In this paper, linear minimum mean square error (LMMSE) turbo equalization for transmission over doubly selective channels is proposed for single carrier (SC) as well as for multi-carrier (MC) systems. The complex exponential basis expansion model (CE-BEM) is used to approximate the time-varying multi-path fading channel. In this BEM, the time-varying channel is viewed as a bank of time-invariant FIR filters and the time-variation is captured by means of time-varying complex exponential basis functions. Based on the Gaussian approximation, exact expressions for the a-priori, a-posteriori and extrinsic information are derived for QPSK modulation. The MC system is implemented using orthogonal frequency-division multiplexing (OFDM). The performance of the proposed turbo equalization schemes are evaluated using numerical simulations.