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A convergence analysis of the blind adaptive step-size constant modulus algorithm (AS-CMA) for direct-sequence code division multiple access (DS-CDMA) receivers is presented. Analytical results show similar convergence behaviours of the AS-CMA receiver and the adaptive step-size stochastic approximation (AS-SA) receiver. Simulations show that the blind AS-CMA algorithm performs comparably with the non-blind AS-SA in a Markovian type of nonstationary environment. The robustness of the proposed algorithm to different settings of the initial step-size is also shown.