Robust Wideband Beamforming by the Hybrid Steepest Descent Method

TLDR

The study applies the hybrid steepest descent method to design robust smart antennas. The authors formulate design criteria and robustness as closed convex sets, define desirable beamformers as points in the generalized convex feasible set, and use a quadratic cost function of data correlations that the hybrid steepest descent method iteratively minimizes, converging to the unique solution. Numerical simulations confirm the effectiveness of the proposed design.

Abstract

This paper uses the hybrid steepest descent method (HSDM) to design robust smart antennas. Several design criteria as well as robustness are mathematically described by a finite collection of closed convex sets in a real Euclidean space. Desirable beamformers are defined as points of the generalized convex feasible set which is well defined even in the case of inconsistent design criteria. A quadratic cost function is formed by the correlations of the incoming data, and the HSDM constructs a point sequence that (strongly) converges to the (unique) minimizer of the cost function over the generalized convex feasible set. Numerical examples validate the proposed design.