  In this paper, we provide a distributed frequency offset estimation algorithm
based on a variant of belief propagation (BP). Each agent in the network
pre-compensates its carrier frequency individually so that there is no
frequency offset from the desired carrier frequency between each pair of
transceiver. The pre-compensated offset for each agent is computed in a
distributed fashion in order to be adaptive to the distributed network. The
updating procedure of the variant of BP is designed in a broadcasting fashion
to reduce communication burden. It is rigorously proved that the proposed
algorithm is convergence guaranteed. Simulations show that this method achieves
almost the optimal frequency compensation accuracy with an error approaching
the Cram\'er-Rao lower bound.
