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For the wideband code-division multiple access (WCDMA) frequency-division duplexing (FDD) downlink of the Universal Mobile Telecommunication System (UMTS), we derive a chip-level equalization algorithm that jointly estimates the signals transmitted from multiple base stations. We focus on a scenario where the mobile terminal is located at the cell edge or in the intersection between different cells. Here, downlink transmission is not only affected by multipath propagation, which destroys the code orthogonality between different users' signals, but also severely by intercell interference caused by signals received from base stations of neighboring cells. We show by simulations that the new equalizer attains low bit-error rates in scenarios with strong intracell as well as intercell interference. Moreover, additional code-constraints based on the common pilot channel (CPICH) and, in case of soft-handover, based on the desired user's data channel are formulated which can further improve the equalizer performance.