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In this study a wireless multiple-input multiple-output (MIMO) communication system operating over a fading channel is considered. Data packets are stored in a finite size buffer before being released into the time-varying MIMO wireless channel. The main objective of this work is to satisfy a specific quality of service (QoS) requirement, i.e. the probability of data loss because of both erroneous wireless transmission and buffer overflow, as well as to maximise the system throughput. The theoretical limit of ergodic capacity in MIMO time-variant channels can be achieved by adapting the transmission rate to the capacity evolving process. In this study, the channel capacity evolving process has been described by a suitable autoregressive model based on the capacity time correlation and a finite state Markov chain (FSMC) has been derived. The joint effect of channel outage at the physical layer and the buffer overflow at the medium access control layer has been considered to describe the probability of data loss in the system. The optimal transmission strategy must minimise that probability of data loss and has been derived analytically through the Markov decision process (MDP) theory. Analytical results show the significant improvements of the proposed optimal transmission strategy in terms of both system throughput and probability of data loss.