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We present a graph-based channel estimation approach for SC-IFDE (single-carrier transmissions with iterative frequency domain equalization) without CP (cyclic prefix) over doubly selective channels using the recently developed Gaussian message passing (GMP) technique. A direct application of the GMP updating rules in the FFG (Forney-style factor graph) of the SC-IFDE system model incurs high complexity. Approximate updating rules are therefore developed to overcome this problem. The proposed GMP-based channel estimation approach has similar complexity as the low-complexity Kalman-filtering based frequency domain channel estimation approach in the literature, but significantly outperforms the latter due to its enhanced capability in capturing the time correlation information of doubly selective channels through bidirectional processing.