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This paper addresses the problem of blind equalization for digital communications using an array of sensors at the receiver to copy constant modulus signals in the presence of heavy-tailed additive channel noise. First, we demonstrate the negative effects of channel noise to the original constant modulus algorithm (CMA) cost function in terms of convergence. Then, we introduce a new CMA criterion based on the fractional lower-order statistics (FLOS) of the received data. The proposed criterion is able to mitigate impulsive noise at the receiver and at the same time restores the constant modulus character of the transmitted communication signal. We perform an analytical study of the properties of the new cost function and we illustrate its convergence behavior through computer simulations.