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A Pearson system-based blind source separation method is used for detecting the signal, which is subject to multiple access interference, coming to a mobile user in a CDMA downlink communication. Considering some fading channel measurements showing that the fading channel coefficients may have an impulsive nature, these coefficients are modeled with an α-stable distribution whose shape parameter a takes values between 1.8 and 1.9. These a values show that the distribution resembles a Gaussian distribution, but has a more impulsive nature. Simulation studies show that the conventional MMSE receiver fails in this impulsive fading scenario. Both the independent component analysis (ICA) method using the conventional hyperbolic tangent score function and the Pearson system-based ICA are successful in estimating the channel coefficients and the proposed Pearson system-based ICA method performs faster.