  In this paper, channel estimation and data detection for multihop relaying
orthogonal frequency division multiplexing (OFDM) system is investigated under
time-varying channel. Different from previous works, which highly depend on the
statistical information of the doubly-selective channel (DSC) and noise to
deliver accurate channel estimation and data detection results, we focus on
more practical scenarios with unknown channel orders and Doppler frequencies.
Firstly, we integrate the multilink, multihop channel matrices into one
composite channel matrix. Then, we formulate the unknown channel using
generalized complex exponential basis expansion model (GCE-BEM) with a large
oversampling factor to introduce channel sparsity on delay-Doppler domain. To
enable the identification of nonzero entries, sparsity enhancing Gaussian
distributions with Gamma hyperpriors are adopted. An iterative algorithm is
developed under variational inference (VI) framework. The proposed algorithm
iteratively estimate the channel, recover the unknown data using Viterbi
algorithm and learn the channel and noise statistical information, using only
limited number of pilot subcarrier in one OFDM symbol. Simulation results show
that, without any statistical information, the performance of the proposed
algorithm is very close to that of the optimal channel estimation and data
detection algorithm, which requires specific information on system structure,
channel tap positions, channel lengths, Doppler shifts as well as noise powers.
