A parametric form of G-Rake and chip equalization for closed-loop transmit diversity is provided, that accounts for impairment correlation between transmit antennas. In a closed-loop transmit diversity system, the base station transmits a signal from two or more antennas, using one of a predetermined set of relative phase offsets at one of the antennas. The parametric estimation of the impairment or data covariance is performed by summing terms, including a term for each possible phase offset. The terms are weighted by fitting parameters. The fitting parameters are jointly solved by fitting the impairment or data covariance estimate to a measured impairment or data covariance. In another aspect, a measured impairment covariance is formed by exploiting a special relationship between the pilot channels of the different transmit antennas.