A Constrained Random Demodulator for Sub-Nyquist Sampling

TL;DR

This paper introduces a constrained random demodulator that reduces hardware complexity for sub-Nyquist sampling of frequency-sparse signals, with theoretical guarantees and validated through simulations.

Contribution

It proposes a modified random demodulator with constrained waveforms, balancing hardware feasibility and recovery performance, and highlights the importance of waveform statistics.

Findings

Hardware requirements are relaxed with minimal recovery loss.

Matching waveform power spectrum to input signal distribution improves recovery.

Theoretical guarantees are confirmed by numerical simulations.

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.