Beating nyquist through correlations: A constrained random demodulator for sampling of sparse bandlimited signals

Technological constraints severely limit the rate at which analog-to-digital converters can reliably sample signals. Recently, Tropp et al. proposed an architecture, termed the random demodulator (RD), that attempts to overcome this obstacle for sparse bandlimited signals. One integral component of the RD architecture is a white noise-like, bipolar modulating waveform that changes polarity at a rate equal to the signal bandwidth. Since there is a hardware limitation to how fast analog waveforms can change polarity without undergoing shape distortion, this leads to the RD also having a constraint on the maximum allowable bandwidth. In this paper, an extension of the RD, termed the constrained random demodulator (CRD), is proposed that bypasses this bottleneck by replacing the original modulating waveform with a run-length limited (RLL) modulating waveform that changes polarity at a slower rate than the signal bandwidth. One of the main contributions of the paper is establishing that the CRD, despite employing a modulating waveform with correlations, enjoys some theoretical guarantees for certain RLL waveforms. In addition, for a given sampling rate and rate of change in the modulating waveform polarity, numerical simulations confirm that the CRD, using an appropriate RLL waveform, can sample a signal with an even wider bandwidth without a significant loss in performance.