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In this paper, we propose a novel low-complexity variable forgetting factor (VFF) mechanism for blind adaptive constrained constant modulus (CCM) recursive least squares (RLS) algorithms applied to linear interference suppression in direct-sequence code-division multiple access (DS-CDMA) systems. The proposed variable forgetting factor mechanism employs an updated component related 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. Convergence and tracking analyses are carried out. Analytical expressions for predicting the mean-squared error of the proposed adaptation technique are obtained. Simulation results are presented for nonstationary environments and show that the proposed variable forgetting factor mechanism achieves superior performance to previously reported methods at a reduced complexity.