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Wideband code division multiple access (W-CDMA) is a third generation (3G) mobile wireless technology that promises much higher data speeds for mobile and portable wireless devices than those which are commonly offered in today's market. In W-CDMA systems, while transmitting information over multipath channels, both intersymbol interference (ISI) as a result of interchip interference (ICI) and multiple access interference (MAI) cannot be easily eliminated. Although it is possible to design multiuser detectors that suppress MAI and ISI, these detectors often require explicit knowledge of at least the desired users' signature waveform. Torlak and Xu proposed a blind estimation algorithm for Asynchronous CDMA (A-CDMA) systems to estimate the multiple users' symbols. In our work, we study a similar blind channel estimation scheme for downlink W-CDMA systems that provide estimates of the subchannels of multiple users by exploiting the structural information of the data output. In particular, we show that the subspace of the (data+noise) matrix contains sufficient information for unique determination of channels, and hence, the signature waveforms and signal constellation. Performance measures like bit error rate and root mean square error are plotted for various channel fading conditions.