In this paper, we will focus on channel estimation (CE) in orthogonal frequency-division multiplexing (OFDM) systems. The time-varying (TV) channelsare modeled by a basis expansion model (BEM). Due to the time-variation, the channel matrix in the frequency domain is no longer diagonal, but approximately banded.We use a pilot-aided algorithm for estimation of rapidly varying wireless channels in OFDM systems. Theperforms is goodwhen the channels vary on the scale of a single OFDM symbol duration, which occurs in mobile communication scenarios such as WiMAX, WAVE, and DVB-T.We recover Fourier coefficients of the channel taps by the pilot information.We then estimate the BEM coefficients of the channel taps from their respective Fourier coefficients using a recently developed inverse reconstruction method.We compare some BEM models in inverse methodsto find out the best ones in certain conditions.