DocumentCode :
82095
Title :
A Constrained Random Demodulator for Sub-Nyquist Sampling
Author :
Harms, Andrew ; Bajwa, Waheed U. ; Calderbank, R.
Author_Institution :
Dept. of Electr. Eng., Princeton Univ., Princeton, NJ, USA
Volume :
61
Issue :
3
fYear :
2013
fDate :
Feb.1, 2013
Firstpage :
707
Lastpage :
723
Abstract :
This paper presents a significant modification to the Random Demodulator (RD) of Tropp for sub-Nyquist sampling of frequency-sparse signals. The modification, termed constrained random demodulator, involves replacing the random waveform, essential to the operation of the RD, with a constrained random waveform that has limits on its switching rate because fast switching waveforms may be hard to generate cleanly. The result is a relaxation on the hardware requirements with a slight, but manageable, decrease in the recovery guarantees. The paper also establishes the importance of properly choosing the statistics of the constrained random waveform. If the power spectrum of the random waveform matches the distribution on the tones of the input signal (i.e., the distribution is proportional to the power spectrum), then recovery of the input signal tones is improved. The theoretical guarantees provided in the paper are validated through extensive numerical simulations and phase transition plots.
Keywords :
compressed sensing; demodulators; signal reconstruction; signal sampling; compressive sensing; constrained random demodulator; constrained random waveform; frequency sparse signals; phase transition plots; power spectrum; signal reconstruction; signal recovery; sub-Nyquist sampling; switching rate; Bandwidth; Demodulation; Energy measurement; Hardware; Magnetic recording; Numerical simulation; Switches; Analog-to-digital conversion; compressive sensing; random demodulator; repetition code; restricted isometry property; run-length limited sequences; sub-Nyquist sampling;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/TSP.2012.2231077
Filename :
6365846
Link To Document :
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