In this paper, we consider a direct-sequence code-division multiple-access (DS-CDMA) system in the framework of a discrete-event dynamic system (DEDS) in order to optimize the system performance. Based on this formulation, we develop infinitesimal perturbation analysis (IPA) for estimating the sensitivity of the average probability of bit error to factors ranging from near-far effects to imperfections in power control. The above estimates are shown to be unbiased, and this technique is then further incorporated into a stochastic gradient algorithm for achieving adaptive multiuser interference rejection for such systems, which is also subject to frequency nonselective slow fading. We use an IPA-based stochastic training algorithm for developing an adaptive linear detector with the average probability of error being the minimization criterion. We also develop a practical implementation of such an adaptive detector where we use a joint estimation-detection algorithm for minimizing the average probability of bit error. A sequential implementation that does not require a stochastic training sequence or a preamble is also developed.