We propose in this paper a turbo channel estimation algorithm for Alamouti's space-time coded system over fast time varying channels. This algorithm performs an iterative estimation of the multiplicative fading channel according to the maximum a posteriori (MAP) criterion. It requires a convenient representation of the fast varying channel based on the Karhunen-Loeve expansion theorem. It takes into account the coded structure of data symbols in the estimation process thanks to the BCJR algorithm. The validity of the proposed structure is highlighted by simulation results.