  This paper considers an integrated sensing and communication system, where
some radar targets also serve as communication scatterers. A location domain
channel modeling method is proposed based on the position of targets and
scatterers in the scattering environment, and the resulting radar and
communication channels exhibit a two-dimensional (2-D) joint burst sparsity. We
propose a joint scattering environment sensing and channel estimation scheme to
enhance the target/scatterer localization and channel estimation performance
simultaneously, where a spatially non-stationary Markov random field (MRF)
model is proposed to capture the 2-D joint burst sparsity. An expectation
maximization (EM) based method is designed to solve the joint estimation
problem, where the E-step obtains the Bayesian estimation of the radar and
communication channels and the M-step automatically learns the dynamic position
grid and prior parameters in the MRF. However, the existing sparse Bayesian
inference methods used in the E-step involve a high-complexity matrix inverse
per iteration. Moreover, due to the complicated non-stationary MRF prior, the
complexity of M-step is exponentially large. To address these difficulties, we
propose an inverse-free variational Bayesian inference algorithm for the E-step
and a low-complexity method based on pseudo-likelihood approximation for the
M-step. In the simulations, the proposed scheme can achieve a better
performance than the state-of-the-art method while reducing the computational
overhead significantly.
