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