In this paper, we consider linear MMSE equalization for wireless downlink transmission with multiple transmit and receive antennas in fast fading environment. We propose a new algorithm based on conjugate-gradient algorithm with enhanced channel estimation. In order to be robust to the channel variations, the channel coefficients are estimated by using a weighted sliding window. Two methods to determine optimal weights with respect to the Doppler frequency are proposed. The algorithm has been tested in fast fading environment (Vehicular A for a velocity for the mobile station of 120 km/h). We show by simulations that good performance are obtained in correlated fast fading environment with reasonable complexity. Moreover, this method outperforms approaches based on forgetting factor, basic sliding window and LMS.