analog-dcas-2006 - Analog-to-Information Conversion via...

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Analog-to-Information Conversion via Random Demodulation Sami Kirolos, Jason Laska, Michael Wakin, Marco Duarte, Dror Baron Tamer Ragheb, Yehia Massoud, Richard Baraniuk Dept. of Electrical and Computer Engineering Rice University Houston, TX Abstract — Many problems in radar and communication signal processing involve radio frequency (RF) signals of very high bandwidth. This presents a serious challenge to systems that might attempt to use a high-rate analog-to-digital converter (ADC) to sample these signals, as prescribed by the Shan- non/Nyquist sampling theorem. In these situations, however, the information level of the signal is often far lower than the actual bandwidth, which prompts the question of whether more efficient schemes can be developed for measuring such signals. In this paper we propose a system that uses modulation, filtering, and sampling to produce a low-rate set of digital measurements. Our “analog-to-information converter” (AIC) is inspired by the recent theory of Compressive Sensing (CS), which states that a discrete signal having a sparse representation in some dictionary can be recovered from a small number of linear projections of that signal. We generalize the CS theory to continuous-time sparse signals, explain our proposed AIC system in the CS context, and discuss practical issues regarding implementation. I. INTRODUCTION The power, stability, and low cost of digital signal process- ing (DSP) have pushed the analog-to-digital converter (ADC) increasingly close to the front-end of many important sensing, imaging, and communication systems. Unfortunately, many systems, especially those operating in the radio frequency (RF) bands, severely stress current ADC technologies. For example, some important radar and communications applications would be best served by an ADC sampling over 5 GSample/s and resolution of over 20 bits, a combination that greatly exceeds current capabilities. It could be decades before ADCs based on current technol- ogy will be fast and precise enough for these applications. And even after better ADCs become available, the deluge of data will swamp back-end DSP algorithms. For example, sampling a 1GHz band using 2 GSample/s at 16 bits-per- sample generates data at a rate of 4GB/s, enough to fill a modern hard disk in roughly one minute. In a typical application, only a tiny fraction of this information is actually relevant; the wideband signals in many RF applications often have a large bandwidth but a small “information rate” [1]. Fortunately, recent developments in mathematics and signal processing have uncovered a promising approach to the ADC bottleneck that enables sensing at a rate comparable to the signal’s information rate. A new field, known as Compressive Sensing (CS) [2], [3], establishes mathematically that a rela- tively small number of non-adaptive, linear measurements can harvest all of the information necessary to faithfully recon- struct sparse or compressible signals. An intriguing aspect of
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This note was uploaded on 05/28/2010 for the course EE EE564 taught by Professor Runyiyu during the Spring '10 term at Eastern Mediterranean University.

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analog-dcas-2006 - Analog-to-Information Conversion via...

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