This study proposes an iterative, joint channel estimation, equalization, and data detection method in the presence of high mobility for a multicarrier downlink system that communicates over rapidly time-varying channels. The proposed method uses a basis expansion method (BEM) which has low computational complexity and helps to reduce the number of coefficients needed to represent a time-varying channel and therefore is extremely easy to implement practically. Unlike the current literature, which is almost entirely focused on the uplink communication systems due to their computational costs, this method prioritizes the goal of being feasible in a downlink system with a reasonable performance. The proposed suboptimal algorithm is based on the space-alternating generalized expectation-maximization (SAGE) algorithm and the time-varying channel is represented by orthogonal basis functions obtained by means of discrete Walsh-Hadamard transform (DWHT). The resulting receiver iterates between maximum a posteriori (MAP) based channel estimation in the subspace spanned by the orthogonal basis functions and successive interference cancellation. Numerical examples show that the proposed algorithm has a satisfactory symbol error rate with low computational complexity and also has a reasonable peak-to-average power ratio (PAPR) reduction effect.