1. A direct sequence-code division multiple access (DS-CDMA) system, having associated therewith cross correlation values among contemporaneous users, the system comprising: a transmitter and a receiver, the transmitter having means for multiplying a modulating signal with a spreading sequence in order to form a spread spectrum signal and means for transmitting the spread spectrum signal on a CDMA channel, and the receiver comprising receiving means for receiving signals on said CDMA channel, and interference cancelling means for cancelling multiple access interference, said interference cancelling means including an input coupled to the receiving means for receiving the received signals, feedforward filtering means coupled to the input for processing the received signals, quantizing means coupled to the feedforward filtering means for producing quantized decisions from information derived from the feedforward filtering means, tentative decision means coupled to the input for making tentative decisions on the received signals, characterizing means, coupled to the tentative decision means and the quantizing means, for characterizing the CDMA channel in dependence on the cross correlation values of all the contemporaneous users, and adjusting means responsive to the characterizing means for adjusting tap weights of at least the feedforward filtering means so as to cancel substantially multiple access interference.