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To take the advantages of the M-ary space-shift keying (MSSK) modulation invented recently, a MSSK fast antenna-hopping space-division multiple-access (MSSK FAH-SDMA) scheme is proposed and studied in this paper. In addition to supporting multiple-access, the FAH is introduced also to achieve transmit diversity by sending every MSSK symbol over several time-slots under the control of a FAH pattern (address). Associated with the MSSK FAH-SDMA, a range of linear and nonlinear detection schemes are studied. Specifically, the linear detection schemes considered include the matched-filtering single-user detector (MF-SUD), zero-forcing multiuser detector (ZF-MUD) and minimum mean-square error (MMSE)-MUD, while the nonlinear detection schemes addressed include the maximum likelihood (ML)-MUD and the receiver multiuser diversity aided multi-stage MMSE (RMD/MS-MMSE) MUD. The single-user pairwise error probability (SU-PEP) and bit error rate (BER) union-bound of the single-user MSSK FAH-SDMA systems employing ML detection are analyzed in detail. Based on the SU-PEP, the minimum transmit diversity order of the MSSK FAH-SDMA systems is specified. For the MSSK FAH-SDMA systems with linear detection, we study two types of MSSK demodulation schemes, which are referred to as the intrauser detections (IUDs), named as the maximum likelihood (ML)-IUD and direct (D)-IUD. For the MSSK FAH-SDMA systems employing the RMD/MS-MMSE MUD, two types of reliability measurement (RM) schemes are proposed, which are the maximum a-posteriori (MAP)-RM and ratio test (RT)-RM. Finally, the BER performance of the MSSK FAH-SDMA systems with various combinations of the proposed techniques is studied, when assuming that the channels from any transmit antennas to any receive antennas experience independent and identically distributed (i.i.d.) Rayleigh fading.