Herein, the problem of estimating propagation delays of the transmitted signals in a direct-sequence code-division multiple access (DS-CDMA) system operating over fading channels is considered. Even though this study is limited to the case when the propagation delays are fixed during the observation interval, the channel gain and phase are allowed to vary in time. Special attention is given to the near-far problem which is catastrophic for the standard acquisition algorithm. An estimator based on subspace identification techniques is proposed, and the Cramer-Rao bound, which serves as an optimality criterion, is derived. The Cramer-Rao bound is shown to be independent of the near-far problem, which implies that there is no fundamental reason for propagation delay estimators to be near-far limited. Furthermore, the proposed algorithm is experimentally shown to be robust against the near-far problem.