Polyphase complex scrambling patterns are designed to extend the zero-correlation zone (ZCZ) of a family of user spreading sequences, called properly scrambled Walsh-Hadamard (PSW) codes, recently proposed for quasi-synchronous (QS) code-division multiple-access systems. The merits of the binary (ZCZ equals 2) and quadri-phase (ZCZ equals 4) PSW codes over the existing QS spreading codes are still retained in the proposed polyphase PSW codes. Scrambling patterns for the case of ZCZ of 8 are derived first. Then, the scrambling pattern design rules are generalized for greater ZCZs and a structured procedure to generate polyphase PSW codes for any ZCZ is developed. Finally, the cross-correlation properties of the proposed spreading codes are evaluated.