Recursive Updating Algorithm for Robust Adaptive Beamforming in a Uniform Circular Array

  • Xin SongEmail author
  • Xiuwei Han
  • Feng Wang
  • Fengming Xin


When the phase-mode transformation technique is used in a uniform circular array, its output performance is known to degrade owing to the approximations applied to the formulation. In this paper, we develop a robust recursive updating algorithm based on the worst-case performance optimization and phase-mode transformation in the uniform circular array, which provides efficient robustness not only against the signal steering vector mismatches, but also against the transformation errors. The proposed algorithm belongs to the class of the diagonal loading technique and the transformation matrix belongs to a certain ellipsoid set. The weight vector is updated by the Lagrange multiplier method, in which the parameters are derived simply. The proposed algorithm has a closed-form solution, in which we analyse the reasonable ranges of two key parameters. The convergence performance and the output SINR performance are also analysed. In additional, the implementation complexity costs of the proposed algorithm and MVDR algorithm are presented in this paper. Our robust algorithm has a low implementation complexity cost and achieves the mean output array SINR consistently close to the optimal one. Simulation results are presented to compare the performances of our algorithm with the conventional algorithms.


Worst-case performance optimization Steering vector mismatches Robust adaptive beamforming Phase-mode transformation 



The authors thank the anonymous reviewers for their insightful comments that helped improve the quality of this study. This work was supported by the National Nature Science Foundation of China under Grant no. 61473066 and no. 61601109, and the Fundamental Research Funds for the Central Universities under Grant No. N152305001.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Engineering Optimization and Smart Antenna InstituteNortheastern UniversityQinhuangdaoChina
  2. 2.State Grid Ningxia Information & Communication CompanyXingqin DistrictChina

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