  We propose new schemes for joint channel and data estimation (JCDE) and radar
parameter estimation (RPE) in doubly-dispersive channels, such that integrated
sensing and communications (ISAC) is enabled by user equipment (UE)
independently performing JCDE, and base stations (BSs) performing RPE. The
contributed JCDE and RPE schemes are designed for waveforms known to perform
well in doubly-dispersive channels, under a unified model that captures the
features of either legacy orthogonal frequency division multiplexing (OFDM),
state-of-the-art (SotA) orthogonal time frequency space (OTFS), and
next-generation affine frequency division multiplexing (AFDM) systems. The
proposed JCDE algorithm is based on a Bayesian parametric bilinear Gaussian
belief propagation (PBiGaBP) framework first proposed for OTFS and here shown
to apply to all aforementioned waveforms, while the RPE scheme is based on a
new probabilistic data association (PDA) approach incorporating a
Bernoulli-Gaussian denoising, optimized via expectation maximization (EM).
Simulation results demonstrate that JCDE in AFDM systems utilizing a single
pilot per block significantly outperforms the SotA alternative even if the
latter is granted a substantial power advantage. Similarly, the AFDM-based RPE
scheme is found to outperform the OTFS-based approach, as well as the sparse
Bayesian learning (SBL) technique, regardless of the waveform used.
