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Blind adaptive multi-user detection (MUD) is one of the key technologies in CDMA systems, and there are lots of optimal and suboptimal detection algorithms during which constant modulus algorithm (CMA) is widely used. All these existing detection algorithms are based on the assumption of Gaussian ambient channel noise, however, more and more researches in recent years show that the actual ambient noise is non-Gaussian distributed. So it is necessary to investigate the problem of multi-user detection in the environment of non-Gaussian noise. While α-stable distribution is a typical statistical model of non-Gaussian signal, its fractional lower order statistics (FLOS) theory is a useful tool in non-Gaussian signal processing. Motivated by the above reasons, we propose a FLOS based generalized constant modulus algorithm (FLOS-GCMA). FLOS-CM algorithm which has been proposed by some researchers for blind equalization can also be used for blind multi-user detection and FLOS-CM algorithm is a special case of FLOS-GCMA. Theoretical analysis and simulation results show that FLOS-GCMA can effectively suppress the non-Gaussian noise.