Efficient Two-Dimensional Direction Finding Algorithm for Rectilinear Sources Under Unknown Mutual Coupling

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.

[1]  Wei Zhang,et al.  Computationally efficient 2-D DOA estimation for uniform rectangular arrays , 2014, Multidimens. Syst. Signal Process..

[2]  Fengzhong Qu,et al.  Source Estimation Using Coprime Array: A Sparse Reconstruction Perspective , 2017, IEEE Sensors Journal.

[3]  Shefeng Yan,et al.  2-D Unitary ESPRIT-Like Direction-of-Arrival (DOA) Estimation for Coherent Signals with a Uniform Rectangular Array , 2013, Sensors.

[4]  P. Stoica,et al.  The stochastic CRB for array processing: a textbook derivation , 2001, IEEE Signal Processing Letters.

[5]  W. Steeb,et al.  Matrix Calculus and Kronecker Product: A Practical Approach to Linear and Multilinear Algebra , 2011 .

[6]  Wei-Ping Zhu,et al.  RARE-based localization for mixed near-field and far-field rectilinear sources , 2019, Digit. Signal Process..

[7]  Xu Xu,et al.  DOA Estimation for Uniform Linear Array with Mutual Coupling , 2009, IEEE Transactions on Aerospace and Electronic Systems.

[8]  Yide Wang,et al.  Improved MUSIC Under the Coexistence of Both Circular and Noncircular Sources , 2008, IEEE Transactions on Signal Processing.

[9]  Wei-Ping Zhu,et al.  Mixed rectilinear sources localization under unknown mutual coupling , 2019, J. Frankl. Inst..

[10]  P. Ioannides,et al.  Uniform circular and rectangular arrays for adaptive beamforming applications , 2005, IEEE Antennas and Wireless Propagation Letters.

[11]  Lisheng Yang,et al.  Robust Joint Calibration of Mutual Coupling and Channel Gain/Phase Inconsistency for Uniform Circular Array , 2016, IEEE Antennas and Wireless Propagation Letters.

[12]  Jian Xie,et al.  DOA Estimation Under Mutual Coupling of Uniform Linear Arrays Using Sparse Reconstruction , 2019, IEEE Wireless Communications Letters.

[13]  Luxi Yang,et al.  Blind Calibration and DOA Estimation With Uniform Circular Arrays in the Presence of Mutual Coupling , 2006, IEEE Antennas and Wireless Propagation Letters.

[14]  Sergey N. Makarov,et al.  Antenna and EM Modeling with MATLAB , 2002 .

[15]  Shing-Chow Chan,et al.  DOA Estimation and Tracking of ULAs with Mutual Coupling , 2011 .

[16]  Yufeng Zhang,et al.  Autocalibration algorithm for mutual coupling of planar array , 2010, Signal Process..

[17]  Michael D. Zoltowski,et al.  Direction-finding with sparse rectangular dual-size spatial invariance array , 1998 .

[18]  M. Leong,et al.  Decoupled 2D Direction of Arrival Estimation Using Compact Uniform Circular Arrays in the Presence of Elevation-Dependent Mutual Coupling , 2010, IEEE Transactions on Antennas and Propagation.

[19]  Hua Chen,et al.  DOA Estimation Algorithm for Strictly Noncircular Sources With Unknown Mutual Coupling , 2019, IEEE Communications Letters.

[20]  Matthew Trinkle,et al.  DOA Estimation under Unknown Mutual Coupling and Multipath with Improved Effective Array Aperture , 2015, Sensors.

[21]  Z. Ye,et al.  2-D DOA Estimation in the Presence of Mutual Coupling , 2008, IEEE Transactions on Antennas and Propagation.

[22]  Shing-Chow Chan,et al.  A cumulant-based approach for direction finding in the presence of mutual coupling , 2014, Signal Process..

[23]  Michael D. Zoltowski,et al.  Closed-form 2-D angle estimation with rectangular arrays in element space or beamspace via unitary ESPRIT , 1996, IEEE Trans. Signal Process..

[24]  Guoqiang Mao,et al.  Direction-of-Arrival Estimation for Coprime Array via Virtual Array Interpolation , 2018, IEEE Transactions on Signal Processing.

[25]  Zhiming Chen,et al.  A Novel Noncircular MUSIC Algorithm Based on the Concept of the Difference and Sum Coarray , 2018, Sensors.

[26]  L. Scharf,et al.  Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals , 2010 .

[27]  Jian Liu,et al.  Direction-of-Arrival Estimation of Noncircular Signals via Sparse Representation , 2012, IEEE Transactions on Aerospace and Electronic Systems.

[28]  Chengwei Zhou,et al.  Off-Grid Direction-of-Arrival Estimation Using Coprime Array Interpolation , 2018, IEEE Signal Processing Letters.

[29]  B. C. Ng,et al.  Sensor-array calibration using a maximum-likelihood approach , 1996 .

[30]  Xin Yang,et al.  Sparsity-Inducing DOA Estimation of Coherent Signals Under the Coexistence of Mutual Coupling and Nonuniform Noise , 2019, IEEE Access.

[31]  Benjamin Friedlander,et al.  Antenna Array Manifolds for High-Resolution Direction Finding , 2018, IEEE Transactions on Signal Processing.

[32]  Qing Wang,et al.  Direction finding and mutual coupling estimation for uniform rectangular arrays , 2015, Signal Process..

[33]  Jean Pierre Delmas,et al.  MUSIC-like estimation of direction of arrival for noncircular sources , 2006, IEEE Transactions on Signal Processing.

[34]  Anthony J. Weiss,et al.  Direction Finding In The Presence Of Mutual Coupling , 1991, Twenty-Second Asilomar Conference on Signals, Systems and Computers.

[35]  Xuemin Shen,et al.  DECOM: DOA estimation with combined MUSIC for coprime array , 2013, 2013 International Conference on Wireless Communications and Signal Processing.

[36]  Tapan K. Sarkar,et al.  2-D unitary matrix pencil method for efficient direction of arrival estimation , 2006, Digit. Signal Process..

[37]  Yongshun Zhang,et al.  A Low Complexity Algorithm for Direction of Arrival Estimation With Direction-Dependent Mutual Coupling , 2020, IEEE Communications Letters.

[38]  Ahmet M. Elbir,et al.  Direction Finding in the Presence of Direction-Dependent Mutual Coupling , 2017, IEEE Antennas and Wireless Propagation Letters.

[39]  Qing Wang,et al.  Computationally Efficient Direction Finding for a Mixture of Circular and Strictly Noncircular Sources with Uniform Rectangular Arrays , 2017, Sensors.

[40]  Wei-Ping Zhu,et al.  Efficient Two-Dimensional Direction-of-Arrival Estimation for a Mixture of Circular and Noncircular Sources , 2016, IEEE Sensors Journal.

[41]  Shibo He,et al.  A Robust and Efficient Algorithm for Coprime Array Adaptive Beamforming , 2017, IEEE Transactions on Vehicular Technology.

[42]  Ling Wang,et al.  Efficient Real-Valued Rank Reduction Algorithm for DOA Estimation of Noncircular Sources Under Mutual Coupling , 2018, IEEE Access.

[43]  Tao Jin,et al.  Compressive sensing-based coprime array direction-of-arrival estimation , 2017, IET Commun..