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In this paper, the effective capacity of a multiple-input multiple-output (MIMO) system in two different cases with receive antenna selection (RAS) and transmit antenna selection (TAS) schemes is investigated. A closed-form solution for the maximum constant arrival rate of this network with statistical delay quality of service (QoS) constraint is extracted in the quasi-static fading channel. This study is conducted in two different cases. When channel state information (CSI) is not available at the MIMO transmitter, implementation of TAS is difficult. Therefore, RAS scheme is employed and one antenna with the maximum instantaneous signal to noise ratio is chosen at the receiver. On the other hand, when CSI is available at the transmitter, TAS scheme is executed. In this case, one antenna is selected at the transmitter. Moreover, an optimal power-control policy is applied to the selected antenna and the effective capacity of the MIMO system is derived. Finally, this optimal power adaptation and the effective capacity are investigated in two asymptotic cases with the loose and strict QoS requirements. In particular, we show that in the TAS scheme with the loose QoS restriction, the effective capacity converges to the ergodic capacity. Then, an exact closed-form solution is obtained for the ergodic capacity of the channel here.