This paper investigates the MMSE-based frequency domain equalization (FDE) algorithms in turbo equalization systems. As opposed to the conventional FDE systems where the cyclic prefix (CP) is discarded at the receiver, we take advantage of the redundancy and make use of all the observed signals for equalization purpose. First, we interpret the conventional frequency domain equalizer as a Forney-style factor graph (FFG), and accordingly an equalization algorithm is derived based on the Gaussian message passing (GMP) technique. Second, the normally discarded CP part is presented similarly using an FFG, and an algorithm that integrates both of the FFGs is proposed. As a result, two extrinsic messages about the data symbols are obtained rather than one, and they are merged together based on a symbol-wise combination. Third, with approximations made on two covariance matrices, the complexity of the proposed equalization algorithm is maintained at the same order as that of the conventional FDE algorithm, i.e. O(NIog2N) per block per iteration. Simulations results verify that, a gain of around 0.7dB is achieved compared with the conventional algorithm at 1/4 CP ratio, for both 16QAM and 64QAM system with Gray mapping over AWGN or ISI channels.