Robust Beamforming via Worst-Case SINR Maximization

• Published in: IEEE transactions on signal processing 2008-04, Vol.56 (4), p.1539-1547
• Main Authors: Seung-Jean Kim, Magnani, A., Mutapcic, A., Boyd, S.P., Zhi-Quan Luo
• Format: Article
• Language: English
• Subjects: Additive noise; Algorithms; Applied sciences; Array signal processing; Beamforming; Cities and towns; Contracts; convex optimization; Covariance matrix; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Information, signal and communications theory; Interference; Mathematical analysis; Mathematical models; Maximization; Optimization; Programming; robust beamforming; Robustness; Sensor arrays; Signal and communications theory; Signal to noise ratio; Signal, noise; signal-to-interference-plus-noise ratio (SINR); Studies; Telecommunications and information theory; Uncertainty; Vectors (mathematics)
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2007.911498

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.