Application of Second-Order Cone Programming Theory to Robust Adaptive Beamforming

Abstract

Due to the array steering vector errors and small-sample errors and so on, the performance of the Standard Capon Beamformer (SCB) may become worse than that of the Conventional Beamformer (CBF) in practical engineering applications. Nowadays, almost all existing algorithms to improve the robustness of SCB utilize the steepest descent method, conjugate gradient method, least mean squares (LMS) method and so on. However, most of them have the slow convergence and inefficient computation. Aiming at the above problems, this paper presents a unified process to solve them by the second-order cone programming (SOCP) theory, which can not only enhance the convergence speed but also improve the calculation accuracy so as to overcome the shortcomings of the previous optimization solutions effectively. It turns out that most adaptive beamforming algorithms involve a non-convex problem which is minimization of a quadratic function subject to infinitely many non-convex quadratic constraints. In this paper, it is shown that the proposed algorithm can be reformulated in a convex form as the so-called SCOP and solved efficiently (in polynomial time) using the well-established interior point method. Finally, computer simulations show the algorithm’s excellent performance as compared with existing adaptive beamforming algorithms via the computer simulation examples.