In this paper we propose two types of receivers, which perform blind interference suppression. The receivers are suitable for the third generation mobile communications systems, which are based on direct-sequence code division multiple access (DS-CDMA). We especially consider the statistical technique called independent component analysis (ICA) as a tuning element attached to an existing single-user or blind multiuser detector. By doing this, the statistical independence of the users’ signals can be exploited. In addition, it makes it possible to alleviate the performance drop due to the erroneous parameters estimation in the receiver. From the ICA point of view, the receiver observes a mixture of users’ original signals, determined by the user-specific spreading codes, the data symbols, and the state of the propagation channel. Since all of them might be complex valued by nature, complex ICA is needed. In the paper, a proof of global convergence is given for the kurtosis-based FastICA algorithm in the case of complex valued source signals with circular distribution, and considered as the ICA component of the advanced receivers. Two types of receivers, RAKE-ICA and MMSE-ICA, are proposed and studied in a Rayleigh block fading channel. Extensive numerical simulations indicate that the performance of RAKE and subspace MMSE detector, respectively, can be greatly improved. Quite significantly, their performance is close to the theoretical bound of an equal length MMSE detector.