  We develop a new approach to robust adaptive beamforming in the presence of
signal steering vector errors. Since the signal steering vector is known
imprecisely, its presumed (prior) value is used to find a more accurate
estimate of the actual steering vector, which then is used for obtaining the
optimal beamforming weight vector. The objective for finding such an estimate
of the actual signal steering vector is the maximization of the beamformer
output power, while the constraints are the normalization condition and the
requirement that the estimate of the steering vector does not converge to an
interference steering vector. Our objective and constraints are free of any
design parameters of non-unique choice. The resulting optimization problem is a
non-convex quadratically constrained quadratic program, which is NP hard in
general. However, for our problem we show that an efficient solution can be
found using the semi-definite relaxation technique. Moreover, the strong
duality holds for the proposed problem and can also be used for finding the
optimal solution efficiently and at low complexity. In some special cases, the
solution can be even found in closed-form. Our simulation results demonstrate
the superiority of the proposed method over other previously developed robust
adaptive beamforming methods for several frequently encountered types of signal
steering vector errors.
