  An important receiver operation is to detect the presence specific preamble
signals with unknown delays in the presence of scattering, Doppler effects and
carrier offsets. This task, referred to as "link acquisition", is typically a
sequential search over the transmitted signal space. Recently, many authors
have suggested applying sparse recovery algorithms in the context of similar
estimation or detection problems. These works typically focus on the benefits
of sparse recovery, but not generally on the cost brought by compressive
sensing. Thus, our goal is to examine the trade-off in complexity and
performance that is possible when using sparse recovery. To do so, we propose a
sequential sparsity-aware compressive sampling (C-SA) acquisition scheme, where
a compressive multi-channel sampling (CMS) front-end is followed by a sparsity
regularized likelihood ratio test (SR-LRT) module.
  The proposed C-SA acquisition scheme borrows insights from the models studied
in the context of sub-Nyquist sampling, where a minimal amount of samples is
captured to reconstruct signals with Finite Rate of Innovation (FRI). In
particular, we propose an A/D conversion front-end that maximizes a well-known
probability divergence measure, the average Kullback-Leibler distance, of all
the hypotheses of the SR-LRT performed on the samples. We compare the proposed
acquisition scheme vis-\`{a}-vis conventional alternatives with relatively low
computational cost, such as the Matched Filter (MF), in terms of performance
and complexity.
