This invention teaches to the details of an interference suppressing receiver for suppressing intra-cell and inter-cell interference in coded, multiple-access, spread spectrum transmissions that propagate through frequency selective communication channels to a multiplicity of receive antennas. The receiver is designed or adapted through the repeated use of symbol-estimate weighting, subtractive suppression with a stabilizing step-size, and mixed-decision symbol estimates. Receiver embodiments may be designed, adapted, and implemented explicitly in software or programmed hardware, or implicitly in standard RAKE-based hardware either within the RAKE (i.e., at the finger level) or outside the RAKE (i.e., at the user or subchannel symbol level). Embodiments may be employed in user equipment on the forward link or in a base station on the reverse link. It may be adapted to general signal processing applications where a signal is to be extracted from interference.