In wireless transmissions great capacity gains can be realized by using multiple-input multiple-output (MIMO) systems. We introduce a closed-loop MIMO architecture with linear array signal processing. The novel architecture uses the feedback channel to request a retransmission of signal parts in critical subspaces. The requested backup subsequently helps the receiver to evade excessive noise amplification in the linear signal reconstruction. Since the backup signal is embedded in the successivetransmission frame, which may require yet another backup, the procedure results in a recursive spatial multiplexing (RSM) scheme. We compare the performance of RSM with other closed-loop MIMO systems by means of the system constrained ergodic capacities. The recursive nature of RSM makes it impossible to guarantee a maximum delay. Exploiting receive diversity in MIMO systems, a reduction of the transmit signal dimensions for a constant number of receive antennas leads to less frequent retransmission requests. For that reason, we introduce optimal transmit antenna selection strategies, which are found by means of machine learning methods.