A geometrical approach to robust minimum variance beamforming

This paper presents a highly efficient geometrical approach for designing robust minimum variance (RMV) beamformers against uncertainties in the array steering vector. Instead of the conventional approach of modeling the uncertainty region by a convex closed space, the proposed algorithm exploits the optimization constraint and shows that optimization only needs to be done on the intersection of a hyperplane and a second-order cone (SOC). The problem can then be cast as a second-order cone programming (SOCP) problem so as to enjoy the high efficiency of a class of interior point algorithms. A general case of modeling the uncertainties of an array using complex-plane trapezoids is investigated. The efficiency and tightness of the proposed method over other schemes are demonstrated with numerical examples.