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In this work, we propose a low-complexity variable forgetting factor (VFF) mechanism for blind adaptive constrained constant modulus (CCM) recursive least square (RLS) algorithms applied to linear interference suppression in direct-sequence code division multiple access (DS-CDMA) systems. The proposed VFF mechanism employs an updated component relating to the time average of the constant modulus (CM) cost function to automatically adjust the forgetting factor in order to ensure good tracking of the interference and the channel. Analytical expressions for predicting the mean-squared error of the proposed adaptation technique are obtained. Simulation results show that the proposed VFF mechanism achieves superior performance to existing methods at a reduced complexity.