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SDP-Based Adaptive Beamforming with a Direction Range

방향범위를 이용한 SDP 기반 적응 빔 형성

  • Choi, Yang-Ho (Kangwon National University, Dept. of Electrical and Electronic Engineering)
  • Received : 2013.12.30
  • Accepted : 2014.04.03
  • Published : 2014.09.30

Abstract

Adaptive arrays can minimize contributions from interferences incident onto an sensor array while preserving a signal the direction vector of which corresponds to the array steering vector to within a scalar factor. If there exist errors in the steering vector, severe performance degradation can be caused since the desired signal is misunderstood as an interference by the array. This paper presents an adaptive beamforming method which is robust against steering vector errors, exploiting a range of the desired signal direction. In the presented method, an correlation matrix of array response vectors is obtained through integration over the direction range and a minimization problem is formulated using some eigenvectors of the correlation matrix such that a more accurate steering vector than initially given one can be found. The minimization problem is transformed into a relaxed SDP (semidefinite program) problem, which can be effectively solved since it is a sort of convex optimization. Simulation results show that the proposed method outperforms existing ones such as ORM (outside-range-based method) and USM (uncertainty-based method).

적응 어레이는 조향벡터를 이용하여 조향벡터 방향의 신호는 보호하면서 간섭신호를 제거한다. 조향벡터에 에러가 있으면 원하는 신호도 감쇠되어 SINR(signal-to-interference-plus-noise ratio) 성능 저하를 가져온다. 본 논문에서는 원하는 신호의 도래범위를 이용하여 조향벡터 에러에 강인한 적응 빔 형성 기법을 제시한다. 제시된 기법에서는 도래범위에서 어레이 응답벡터에 관한 상관행렬을 적분을 통해 구하고, 이 상관행렬의 고유벡터 일부를 이용하여 조향벡터를 구하기 위한 최소화 문제를 정의한다. 이 최소화 문제를 컨벡스 최적화(convex optimization)의 일종인 SDP(semidefinite program) 문제로 완화하여 효과적으로 해결한다. 시뮬레이션 결과에 따르면, 제안방식은 기존의 강인한 빔 형성 방식인 ORM(outside-range-based method), USM(uncertainty-based method)보다 우수한 SINR 성능을 나타낸다.

Keywords

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