Robust Capon Beamforming via Refining Steering Vector Based on Fractional Semidefinite Relaxation

Robust adaptive beamforming is a very important technique in array processing applications. In this paper, we propose a new design of robust Capon beamformer via refining the signal steering vector. Specifically, with an approximate range of the direction of the signal of interest (SOI) and the norm bound of allowable error on the presumed steering vector, we formulate a novel objective function in the form of quadratic fractional programming. This objective function aims at maximizing the output power of the beamformer and simultaneously focusing the SOI power at the array output as much as possible. Such an objective promotes the estimated steering vector approaching the true one and prevents the estimate converging to the interference subspace. It turns out that the proposed design is a non-convex fractional quadratically constrained quadratic programming problem, which is NP-hard and difficult to solve. We efficiently and exactly solve the problem with the aid of fractional semidefinite relaxation technique. Finally, numerical examples are provided to demonstrate the superiority of the derived beamformer over several existing state-art-of robust adaptive beamformers.