  Efficient estimation of line spectral from quantized samples is of
significant importance in information theory and signal processing, e.g.,
channel estimation in energy efficient massive MIMO systems and direction of
arrival estimation. The goal of this paper is to recover the line spectral as
well as its corresponding parameters including the model order, frequencies and
amplitudes from heavily quantized samples. To this end, we propose an efficient
grid-less Bayesian algorithm named VALSE-EP, which is a combination of the
variational line spectral estimation (VALSE) and expectation propagation (EP).
The basic idea of VALSE-EP is to iteratively approximate the challenging
quantized model of line spectral estimation as a sequence of simple pseudo
unquantized models so that the VALSE can be applied. Note that the noise in the
pseudo linear model is heteroscedastic, i.e., different components having
different variances, and a variant of the VALSE is re-derived to obtain the
final VALSE-EP. Moreover, to obtain a benchmark performance of the proposed
algorithm, the Cram\'{e}r Rao bound (CRB) is derived. Finally, numerical
experiments on both synthetic and real data are performed, demonstrating the
near CRB performance of the proposed VALSE-EP for line spectral estimation from
quantized samples.
