Multidimensional Systems and Signal Processing

, Volume 30, Issue 1, pp 465–491 | Cite as

DOA estimation with double L-shaped array based on Hadamard product and joint diagonalization in the presence of sensor gain-phase errors

  • Weiwei HuEmail author
  • Guozheng Xu


A method with double L-shaped array for direction-of-arrival (DOA) estimation in the presence of sensor gain-phase errors is presented. The reason for choosing double L-shaped array is that the shared elements between sub-arrays are the most and rotation invariant property can be applied for this array. The proposed method is introduced as follows. (1) If the number of signal is one, first the gain errors are estimated and removed with the diagonal of the covariance matrix of the array output. Then the array is rotated by an unknown angle and DOA can be estimated with the relationship between signal subspace and steering vector of signal. (2) If signals are more than one, the method for eliminating gain errors is the same with the previous case, and then the phase errors are removed by the Hadamard product of the (cross) covariance matrix and its conjugate. After the errors are eliminated, the DOAs can be estimated by rotation invariant property and orthogonal joint diagonalization for the Hadamard product. This method requires neither calibrated sources nor multidimensional parameter search, and its performance is independent of the phase errors. Simulation results demonstrate the effectiveness of the proposed method.


Array signal processing DOA estimation Double L-shaped array Gain-phase errors Hadamard product Joint diagonalization 



The authors would like to thank the anonymous reviewers for their many insightful comments and suggestions, which helped improve the quality and readability of this paper.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of AutomationNanjing University of Posts and TelecommunicationsNanjingPeople’s Republic of China

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