Effective Capon Beamforming Robust to Steering Vector Errors

조향벡터 에러에 강인한 효과적인 Capon 빔 형성기법

  • Choi, Yang-Ho (Dept. of Electronic and Communication Engineering, Kangwon National University)
  • 최양호 (강원대학교 전자통신전공)
  • Received : 2011.01.28
  • Accepted : 2011.06.07
  • Published : 2011.09.25

Abstract

Adaptive arrays suffer from severe performance degradation when there are errors in the steering vector. The DCRCB (doubly constrained robust Capon beamformer) overcomes such a problem, introducing a spherical uncertainty set of the steering vector together with a norm constraint. However, in the standard DCRCB, it is a difficult task to determine the bound for the uncertainty, the radius of the spherical set, such that a near best solution is obtained. A novel beamforming method is presented which has no difficulty of the uncertainty bound setting, employing a recursive search for the steering vector. Though the basic idea of recursive search has been known, the conventional recursive method needs to set a parameter for the termination of the search. The proposed method terminates it by using distances to the signal subspace, without the need for parameter setting. Simulation demonstrates that the proposed method has better performance than the conventional recursive method and than the non-recursive standard DCRCB, even the one with the optimum uncertainty bound.

조향벡터(steering vector)에 에러가 있으면 적응 어레이(adaptive array)는 심한 성능저하를 겪게 된다. 이러한 에러로 인한 성능저하를 개선하기위해 DCRCB(doubly constrained robust Capon beamformer)에서는 벡터 norm 제한아래 구체 불확실 집합(spherical uncertainty set) 내의 벡터 중 출력전력을 최대로 하는 벡터를 조향벡터(steering vector)로 사용한다. 좋은 성능 개선을 위해서 불확실 집합의 반경, 즉 불확실 한계를 적절히 설정해야 하는 문제가 있다. 본 논문에서는 이를 해결하기 위해 반복탐색을 통해 조향벡터를 구하는 방식을 제안한다. 기존의 알려진 반복탐색 방식에서는 반복 종료를 위해 어떤 기준값을 결정해야 하는데, 이에 따른 어려움이 있다. 제안방식에서는 추정된 벡터와 신호부공간 거리가 더 이상 작아 지지 않으면 반복을 종료하며, 값 설정과 관련된 어떤 어려움도 없다. 시뮬레이션 결과에 따르면, 제안방식은 기존반복방식 그리고 최적의 불확실 한계로 설정된 표준 DCRCB 보다도 우수한 성능을 보여준다.

References

  1. M. Wax and Y. Anu, "Performance analysis of the minimum variance beamformer in the presence of steering vector errors," IEEETrans. Signal Process., vol. 44, no. 4, pp. 938-947, Apr. 1996. https://doi.org/10.1109/78.492546
  2. R. T. Compton, Jr., "The effect of random steering vector errors in the Applebaum adaptive array," IEEE Trans. Aerosp. Electron. Syst.,vol. 18, no. 5, pp. 392-400, Sept. 1982.
  3. Y.-H. Choi, "Interference subspace approximation based adaptive beamforming in the presence of a desired Signal," IEE Proc. Radar, Sonar and Navig., vol. 152 no. 4, pp. 232-238, Aug. 2005. https://doi.org/10.1049/ip-rsn:20059057
  4. J. Li, P. Stoica, and Z.-S. Wang,, "Doubly constrained robust Capon beamforming," IEEE Trans. Signal Process., vol. 52, no. 9, pp.2407-2423, Sept. 2004. https://doi.org/10.1109/TSP.2004.831998
  5. S. E. Nai, W. Ser, Z. L. Yu, and S. Rahardja, "Iterative Robust Capon Beamformer," in Proc IEEE Statistical Signal Processing (SSP'07) Workshop, Madison, WI, Aug. 2007, pp. 542-545.
  6. J. Li, P. Stoica, and Z. Wang, "On robust Capon beamforming and diagonal loading," IEEE Trans. Signal Process., vol.51, no.7, pp. 1702-1715, Jul. 2003. https://doi.org/10.1109/TSP.2003.812831
  7. S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge UK: Cambridge University Press, 2004.