In this article, the performance of a power domain downlink multiple-input multiple-output non-orthogonal multiple access system, where the base station (BS) equipped with three antennas communicates simultaneously with three mobile users equipped with multiple antennas, is analyzed over Nakagami-m fading channels in the presence of channel estimation error (CEE), feedback delay (FBD), and imperfect successive interference cancellation. In the considered system, the BS applies transmit antenna selection (TAS)/Alamouti-space-time block coding (STBC) scheme while mobile users are assumed to adopt maximum-ratio combining technique in order to take advantage of the combination of transmit and receive diversities. In particular, in order to apply Alamouti-STBC scheme at the BS, one of the transmit antennas is determined randomly while the other one is selected according to decision of the majority of mobile users. For performance metrics, closed-form outage probability (OP) and ergodic capacity (EC) expressions derived with the help of moment generating function approach. Moreover, asymptotic analyses are maintained to demonstrate the effects of CEE and FBD in terms of diversity order and array gain. We show that the proposed system provides better OP and EC performance than the system without antenna selection for different users and conditions.