  It is well-known that the high computational complexity and the insufficient
samples in large-scale array signal processing restrict the real-world
applications of the conventional full-dimensional adaptive beamforming (sample
matrix inversion) algorithms. In this paper, we propose a computationally
efficient and fast adaptive beamforming algorithm under small sample support.
The proposed method is implemented by formulating the adaptive weight vector as
a linear combination of training samples plus a signal steering vector, on the
basis of the fact that the adaptive weight vector lies in the
signal-plus-interference subspace. Consequently, by using the well-known linear
kernel methods with very good small-sample performance, only a low-dimension
combination vector needs to be computed instead of the high-dimension adaptive
weight vector itself, which remarkably reduces the degree of freedom and the
computational complexity. Experimental results validate the good performance
and the computational effectiveness of the proposed methods for small samples.
