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We present a blind per-survivor processing (PSP)-based multiuser detector (MUD) for synchronous multicarrier (MC) direct sequence (DS) CDMA systems. We modify the branch metric conventionally used for the single-carrier (SC) PSP-based MUD in order to detect synchronous MC DS-CDMA signals. Subsequently, we characterise the performance of rate R= 1/2 low density parity check (LDPC)-coded, convolutional-based turbo (CT)-coded and convolutional-coded (CC) MC DS-CDMA systems, which employ four subcarriers. We assume that each subcarrier experienced uncorrelated narrowband Rayleigh fading and quantified the BER performance, computational complexity and system delay. It is observed that when interleaving is performed over a single transmission burst, it is sufficient to utilise low-complexity CC codes. When the MC DS-CDMA system is not constrained by the tolerable system delay and hence interleaving is performed over several transmission bursts, CT codes yield the best performance. LDPC codes are also capable of approaching the performance attained by the CT codes, although at a factor of 2.4 higher computational complexity.