Since accurate channel state information plays an important role in single carri er frequency domain equalization (SC FDE), a frequency domain state space appr oach to the least squares (LS) estimation is proposed with the aid of Gaussian m essage passing. Based on the generalized distribution law, the likelihood functi on is divided into several blocks in Forney style factor graphs (FFG), and then a recursive algorithm is developed by defining an auxiliary matrix. Through exc hanging soft information on code bits, channel estimation can be performed joint ly with frequency equalization on the basis of turbo principle. Due to the speci al forms of the state transition matrix, an unbiased recursive estimators is obt ained by properly forcing a covariance matrix in the recursive algorithm to be d iagonal. The complexity of the proposed approach avoids matrix inversion and gro ws logarithmically with the length of the observation vector. Simulation results show that the new algorithm can achieve good performance with low computational complexity.