  In this paper, we consider signals with a low-rank covariance matrix which
reside in a low-dimensional subspace and can be written in terms of a finite
(small) number of parameters. Although such signals do not necessarily have a
sparse representation in a finite basis, they possess a sparse structure which
makes it possible to recover the signal from compressed measurements. We study
the statistical performance bound for parameter estimation in the low-rank
signal model from compressed measurements. Specifically, we derive the
Cramer-Rao bound (CRB) for a generic low-rank model and we show that the number
of compressed samples needs to be larger than the number of sources for the
existence of an unbiased estimator with finite estimation variance. We further
consider the applications to direction-of-arrival (DOA) and spectral estimation
which fit into the low-rank signal model. We also investigate the effect of
compression on the CRB by considering numerical examples of the DOA estimation
scenario, and show how the CRB increases by increasing the compression or
equivalently reducing the number of compressed samples.
