  Employing low-resolution analog-to-digital converters (ADCs) coupled with
large antenna arrays at the receivers has drawn considerable interests in the
millimeter wave (mm-wave) system. Since mm-wave channels are sparse in angular
dimensions, exploiting the structure could reduce the number of measurements
while achieve acceptable performance at the same time. Motivated by the
variational Bayesian line spectral estimation (VALSE) algorithm which treats
the angles as random parameters, in contrast with previous works which confine
the estimate to the set of grid angle points and induce grid mismatch, this
paper proposes the grid-less quantized variational Bayesian channel estimation
(GL-QVBCE) algorithm for antenna array systems with low resolution ADCs.
Compared to the traditional least squares (LS) approach, numerical results show
that GL-QVBCE performs significantly better and asymptotically approaches the
Cram\`{e}r Rao bound (CRB).
