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The multiple-input multiple-output (MIMO) technique can be used to improve the performance of ad hoc networks. Various medium access control (MAC) protocols with multiple contention slots have been proposed to exploit spatial multiplexing for increasing the transport throughput of MIMO ad hoc networks. However, the existence of multiple request-to-send/clear-to-send (RTS/CTS) contention slots represents a severe overhead that limits the improvement on transport throughput achieved by spatial multiplexing. In addition, when the number of contention slots is fixed, the efficiency of RTS/CTS contention is affected by the transmitting power of network nodes. In this study, a joint optimisation scheme on both transmitting power and contention slots number for maximising the transport throughput is presented. This includes the establishment of an analytical model of a simplified MAC protocol with multiple contention slots, the derivation of transport throughput as a function of both transmitting power and the number of contention slots, and the optimisation process based on the transport throughput formula derived. The analytical results obtained, verified by simulation, show that much higher transport throughput can be achieved using the joint optimisation scheme proposed, compared with the non-optimised cases and the results previously reported.