BEATING NYQUIST THROUGH CORRELATIONS: A CONSTRAINED RANDOM DEMODULATOR FOR SAMPLING OF SPARSE BANDLIMITED SIGNALS

Compressed Sensing and Sparse Representation of Signals

Presented by: Andrew Harms, Author(s): Andrew Harms, Princeton University, United States; Waheed U. Bajwa, Robert Calderbank, Duke University, United States

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 sig- nals. 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 undergo- ing 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 pro- posed that bypasses this bottleneck by replacing the original modu- lating waveform with a run-length limited (RLL) modulating wave- form 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 modulat- ing 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.

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