An equalizer operates on chip or sub-chip resolution input samples of a received spread-spectrum multipath signal to remove interference from one or more secondary propagation path signals within the multipath signal. The equalizer may be configured for cancellation of secondary signals arriving before and after a main propagation path signal, referred to as pre- and post-cursor signals, respectively. An associated communications system provides the equalizer with a path coefficient and delay value for each secondary path signal for which cancellation is desired. With its unique architecture, the equalizer cancels secondary signals displaced in time by amounts as small as the input sample time resolution or by amounts exceeding multiple chips, or even multiple symbols. The length of sample delay buffers within the equalizer, in combination with the input sample rate, determines the maximum secondary signal delay accommodated by the equalizer. Post-cursor cancellation requires only a hard-decision value buffer, while pre-cursor cancellation requires an additional input or compensated sample buffer. The equalizer makes a hard-decision about the phase value of each input sample and buffers these hard-decision values for use in secondary signal cancellation. Hard-decision values delayed from current input samples by delay times corresponding to the path delays of the secondary signals for which cancellation is desired are used to rotate the phase of corresponding path coefficients. These adjusted values are fed back for subtraction from input samples for post-cursor cancellation, and fed forward for subtraction from delayed input samples for pre-cursor cancellation.