Gridless variational Bayesian inference of line spectral from quantized samples

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 high resolution and low complexity gridless 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, where VALSE is applied. Moreover, to obtain a benchmark of the performance of the proposed algorithm, the Cramer 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.