  The robust adaptive beamforming (RAB) problem is considered via the
worst-case signal-to-interference-plus-noise ratio (SINR) maximization over
distributional uncertainty sets for the random interference-plus-noise
covariance (INC) matrix and desired signal steering vector. The distributional
uncertainty set of the INC matrix accounts for the support and the positive
semidefinite (PSD) mean of the distribution, and a similarity constraint on the
mean. The distributional uncertainty set for the steering vector consists of
the constraints on the known first- and second-order moments. The RAB problem
is formulated as a minimization of the worst-case expected value of the SINR
denominator achieved by any distribution, subject to the expected value of the
numerator being greater than or equal to one for each distribution. Resorting
to the strong duality of linear conic programming, such a RAB problem is
rewritten as a quadratic matrix inequality problem. It is then tackled by
iteratively solving a sequence of linear matrix inequality relaxation problems
with the penalty term on the rank-one PSD matrix constraint. To validate the
results, simulation examples are presented, and they demonstrate the improved
performance of the proposed robust beamformer in terms of the array output
SINR.
