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A redundant residue number system (RRNS)-assisted multicarrier direct-sequence code-division dynamic multiple-access (MC/DS-CDDMA) scheme is proposed for application in cognitive radios (CRs). Taking the advantages of both multicarrier direct-sequence code-division multiple access and RRNS, the RRNS MC/DS-CDDMA has a low complexity for implementation and a high flexibility for reconfiguration and is robust to dynamic spectrums. Associated with the RRNS MC/DS-CDDMA, in this paper, the so-called receiver multiuser diversity aided multistage minimum mean-square error multiuser detector (RMD/MS-MMSE MUD) is considered for signal detection. Specifically, three types of RMD/MS-MMSE MUDs are proposed: Type-I.1, Type-II.1, and Type-I.2 RMD/MS-MMSE MUDs. In these MUD schemes, the Type-I.1 MUD carries out the joint detection of all the subcarrier signals using both the observations and the channel state information (CSI) of all the subcarriers. In the Type-I.2 and Type-II.1 RMD/MS-MMSE MUDs, the embedded MMSE-MUDs are implemented subcarrier by subcarrier independently. Furthermore, in the Type-I.2 RMD/MS-MMSE MUD, the autocorrelation matrices used by the MMSE-MUDs are free from CSI. Explicitly, both Type-II.1 and Type-I.2 RMD/MS-MMSE MUDs are suitable for operation in dynamic spectrum environments. Furthermore, our simulation results show that the preceding three types of RMD/MS-MMSE MUDs are capable of making the RRNS MC/DS-CDDMA systems achieve similar error and throughput performance. Owing to the foregoing merits, the RRNS MC/DS-CDDMA employing either Type-I.2 or Type-II.1 RMD/MS-MMSE MUD may be considered one of the highly promising dynamic multiple-access schemes for application in CR systems.