  This short note addresses the design of a partially adaptive filter to
retrieve a signal of interest in the presence of strong low-rank interference
and thermal noise. We consider a generalized sidelobe canceler implementation
where the dimension-reducing transformation is build resorting to ideas
borrowed from randomized matrix approximations. More precisely, the main
subspace of the auxiliary data $Z$ is approximated by $Z\Omega$ where $\Omega$
is a random matrix or a matrix that picks at random columns of $Z$. These
transformations do not require eigenvalue decomposition, yet they provide
performance similar to those of a principal component filter.
