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We discuss linear equalization and intracell interference cancellation (IIC) in the downlink of wideband code division multiple access (W-CDMA) systems. A new reception scheme suitable for multirate systems (with different spreading codes) is proposed. The only knowledge supposed is the one available at the mobile unit. The effective spreading codes are detected blindly using fast walsh transform (FWT). The received signal is equalized then passed through an IIC stage to obtain better estimates of the transmitted symbols. We compare our scheme with equalization and IIC alone, and discuss practical issues when implementing this receiver.