  In this paper, we propose an iterative receiver based on gridless variational
Bayesian line spectra estimation (VALSE) named JCCD-VALSE that \emph{j}ointly
estimates the \emph{c}arrier frequency offset (CFO), the \emph{c}hannel with
high resolution and carries out \emph{d}ata decoding. Based on a modularized
point of view and motivated by the high resolution and low complexity gridless
VALSE algorithm, three modules named the VALSE module, the minimum mean squared
error (MMSE) module and the decoder module are built. Soft information is
exchanged between the modules to progressively improve the channel estimation
and data decoding accuracy. Since the delays of multipaths of the channel are
treated as continuous parameters, instead of on a grid, the leakage effect is
avoided. Besides, the proposed approach is a more complete Bayesian approach as
all the nuisance parameters such as the noise variance, the parameters of the
prior distribution of the channel, the number of paths are automatically
estimated. Numerical simulations and sea test data are utilized to demonstrate
that the proposed approach performs significantly better than the existing
grid-based generalized approximate message passing (GAMP) based \emph{j}oint
\emph{c}hannel and \emph{d}ata decoding approach (JCD-GAMP). Furthermore, it is
also verified that joint processing including CFO estimation provides
performance gain.
