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Closed-form steady-state performance analysis of the signal-to-interference plus noise ratio (SINR) at the output of well-known adaptive implementations of the linear minimum mean-square error (MSE) receiver for direct-sequence code-division multiple access show that nondata-aided (NDA) schemes may suffer from a considerable performance degradation with respect to their data-aided counterparts. Motivated by this fact, we propose a new two-stage NDA scheme where symbol-by-symbol predecisions at the output of a first adaptive stage are used to train a second stage. We derive closed-form steady-state performance analysis for both the two-stage and classical decision-directed schemes, taking into account detection errors in decision-directed adaptation. Our analysis shows that the SINR of the two-stage algorithm is close to optimal over a large range of values, while the SINR of the decision-directed scheme is far from optimal when the optimal SINR is small. Finally, we consider the case of time-varying fading channels. We derive modified recursive least square and least mean square adaptation schemes by considering SINR maximization rather than MSE minimization (that is useless under the assumption of zero-mean random channels). The resulting two-stage receiver shows good tracking properties in heavy near-far conditions (at least for moderate normalized Doppler bandwidth), while the decision-directed receiver may easily loose tracking after deep fades.