Application of compressive sensing to the design of wideband signal acquisition receivers

Compressive sensing (CS) exploits the sparsity present in many signals to reduce the number of measurements needed for digital acquisition. With this reduction would come, in theory, commensurate reductions in the size, weight, power consumption, and/or monetary cost of both signal sensors and any associated communication links. This paper examines the use of CS in environments where the input signal takes the form of a sparse combination of narrowband signals of unknown frequencies that appear anywhere in a broad spectral band. We formulate the problem statement for such a receiver and establish a reasonable set of requirements that a receiver should meet to be practically useful. The performance of a CS receiver for this application is then evaluated in two ways: using the applicable (and still evolving) CS theory and using a set of computer simulations carefully constructed to compare the CS receiver against the performance expected from a conventional implementation. This sets the stage for work in a sequel that will use these results to produce comparisons of the size, weight, and power consumption of a CS receiver against an exemplar of a conventional design.