  In this paper, we address the problem of robust adaptive beamforming of
signals received by a linear array. The challenge associated with the
beamforming problem is twofold. Firstly, the process requires the inversion of
the usually ill-conditioned covariance matrix of the received signals.
Secondly, the steering vector pertaining to the direction of arrival of the
signal of interest is not known precisely. To tackle these two challenges, the
standard capon beamformer is manipulated to a form where the beamformer output
is obtained as a scaled version of the inner product of two vectors. The two
vectors are linearly related to the steering vector and the received signal
snapshot, respectively. The linear operator, in both cases, is the square root
of the covariance matrix. A regularized least-squares (RLS) approach is
proposed to estimate these two vectors and to provide robustness without
exploiting prior information. Simulation results show that the RLS beamformer
using the proposed regularization algorithm outperforms state-of-the-art
beamforming algorithms, as well as another RLS beamformers using a standard
regularization approaches.
