Abstract

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 probabil-ity 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-à-vis conventional alternatives with relatively low computational cost, such as the Matched Filter (MF), in terms of performance and complexity. Our experiments suggest that one can use the proposed C-SA acquisition scheme to scale down the implementation cost with greater flexibility than MF architectures. However, we find that they both have overall complexities that scale linearly with the search space despite of the compressed samples. Furthermore, it is shown that compressive measurements used in the SR-LRT at low SNR lead to a performance loss as one could expect given that they use less observations, while at high SNR on the other hand, the SR-LRT has better performance in spite of the compression.