Array Signal Processing with Robust Rejection Constraints via Second-Order Cone Programming

We consider the array signal processing problem of choosing the weight vector to minimize noise power, subject to a unit array gain for the desired wave, and subject to rejection constraints on interferences. We model the variations in the array response with ellipsoidal uncertainty, and take the worst-case robust optimization approach, i.e., we require the constraints to hold for all possible data in the uncertainty ellipsoid. We show that this robust array signal processing problem can be formulated as a second-order cone program, which interior-point algorithms can solve efficiently. The robust solution is demonstrated with an example.