  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.
