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Efficient estimation of line spectral from quantized samples is ofsignificant importance in information theory and signal processing, e.g.,channel estimation in energy efficient massive MIMO systems and direction ofarrival estimation. The goal of this paper is to recover the line spectral aswell as its corresponding parameters including the model order, frequencies andamplitudes from heavily quantized samples. To this end, we propose an efficientgrid-less Bayesian algorithm named VALSE-EP, which is a combination of thevariational line spectral estimation (VALSE) and expectation propagation (EP).The basic idea of VALSE-EP is to iteratively approximate the challengingquantized model of line spectral estimation as a sequence of simple pseudounquantized models so that the VALSE can be applied. Note that the noise in thepseudo linear model is heteroscedastic, i.e., different components havingdifferent variances, and a variant of the VALSE is re-derived to obtain thefinal VALSE-EP. Moreover, to obtain a benchmark performance of the proposedalgorithm, the Cram\'{e}r Rao bound (CRB) is derived. Finally, numericalexperiments on both synthetic and real data are performed, demonstrating thenear CRB performance of the proposed VALSE-EP for line spectral estimation fromquantized samples.

Grid-less Variational Bayesian Inference of Line Spectral from Quantized Samples