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-
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conventional alternatives with relatively low computational cost, such as the Matched
Filter (MF), in terms of performance and complexity.