Abstract: This invention reformulates the MMSE criterion to apply to systems in which the desired data to be tracked is the ratio of the data appearing in successive observation intervals. The resulting differential MMSE criterion leads to a number of novel algorithms for adaptive implementation of the MMSE receiver. Applications include equalization for single user systems, and multiuser detection, or interference suppression, for direct sequence CDMA with short spreading sequences (i.e., the period of the spreading sequence equals the symbol interval). The invention also provides blind (i.e., without the requirement of a training symbol sequence for the user of interest) equalization and beamforming (using a receive antenna array) for direct sequence CDMA systems with long spreading sequences (i.e., systems in which the spreading sequences are aperiodic, or have period much larger than the symbol interval). The invention enables recovery of the desired symbol sequence up to an unknown phase.