A Constrained Random Demodulator for Sub-Nyquist Sampling

DOI10.1109/TSP.2012.2231077zbMATH Open1393.94685arXiv1204.0839MaRDI QIDQ4578391

Waheed U. Bajwa, Andrew Harms, Robert Calderbank

Publication date: 22 August 2018

Published in: IEEE Transactions on Signal Processing (Search for Journal in Brave)

Abstract: This paper presents a significant modification to the Random Demodulator (RD) of Tropp et al. 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.

Full work available at URL: https://arxiv.org/abs/1204.0839

Mathematics Subject Classification ID

Sampling theory in information and communication theory (94A20)