This article presents a two-step dynamic mode decomposition (TSDMD) approach to estimate the direction of arrival (DOA) and frequency for multiple narrow-band sources with single uniform linear array (ULA). The proposed algorithm first decomposes the receiving spatial-temporal data into temporal dynamic modes and corresponding spatial spectrum that yields the DOA information. Then the decomposed temporal dynamic modes are analyzed via the augmented DMD to retrieve the frequency information. The estimated DOAs and frequencies are automatically paired without the extra computational cost with such a temporal-spectral correlated decomposition scheme. Also, the obtained spatial spectrum distribution implies the actual number of the sources, which enables the proposed method to be used for the unknown number of sources case in wireless communication. Simulations demonstrate that the TSDMD accurately and effectively retrieves the sources' DOA and frequency information. It is found that the new approach can provide comparable performance but with less execution time compared with previous works. Our work provides a practical data-driven scheme for joint angle-frequency estimation.


Electrical and Computer Engineering

Keywords and Phrases

data-driven approach; Joint angle-frequency estimation; pairing issue; two-step dynamic mode decomposition; unknown source number

International Standard Serial Number (ISSN)

1939-9359; 0018-9545

Document Type

Article - Journal

Document Version


File Type





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

Publication Date

01 Dec 2023