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This paper proposes various new acquisition schemes based on iterative maximum likelihood estimation (MLE) for multiuser DS-CDMA system. Without high complexity of joint multiuser MLE, the iterative MLE partitions the multi-parameters estimation into iterative single-parameter estimation. A simple closed form of acquisition based on expectation-maximum (EM) and space alternating generalized EM (SAGE) are proposed. Comparing to conventional acquisition structures, the proposed EM and serial SAGE acquisition systems are similar to multistage and serial search acquisition, respectively. Lower complexity of serial SAGE acquisition with adaptive threshold decision is also demonstrated. Computer simulation demonstrates that EM and serial SAGE acquisitions are effective in multiple access interference.