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The code-constrained constant modulus algorithm (CCM) is a very effective blind approach for intersymbol interference (ISI) and multiaccess interference (MAI) suppression when a communication channel is frequency-selective. In non-stationary wireless environment, users frequently enter and exit the system, making it very difficult for the receiver to compute a pre-determined step size. This suggests the deployment of mechanisms to automatically adjust the step size in order to ensure good tracking of the interference and the channel. In this work, we propose a novel low-complexity variable step size mechanism for blind CCM CDMA receivers. The simulation results show that our proposed algorithm can work very well in the non-stationary environment The convergence analysis of the proposed algorithm is carried out.