Abstract:  A lot of ambient noises are non-Gaussian in actual blind multi-user detection systems, and non-Gaussianity often results in significant performance degradation or even invalidation to constant modulus blind multi-user detection algorithm with the channel model premised upon the Gaussian noise assumption. Alpha-stable distributions are one of the most important non-Gaussian models and can provide useful model for many phenomena observed in different fields. Facing with this problem, we present a fractional lower order statistics based generalized constant modulus algorithm (FLOS-GCMA). This FLOS-GCMA, which is a generalization of FLOS-CMA, can work efficiently under non-Gaussian noise condition and can be used in many areas. With DS-CDMA system as an example, we compare our algorithm with the constant modulus algorithm (CMA) and fractional lower order statistics based constant modulus algorithm (FLOS-CMA) analytically and numerically. The simulation results show that FLOS-GCMA can suppress multiple access interference (MAI) and non-Gaussian noise effectively, and converges fast either under Gaussian noise or alpha-stable distributed noise environment.