Proposed herein is a pre-processing technique applicable to maximum-SINR beamformers for blind space-time Rake receivers in single-user-type DS-CDMA detection. This smart-antennas signal-processing technique enhances the constructive summation of multipaths and the rejection of co-channel interference, both of which decrease the bit-error-rate and lower the error-floor of the cellular uplink's near-far problem at high SNR. This technique is blind in that it needs neither prior knowledge nor explicit estimation of (1) the channel-faded multipaths' arrival angles, relative arrival delays or power profiles, (2) the receiving antenna array's nominal or actual gain-phase-polarization response, and (3) the co-channel multi-access users' signature-spreading codes. Monte Carlo simulations show that the proposed scheme can enhance the output-SINR by 1 - 10 dB. A mathematical analysis shows this proposed pre-processing scheme to always improve the asymptotic output-SINR. A formula is analytically derived to predict this asymptotic output-SINR. This formula lies within 1 dB of limited simulation results at an input-SIR above -7 dB and a chip-rate space time-sampling, but the formula is less accurate otherwise