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We address the problem of joint common-dedicated pilots downlink user dedicated channel estimation for W-CDMA receivers, in particular in the presence of dedicated channel transmit beamforming. The optimal dedicated channel estimate is derived via a three steps procedure, consisting of building brute FIR dedicated and common channel estimates on a per-slot basis, exploiting the dedicated and common pilots respectively, building a refined unbiased minimum mean square error dedicated channel estimate by optimally combining the previous dedicated and common channels estimates, further refining the obtained dedicated channel estimate by Wiener filtering across slots. An adaptive filtering implementation is addressed for the implementation of the optimal Wiener filtering. The proposed channel estimation technique is suited for structured multipath channels where the FIR channel estimates resulting from the previous three steps procedure are optimally approximated by a multipath model in every slot.