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.
Bibliographical noteFunding Information:
Manuscript received May 29, 2007; revised August 20, 2007. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Andreas Jakobsson. The research reported here was supported in part by the National Science Foundation under grants 0423905 and (through October 2005) 0140700, by the Air Force Office of Scientific Research under grant F49620-01-1-0365, by MARCO Focus center for Circuit & System Solutions contract 2003-CT-888, and by MIT DARPA contract N00014-05-1-0700.
- Convex optimization
- Robust beamforming
- Signal-to-interference-plus-noise ratio (SINR)