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In this work, a generalized form of spreading-code-phase-shift-keying (SCPSK) modulation is proposed. The performance of M-SCPSK modulation with a coherent receiver in an AWGN channel, exposed to multi-user interference, is investigated. Two types of M-ary SCPSK modulation - one employing short spreading codes and the other employing long spreading codes - are examined and the union bounds of symbol error probabilities are derived. Additionally, feasible designs of the M-CPSK transmitter and receiver are proposed. The M-SCPSK system employing long spreading codes is found to be more flexible and therefore more suitable for packet data service applications.