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This paper analyzes the behavior of the Least Mean Square (LMS) adaptive algorithm in the minimum mean-squared error (MMSE) single user adaptive receiver for the asynchronous direct sequence-code division multiple access (DS-CDMA) system. It is known that in this context the adaptive algorithm can be iterated several times during the same bit interval in order to achieve a faster convergence rate for the receiver, which further reduces the length of the training sequence. Instead of using such multiple iterations we propose a single equivalent formula for updating the receiver coefficients, saving significant time processing. The simulation results prove the equivalency of these approaches in terms of convergence rate performances.