In a receive node (230) of a wireless network (100), an iterative multi-user multi-stage interference cancellation receiver (500, 1400, 1700) is used. The receiver (500, 1400, 1700) performs code-averaged equalization and chip chip-level code-specific interference over-cancellation on the received signals. This can result in a unified interference cancellation processing, and can avoid cumbersome calculations of code cross correlations that is required in symbol-level interference cancellation. A symbol-level code-averaged desired signal add-back is performed to address the over- cancellation of some desired signals.