Robust wideband beamforming by the hybrid steepest descent method

Konstantinos Slavakis, Isao Yamada

Research output: Contribution to journalArticlepeer-review

88 Scopus citations


This paper uses the Hybrid Steepest Descent Method (HSDM) to design robust smart antennas. Several design criteria as well as robustness are mathematically described by a finite collection of closed convex sets in a real Euclidean space. Desirable beamformers are defined as points of the generalized convex feasible set which is well defined even in the case of inconsistent design criteria. A quadratic cost function is formed by the correlations of the incoming data, and the HSDM constructs a point sequence that (strongly) converges to the (unique) minimizer of the cost function over the generalized convex feasible set. Numerical examples validate the proposed design.

Original languageEnglish (US)
Pages (from-to)4511-4522
Number of pages12
JournalIEEE Transactions on Signal Processing
Issue number9
StatePublished - Sep 2007

Bibliographical note

Funding Information:
The authors would like to thank Dr. A. Georgiadis for the valuable comments on antennas and Dr. M. Fukuda for pointing out [34] and [35] and for the discussion on the computational complexity of interior point methods. The authors would also like to thank the anonymous reviewers who helped us improve the original manuscript. Finally, K. Slavakis is greatly indebted to the Japan Society for the Promotion of Science (JSPS) for supporting this work and his stay at the Tokyo Institute of Technology.


  • Convex feasibility problems
  • Fixed point theory
  • Hybrid steepest descent method
  • Wideband beamforming


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