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This paper considers the problem of channel estimation for OFDM systems, where the number of channel taps and their power delay profile (PDP) are unknown. Using a Bayesian approach, we construct a model in which we estimate jointly the coefficients of the channel taps, the channel order and decay rate of the PDP. In order to sample from the resulting posterior distribution we develop a novel Trans-dimensional Markov chain Monte Carlo (TDMCMC) algorithm. This is done using a Stochastic Approximation (SA) approach to develop an adaptively learning algorithm to improve mixing rates of the basic Birth-Death (B-D) Markov chain for the between model subspaces. Using simulations we assess its performance in terms of channel order estimation and bit error rate (BER). It is shown that the proposed algorithm can achieve results very close to the case where both the channel length and the PDP are known.