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This paper proposes an efficient random access channel (RACH) transmission method that utilizes soft-combining of consecutively retransmitted message data packets according to the quality of service (QoS) requirements for broadband multi-carrier/DS-CDMA (MC/DS-CDMA) in the reverse link. In the proposed scheme, the relative transmission power of message data compared to that of a successfully detected preamble for non-real time (NRT) traffic data is significantly reduced to achieve error-free transmission by soft-combining several retransmitted message data packets thanks to time diversity since the delay requirement is relaxed. Meanwhile, for real time (RT) traffic data with rigid delay requirements, the relative transmission power of the message data compared to that of the detected preamble is increased to reduce the residual packet error rate with a limited number of retransmissions. Simulation results elucidate that the total required average received signal energy per bit-to-background noise power spectrum density ratio (Eb/N0) for error-free transmission with time diversity for NRT traffic data is reduced by approximately 2.4 dB compared to that for RT traffic data in a 12-path fading channel with exponential distribution at the fading maximum Doppler frequency of fD = 20 Hz.