Channel estimation and data detection for OFDM systems over time- and frequency-selective channels are investigated. Relying on the complex exponential basis expansion channel model, a pilot-embedded channel estimation scheme with low computational complexity and spectral efficiency is proposed. A periodic pilot sequence is superimposed at a low power on information bearing sequence at the transmitter before modulation and transmission. The channel state information(CSI) can be estimated using the first-order statistics of the received data. In order to enhance the performance of channel estimation, we recover the transmitted data which can be exploited to estimate CSI iteratively. Simulation results show that the proposed method is suitable for doubly-selective channel estimation for the OFDM systems and the performance of the proposed method can be better than that of the Wiener filter method under some conditions. Through simulations, we also analyze the factors which can affect the system performances.