  This paper presents an algorithm for iterative joint channel parameter
(carrier phase, Doppler shift and Doppler rate) estimation and decoding of
transmission over channels affected by Doppler shift and Doppler rate using a
distributed receiver. This algorithm is derived by applying the sum-product
algorithm (SPA) to a factor graph representing the joint a posteriori
distribution of the information symbols and channel parameters given the
channel output. In this paper, we present two methods for dealing with
intractable messages of the sum-product algorithm. In the first approach, we
use particle filtering with sequential importance sampling (SIS) for the
estimation of the unknown parameters. We also propose a method for fine-tuning
of particles for improved convergence. In the second approach, we approximate
our model with a random walk phase model, followed by a phase tracking
algorithm and polynomial regression algorithm to estimate the unknown
parameters. We derive the Weighted Bayesian Cramer-Rao Bounds (WBCRBs) for
joint carrier phase, Doppler shift and Doppler rate estimation, which take into
account the prior distribution of the estimation parameters and are accurate
lower bounds for all considered Signal to Noise Ratio (SNR) values. Numerical
results (of bit error rate (BER) and the mean-square error (MSE) of parameter
estimation) suggest that phase tracking with the random walk model slightly
outperforms particle filtering. However, particle filtering has a lower
computational cost than the random walk model based method.
