In a receive node of a wireless network, an iterative multi-user multi-stage interference cancellation receiver is used. The receiver 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.