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tdb-dasp-2009 - APPLICATION OF COMPRESSIVE SENSING TO THE...

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APPLICATION OF COMPRESSIVE SENSING TO THE DESIGN OF WIDEBAND SIGNAL ACQUISITION RECEIVERS John Treichler Applied Signal Technology, Inc. Sunnyvale, California Mark Davenport, Richard Baraniuk Rice University Houston, Texas ABSTRACT 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 un- known 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 com- pare 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. 1. INTRODUCTION Compressive sensing (CS) [1–3] exploits the sparsity present in many signals to reduce the number of measurements needed for acqusition. It has been shown theoretically that, under the right set of circumstances, CS can dramatically reduce the number of measurements needed to detect, char- acterize, and/or extract signals, and therefore can reduce by the same factor the storage and/or transmission rate needed to handle the signal at the sensing point. Conversely, signals with much larger bandwidths could be accepted by existing acquisition systems. If these reductions were found to pro- portionally reduce the size, weight, and power consumption (SWAP) and cost of operational signal acquisition systems, then the practical impact could be transformative. This paper examines the potential practicality of CS to build signal acquisition receivers for the specific, but impor- tant, case where the receiver’s input signal takes the form of a sparse combination of narrowband signals of unknown fre- Front-End Sensor Forwarding Link Outputs Back-End Processor Fig. 1 . A wideband signal acquisition receiver. quencies that can appear anywhere in a broad spectral band. Our objective here is to examine the specific application of the acquisition receiver, thus providing the opportunity to test the robustness of CS techniques to imperfect match with its underlying theoretical assumptions.
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