Abstract: Method and apparatus for optimally decoding messages from CDMA signal sent by a plurality of users and received asynchronously at one receiver, using a minimal number of computations and minimal memory and processing resources. It is based on a novel approach to signal correlation, as well as to subsequent decoding by decorrelation, that requires a correlation period of only one symbol length, by providing for each user a pair of partial signatures sequences, with which the signal is correlated, deccorelating the results with the inverse of the cross-correlation matrix of all partial sequences, and combining the resultant partial symbol estimates--to obtain final estimated symbol values. The partial sequences are formed by separating each original sequence at a point corresponding to the estimated symbol boundary time, relative to an arbitrary correlation window, of one symbol length.