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In the uplink of a long-code CDMA system, base station knows spreading codes of all serviced users. Given propagation delays, a blind adaptive CMA-based approach, with the aid of a set of MMSE-like constraints parameterized by channel-like vectors, is proposed to detect all users' symbols simultaneously. As by-products, the channel-like vectors are also obtained for all users. Since the constraints involve covariance of the received data, which is time varying and can not be obtained by traditional sample average, we thus propose to approximate it using estimated signature matrix and noise power. Simulation results show satisfactory performance of the proposed method.