This paper proposes several blind adaptive receivers to eliminate multiple-access interference (MAI), intersymbol interference (ISI), and interchip interference (ICI) in direct-sequence code-division multiple access (DS/CDMA) downlink multiuser systems. We use the following concepts to formulate the cost function: 1) the variance of the despreading output approaches to the variance of the desired signal and 2) the discreteness property of the input signal. The proposed approaches are called variance-oriented approaches (VOAs). The VOA is then applied to three proposed receiver structures, especially the generalized sidelobe canceller (GSC) scheme that is generally the concept of spatial domain in beamforming system, to eliminate the MAI by one particular constraint in temporal domain. Besides, by this constraint, GSC filter possesses the property of global convergence in multipath environment once the channel estimation is appropriate. Simulation examples are shown to demonstrate the effectiveness and comparison of the proposed blind adaptive receivers.