In this work, we develop a new second-order statistics based multiuser multipath channel estimation algorithm for uplink wireless space-time coded CDMA systems. The estimation procedure is based on the parameterization, with respect to the multiuser channel response vector, of the received data covariance matrix. As a side result, we also obtain an improved covariance matrix estimator. Then we utilize both the channel and the covariance matrix estimates to obtain an estimate of the linear MMSE receiver. Simulation studies illustrate the performance improvements of the proposed estimators relative to existing methods in terms of channel estimation mean-square error as well as receiver filter output SINR and receiver BER.