Doubly constrained robust capon beamformer with ellipsoidal uncertainty sets

Amir Beck, Yonina C. Eldar

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)753-758
Number of pages6
JournalIEEE Transactions on Signal Processing
Issue number2
StatePublished - Feb 2007
Externally publishedYes


  • Nonconvex quadratic optimization
  • Robust Capon beam-forming
  • S-lemma
  • Strong duality


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