Abstract
Digital communication signals in wireless systems may possess noncircularity, which can be used to enhance the degrees of freedom for direction-of-arrival (DOA) estimation in sensor array signal processing. On the other hand, the electromagnetic characteristics between sensors in uniform rectangular arrays (URAs), such as mutual coupling, may significantly deteriorate the estimation performance. To deal with this problem, a robust real-valued estimator for rectilinear sources was developed to alleviate unknown mutual coupling in URAs. An augmented covariance matrix was built up by extracting the real and imaginary parts of observations containing the circularity and noncircularity of signals. Then, the actual steering vector considering mutual coupling was reparameterized to make the rank reduction (RARE) property available. To reduce the computational complexity of two-dimensional (2D) spectral search, we individually estimated y-axis and x-axis direction-cosines in two stages following the principle of RARE. Finally, azimuth and elevation angle estimates were determined from the corresponding direction-cosines respectively. Compared with existing solutions, the proposed method is more computationally efficient, involving real-valued operations and decoupled 2D spectral searches into twice those of one-dimensional searches. Simulation results verified that the proposed method provides satisfactory estimation performance that is robust to unknown mutual coupling and close to the counterparts based on 2D spectral searches, but at the cost of much fewer calculations.
Highlights
Uniform rectangular array (URA), due to its versatility in providing both azimuthal and elevational coverage simultaneously, has attracted much attention in many applications, such as radar, sonar, and wireless communication [1]
Our technique proceeds through the following stages: (1) based on the rectilinearity of the signal, the received data is transformed into the real-valued domain; (2) the structure of the virtual steering vector is utilized to decouple the DOA parameter from other nuisance parameters; (3) according to the rank reduction (RARE) principle, the y-axis direction-cosine estimates can be obtained via a 1D spectral search; (4) with the y-axis direction-cosine estimates, the x-axis direction-cosine can be found through another RARE estimator, which only requires a 1D spectral search
2P + 2) covariance matrix, takes the eigenvalue decomposition (EVD) of this matrix, and performs a 2D spectral search for DOA estimation, which require a computational complexity of O(4(Mx − 2P + 2)2 (M y − 2P + 2)2 L), O(4(Mx − 2P + 2)3 (M y − 2P + 2)3 /3), and O(4(Mx − 2P + 2)2 (M y − 2P + 2)2 (360◦ /∆θ)(90◦ /∆θ)), respectively. 2D rank reduction-based method (2D-RARE) constructs a Mx My × Mx My covariance matrix, performs the EVD, calculates the rank reduction testing matrix, and performs a 2D RARE spectral search, which require a computational complexity of O(4(Mx M y )2 L), O(4(Mx M y )3 /3), and O((360◦ /∆θ)(90◦ /∆θ))(Mx M y
Summary
Uniform rectangular array (URA), due to its versatility in providing both azimuthal and elevational coverage simultaneously, has attracted much attention in many applications, such as radar, sonar, and wireless communication [1]. In [31], the authors proposed a RARE-based low complexity DOA estimation method to solve the direction-dependent mutual coupling problem. In [36], the authors proposed a blind calibration scheme for uniform circular array based on azimuthal symmetric structures in the mutual coupling matrix It only provides the azimuth angle estimates of the radiating sources, while the elevation angles are assumed to be zeros. In order to mitigate the array aperture loss problem in the auxiliary sensor-based method, Wu et al proposes a RARE-based auto-calibration method for URA [40], which can fully utilize the array observations All these planar array calibration methods require exhaustive 2D spectral searches for the DOA estimation, which is computationally demanding.
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