Beamforming with Uncertain Weights
A. Mutapcic, S.-J. Kim, and S. Boyd
IEEE Signal Processing Letters, 14(5):348-351, May 2007.
In this letter, we show that worst-case robust beamforming, with uncertain weights subject to multiplicative variations, can be cast as a convex optimization problem. We interpret this robust beamforming as a weighted complex l1-regularization, and show that it can be solved with the same computational complexity as nominal beamforming, ignoring the variations. We derive a simple lower bound on how much worse the robust beamformer will be compared to the nominal beamformer solution with no weight uncertainty. We demonstrate the robust approach with a simple narrowband beamformer.