Doubly Constrained Robust Capon Beamformer With Ellipsoidal Uncertainty Sets

The doubly constrained robust (DCR) Capon beamformer with a spherical uncertainty set was introduced and studied by Stoica and Wang. Here, we consider the generalized DCR problem (GDCR) in which the uncertainty set is an ellipsoid rather than a sphere. Although, as noted previously by Stoica and Wan...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2007-02, Vol.55 (2), p.753-758
Main Authors: Beck, A., Eldar, Y.C.
Format: Article
Language:English
Subjects:
Applied sciences
Constraints
Detection, estimation, filtering, equalization, prediction
Ellipsoids
Exact sciences and technology
Filtering
Filters
Formulations
Higher order statistics
Information, signal and communications theory
Nonconvex quadratic optimization
Optimization
Polynomials
Programming
Pulse width modulation
robust Capon beamforming
Robustness
S-lemma
Signal and communications theory
Signal processing
Signal processing algorithms
Signal, noise
strong duality
Telecommunications and information theory
Uncertainty
Working environment noise
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Summary:The doubly constrained robust (DCR) Capon beamformer with a spherical uncertainty set was introduced and studied by Stoica and Wang. Here, we consider the generalized DCR problem (GDCR) in which the uncertainty set is an ellipsoid rather than a sphere. Although, as noted previously by Stoica and Wang, this problem is nonconvex and appears to be intractable, we show that it can be solved efficiently. In fact, we prove that the GDCR beamformer can be obtained as a solution to a convex optimization problem. To this end, we first derive a strong duality result for nonconvex quadratic programs with two quadratic constraints over the complex domain. Specializing the results to our context leads to a semidefinite programming formulation of the GDCR beamformer
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2006.885729