained with automatic pairing. Likewise, the z-axis data analysis reveals the paired z-direction electrical angle and frequency. Then, the x- and z-direction electrical angles are linked by the frequency information in the two sets of paired parameters. Finally, the paired elevation angle, azimuth angle, and frequency are extracted through the inversion relationship within the L-shaped array. In addition, because the proposed method can determine the number of signal sources in the estimation process, it is suitable for the estimation cases where the number of signal sources is not known in advance. Several numerical experiments benchmark the proposed method. It is found that compared with previous similar methods, JTDDMD can achieve similar results with less execution time. Consequently, this article can serve as an effective tool for jointly estimating the direction of arrivals and frequency.


Electrical and Computer Engineering


Research Grants Council, University Grants Committee, Grant 2619006

Keywords and Phrases

Azimuth; data-driven approach; elevation and frequency estimation; joint two-dimensional dynamic mode decomposition (JTDDMD); L-shaped array; pair-matching problem; source number estimation

International Standard Serial Number (ISSN)

1557-9603; 0018-9251

Document Type

Article - Journal

Document Version


File Type





© 2024 Institute of Electrical and Electronics Engineers, All rights reserved.

Publication Date

01 Aug 2023