This paper extends the self-contained theory of linear precoding to the field of covariance based spatio-temporal downlink processing for direct-sequence code-division multiple-access (CDMA) systems and shows the applicability to the release 6 of high-speed downlink packet access (HSDPA). To this end, a unifying theory is developed to formulate the three known linear filters, namely, the transmit matched filter, the transmit zero-forcing filter, and the transmit Wiener filter, as optimization problems even in systems, where only covariance knowledge is available at the transmitter. Second, the solutions of these transmit filters are given for such systems with partial channel state information (CSI). Finally, it is shown how covariance-based linear precoding can be employed in the new generation CDMA system HSDPA, i.e., how channel estimation on the secondary common pilot channel allows for optimum full rank linear precoding employing only partial CSI.