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

Efficient estimation of line spectral from quantized samples is of vital 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 such as model order, frequency and amplitudes from heavily quantized samples. To this end, we propose an efficient grid-less Bayesian algorithm named VALSE-EP, which is based on 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 algorithm can be applied. Note that since the noise in the pseudo linear model is heteroscedastic (different components having different variance), 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 results show that the performance of VALSE-EP is close to the CRB, demonstrating effectiveness of VALSE-EP for line spectral estimation from quantized samples.