From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum....

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Published in:	IEEE journal of selected topics in signal processing Vol. 4; no. 2; pp. 375 - 391
Main Authors:	Mishali, Moshe, Eldar, Yonina C.
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.04.2010 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Analog-to-digital conversion (ADC) Bandwidth compressive sampling (CS) Computation Converters Digital Frequency Hardware infinite measurement vectors (IMV) Low pass filters multiband sampling Nonuniform Numerical simulation Robust stability Sampling Sampling methods Signal sampling spectrum-blind reconstruction Studies sub-Nyquist sampling Sufficient conditions Theory Wideband
ISSN:	1932-4553, 1941-0484
Online Access:	Get full text
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Abstract	Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then low-pass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, real-time performance for signals with time-varying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of state-of-the-art analog conversion technologies such as interleaved converters.
AbstractList	Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then low-pass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, real-time performance for signals with time-varying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of state-of-the-art analog conversion technologies such as interleaved converters.
Author	Mishali, Moshe Eldar, Yonina C.
Author_xml	– sequence: 1 givenname: Moshe surname: Mishali fullname: Mishali, Moshe email: moshiko@tx.technion.ac.il organization: Technion-Israel Institute of Technology, Haifa, Israel – sequence: 2 givenname: Yonina C. surname: Eldar fullname: Eldar, Yonina C. email: yonina@ee.technion.ac.il organization: Technion-Israel Institute of Technology, Haifa, Israel
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Snippet	Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging...
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SubjectTerms	Analog-to-digital conversion (ADC) Bandwidth compressive sampling (CS) Computation Converters Digital Frequency Hardware infinite measurement vectors (IMV) Low pass filters multiband sampling Nonuniform Numerical simulation Robust stability Sampling Sampling methods Signal sampling spectrum-blind reconstruction Studies sub-Nyquist sampling Sufficient conditions Theory Wideband
Title	From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals
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