A method for acquiring signals received from multiple users in a single burst groups signals by power and sequentially processes the signal groups. A received sum of a plurality of user signals received in a burst is stored, and the transmitted symbols for each signal within a first group of the stored signals is estimated. A modified set of signals is then determined that excludes the signals of the first group. From the modified set of signals, the method continues by canceling multiuser interference among signals within a second group, and estimating transmitted symbols for each signal within the second group. The first and second groups includes all signals within a power band that defines the group, and the first band represents a higher power band than the second. Such iterative processing may continue for sequentially lower power bands until all signals are processed. A receiver is also detailed.