Robust beamforming via worst-case SINR maximization

Seung Jean Kim, Alessandro Magnani, Almir Mutapcic, Stephen P. Boyd, Zhi Quan Luo

Research output: Contribution to journalArticlepeer-review

89 Scopus citations


Minimum variance beamforming, which uses a weight vector that maximizes the signal-to-interference-plus-noise ratio (SINR), is often sensitive to estimation error and uncertainty in the parameters, steering vector and covariance matrix. Robust beamforming attempts to systematically alleviate this sensitivity by explicitly incorporating a data uncertainty model in the optimization problem. In this paper, we consider robust beamforming via worst-case SINR maximization, that is, the problem of finding a weight vector that maximizes the worst-case SINR over the uncertainty model. We show that with a general convex uncertainty model, the worst-case SINR maximization problem can be solved by using convex optimization. In particular, when the uncertainty model can be represented by linear matrix inequalities, the worst-case SINR maximization problem can be solved via semidefinite programming. The convex formulation result allows us to handle more general uncertainty models than prior work using a special form of uncertainty model. We illustrate the method with a numerical example.

Original languageEnglish (US)
Pages (from-to)1539-1547
Number of pages9
JournalIEEE Transactions on Signal Processing
Issue number4
StatePublished - Apr 1 2008


  • Beamforming
  • Convex optimization
  • Robust beamforming
  • Signal-to-interference-plus-noise ratio (SINR)

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