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On the Relationship Between Robust Minimum Variance Beamformers With Probabilistic and Worst-Case Distortionless Response Constraints

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3 Author(s)
Vorobyov, S.A. ; Dept. of Electr. & Comput. Eng., Univ. of Alberta, Edmonton, AB ; Haihua Chen ; Gershman, A.B.

An interesting relationship between the probability-constrained and worst-case optimization based robust minimum variance (MV) beamformers has been discovered. It is shown that both in the cases of circularly symmetric Gaussian and worst-case distributions of the steering vector mismatch, the probability-constrained robust MV beamforming problem can be tightly approximated as a convex second-order cone programming (SOCP) problem. The latter problem is mathematically equivalent to that resulting from the deterministic worst-case approach and, therefore, probability-constrained beamformers can be interpreted and implemented using their deterministic worst-case counterparts. However, an important advantage of the developed probability-constrained MV beamformers with respect to their standard worst-case counterparts is that the former approaches enable to explicitly quantify the parameters of the uncertainty region in terms of the beamformer outage probability.

Published in:

Signal Processing, IEEE Transactions on  (Volume:56 ,  Issue: 11 )

Date of Publication:

Nov. 2008

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