Multiple-access interference mitigation is important in code-division multiple-access (CDMA) systems for both information recovery and signal acquisition. Therefore, in this letter, we propose an open-loop adaptive filter based on the reiterative minimum mean-square error for the acquisition of CDMA signals. The method is based on the existing multistatic adaptive pulse compression method, appropriately adapted to the characteristics of CDMA continuous-wave signals. The efficacy of the proposed method in such systems is verified by simulation, and its superiority when compared with the existing least-mean-square method in terms of the number of reiterations is established.