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This paper proposes a new random-access protocol over 2 times M multiple-input-multiple-output (MIMO) multiaccess channels, namely, adaptive space-time diversity slotted ALOHA (ASTDSA), to address the issues on collision diversity while maintaining implementation simplicity. The proposed scheme exploits the advantages of both V-BLAST and Alamouti space-time block coding (STBC). In particular, it adaptively only transmits space-time-coded copies to remediable collisions. The coded replicas contain the same information as the packets involved in collisions and are immediately sent after a colliding slot. Combining the packets received in two consecutive slots, the Alamouti STBC scheme can be reconstructed to linearly resolve the collision without sacrificing the space-time diversity gain. An embedded Markov chain is developed to derive performance metrics with respect to throughput, diversity gain, delay, and stability. The tradeoff among those metrics is investigated. The results demonstrate that ASTDSA significantly outperforms the existing schemes, and simulations are used to validate the analytical model.