  Integrated sensing and communications (ISAC) systems have gained significant
interest because of their ability to jointly and efficiently access, utilize,
and manage the scarce electromagnetic spectrum. The co-existence approach
toward ISAC focuses on the receiver processing of overlaid radar and
communications signals coming from independent transmitters. A specific ISAC
coexistence problem is dual-blind deconvolution (DBD), wherein the transmit
signals and channels of both radar and communications are unknown to the
receiver. Prior DBD works ignore the evolution of the signal model over time.
In this work, we consider a dynamic DBD scenario using a linear state space
model (LSSM) such that, apart from the transmit signals and channels of both
systems, the LSSM parameters are also unknown. We employ a factor graph
representation to model these unknown variables. We avoid the conventional
matrix inversion approach to estimate the unknown variables by using an
efficient expectation-maximization algorithm, where each iteration employs a
Gaussian message passing over the factor graph structure. Numerical experiments
demonstrate the accurate estimation of radar and communications channels,
including in the presence of noise.
