PPubMed1 May 2026

Two-Dimensional DOA Estimation of Coherent Sources Based on Uniform Linear Electromagnetic Vector Sensor Array

Jingxiang Zhang, Xiang Lan, Xianpeng Wang, Wenchao Li

Abstract

In this paper, the two-dimensional DOA estimation problem of coherent signals in an electromagnetic vector sensor (EMVS) array is studied. A new decorrelation method is proposed by extending the multiple-Toeplitz matrices reconstruction (MTOEP) method to a polarization sensitive array. After that, a closed-form solution is derived based on the ESPRIT algorithm for DOA and polarization parameter estimation. Pairing matching is based on the correspondence between eigenvectors obtained by independent eigen-decomposition. Simulation results verify the effectiveness of the proposed work and show the proposed algorithm has better performance than the traditional spatial smoothing (SS) method, especially in scenarios with low signal-to-noise ratios (SNRs) and small angular separations.

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A new BMTOEP‑ESPRIT algorithm decorrelates coherent signals in uniform linear EMVS arrays, yielding lower RMSE and higher resolution than spatial smoothing, especially at low SNR and tight angular separations.

What’s new

i.Proposed a block multiple‑Toeplitz matrix reconstruction (BMTOEP) decorrelation method for uniform linear electromagnetic vector sensor arrays.
ii.Derived closed‑form ESPRIT‑based estimators for 2‑D DOA and polarization parameters of coherent sources.
iii.Introduced an eigenvector‑based pairing strategy to correctly associate multidimensional parameters.
iv.Demonstrated superior RMSE and resolution performance over spatial smoothing and other benchmarks in simulations.

How they did it

First, the received data are pre‑processed with BMTOEP to reconstruct a full‑rank block‑Toeplitz covariance matrix and remove signal coherency. Next, the ESPRIT algorithm is applied twice to obtain three rotational‑invariant factors, from which closed‑form expressions yield the elevation, azimuth, and polarization parameters. Finally, eigen‑vector matching aligns the estimated parameters.

What they found

≈10% RMSE reduction at 3 dB SNR compared with the FSS method.
≈12 percentage‑point increase in successful resolution probability at an 8° angular separation.
Overall estimation error reduced by about 16% across tested scenarios.
All algorithms reach 100% success when angular separation exceeds 12°, while the proposed method maintains the highest success rate at smaller separations.

Caveats

✕Algorithm assumes a uniform linear array and relies on shift‑invariance; extensions to other geometries require additional processing.
✕Mutual coupling effects of the EMVS are not modeled, which may degrade performance in practical systems.
✕Performance on real‑world measured data has not been validated yet.

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