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This paper proposes RADICAL independent component analysis (ICA) algorithm for detection of DS-CDMA signals and also effect of fading on ICA based detection of DS-CDMA has been studied. ICA based technique is based on independence of source signals and these conditions are satisfied in multi-user CDMA environment. Combining an ICA element to conventional signal detection reduces multiple access interference (MAI) and enables a robust, computationally efficient structure. The proposed algorithm takes advantage of differential entropy estimation, spacing estimation and converges quickly. Rayleigh fading channel has been considered for simulations. Bit error rate simulations of this algorithm has been given for different number of users, SNR and compared with JADE algorithm. The results show that RADICAL algorithm performs best at separating the source signals from the mixed CDMA signals.