Robust Adaptive Beamforming for General-Rank Signal Model with Positive Semi-Definite Constraint via POTDC

TL;DR

This paper introduces a novel polynomial-time DC algorithm for robust adaptive beamforming with a positive semi-definite constraint, providing a potentially globally optimal solution and outperforming existing methods.

Contribution

The paper rigorously solves a non-convex DC problem in RAB, proposing a new POTDC algorithm that suggests global optimality and improves performance over prior approaches.

Findings

The proposed method achieves superior beamforming performance.

The solution satisfies KKT optimality conditions.

Evidence suggests the solution is globally optimal.

Abstract

The robust adaptive beamforming (RAB) problem for general-rank signal model with an additional positive semi-definite constraint is considered. Using the principle of the worst-case performance optimization, such RAB problem leads to a difference-of-convex functions (DC) optimization problem. The existing approaches for solving the resulted non-convex DC problem are based on approximations and find only suboptimal solutions. Here we solve the non-convex DC problem rigorously and give arguments suggesting that the solution is globally optimal. Particularly, we rewrite the problem as the minimization of a one-dimensional optimal value function whose corresponding optimization problem is non-convex. Then, the optimal value function is replaced with another equivalent one, for which the corresponding optimization problem is convex. The new one-dimensional optimal value function is minimized iteratively via polynomial time DC (POTDC) algorithm.We show that our solution satisfies the Karush-Kuhn-Tucker (KKT) optimality conditions and there is a strong evidence that such solution is also globally optimal. Towards this conclusion, we conjecture that the new optimal value function is a convex function. The new RAB method shows superior performance compared to the other state-of-the-art general-rank RAB methods.