Compressive sampling for spectrally sparse signal recovery via one-bit random demodulator

Abstract

The one-bit compressive sampling (CS) framework aims at alleviating the quantization burden on analog-to-digital converters by quantizing each sample to one bit, i.e., capturing just the signs of samples. Motivated by one-bit CS theory, this paper addresses a new type of data acquisition system to recover spectrally sparse signals. This system is composed of a random demodulator and a one-bit quantizer. The former yields the signal compressed samples while the latter records the sign of each sample. With the observation sign data, the signal is eventually recovered by using the binary iterative hard thresholding algorithm. Through numerical experiments, we demonstrate that our scheme is high-efficient for spectrally sparse signal recovery in the situations of low signal-to-noise ratio, stringent bit budget and weak sparsity.