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Herein presented is a finite-data-record performance analysis of a "blind" space-time RAKE-receiver algorithm previously proposed by Wong, Lok, Lehnert & Zoltowski (WLLZ) [T.F. Wong, T.M. Lok, J.S. Lehnert & M.D. Zoltowski, 1998] for uplink DS-CDMA cellular radiowave wireless communications using only single-user-type "conventional" detectors. Derived are two approximations of the detector's finite sample mean output-SINR. This analysis reveals how the output-SINR depends on the multi-user access cellular system's various system parameters, and the fading-channel's delay spread and temporal variability. Simulations confirm this analysis' validity, except when the detector breaks down in certain small-sample-support situations. Such breakdown is further shown to be alleviated by overlapping time-segments in the estimation of the covariance matrix of the interference-plus-noise delay-segments of the despread signal.