  We propose several sampling architectures for the efficient acquisition of an
ensemble of correlated signals. We show that without prior knowledge of the
correlation structure, each of our architectures (under different sets of
assumptions) can acquire the ensemble at a sub-Nyquist rate. Prior to sampling,
the analog signals are diversified using simple, implementable components. The
diversification is achieved by injecting types of "structured randomness" into
the ensemble, the result of which is subsampled. For reconstruction, the
ensemble is modeled as a low-rank matrix that we have observed through an
(undetermined) set of linear equations. Our main results show that this matrix
can be recovered using standard convex programming techniques when the total
number of samples is on the order of the intrinsic degree of freedom of the
ensemble --- the more heavily correlated the ensemble, the fewer samples are
needed.
  To motivate this study, we discuss how such ensembles arise in the context of
array processing.
