Nyström-Based 2D DOA Estimation for URA: Bridging Performance–Complexity Trade-Offs

Liping Yuan, Ke Wang and Fengkai Luan ()
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Liping Yuan: School of Information Engineering, Wuhan University of Technology, Wuhan 430070, China
Ke Wang: School of Information Engineering, Wuhan University of Technology, Wuhan 430070, China
Fengkai Luan: School of Information Engineering, Wuhan University of Technology, Wuhan 430070, China

Mathematics, 2025, vol. 13, issue 19, 1-13

Abstract: To address the computational efficiency challenges in two-dimensional (2D) direction-of-arrival (DOA) estimation, a two-stage framework integrating the Nyström approximation with subspace decomposition techniques is proposed in this paper. The methodology strategically integrates the Nyström approximation with subspace decomposition techniques to bridge the critical performance–complexity trade-off inherent in high-resolution parameter estimation scenarios. In the first stage, the Nyström method is applied to approximate the signal subspace while simultaneously enabling construction of a reduced rank covariance matrix, which effectively reduces the computational complexity compared with eigenvalue decomposition (EVD) or singular value decomposition (SVD). This innovative approach efficiently derives two distinct signal subspaces that closely approximate those obtained from the full-dimensional covariance matrix but at substantially reduced computational cost. The second stage employs a sophisticated subspace-based estimation technique that leverages the principal singular vectors associated with these approximated subspaces. This process incorporates an iterative refinement mechanism to accurately resolve the paired azimuth and elevation angles comprising the 2D DOA solution. With the use of the Nyström approximation and reduced rank framework, the entire DOA estimation process completely circumvents traditional EVD/SVD operations. This elimination constitutes the core mechanism enabling substantial computational savings without compromising estimation accuracy. Comprehensive numerical simulations rigorously demonstrate that the proposed framework maintains performance competitive with conventional high-complexity estimators while achieving significant complexity reduction. The evaluation benchmarks the method against multiple state-of-the-art DOA estimation techniques across diverse operational scenarios, confirming both its efficacy and robustness under varying signal conditions.

Keywords: DOA estimation; Nyström method; uniform rectangular array; reduced rank (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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