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In this letter, we combine the LSCMA(least square constant modulus algorithm) with the subspace approach and present a LSCM_SUB blind adaptive multiuser detection in AWGN CDMA channels. The poor performance of LSCMA in the low SNR will be improved by the LSCM_SUB algorithm. The performance of the proposed LSCM_SUB algorithm is compared with that of LSCMA. Simulation results show that the LSCM_SUB algorithm is superior to the LSCMA especially in the low SNR.