  Due to the utilization of large antenna arrays at base stations (BSs) and the
operations of wireless communications in high frequency bands, mobile terminals
often find themselves in the near-field of the array aperture. In this work, we
address the signal processing challenges of integrated near-field localization
and communication in uplink transmission of an integrated sensing and
communication (ISAC) system, where the BS performs joint near-field
localization and signal detection (JNFLSD). We show that JNFLSD can be
formulated as a matrix factorization (MF) problem with proper structures
imposed on the factor matrices. Then, leveraging the variational inference (VI)
and unitary approximate message passing (UAMP), we develop a low complexity
Bayesian approach to MF, called UAMP-MF, to handle a generic MF problem. We
then apply the UAMP-MF algorithm to solve the JNFLSD problem, where the factor
matrix structures are fully exploited. Extensive simulation results are
provided to demonstrate the superior performance of the proposed method.
