Switching between antenna selection and spatial multiplexing in the nonregenerative MIMO relay channel

The use of a relay to aid communication between a data source and its desired destination is an attractive solution for low-cost coverage extension, capacity enhancement, and reliability improvement. The relays need not even decode the signal in order to aid the transmission. Multi-antenna relays, in particular, may apply a linear transfer matrix to improve transmission while maintaining a simple design. The usage of multiple antennas, however, raises questions about which of the multitude of transmission strategies should be used for a given channel realization. In this paper, the use of pre-existing adaptation techniques is shown to be inapplicable to the linear MIMO relay channel, motivating the derivation of new techniques. To simplify the task, the source is limited to transmitting using either spatial multiplexing with no channel state information, or antenna selection based on a limited amount of feedback from the destination. Transmission is assumed to be fixed-rate and adaptation is based on minimizing the symbol error rate. A sufficient condition for multiplexing to outperform antenna selection is derived and, out of this, a value that behaves as an effective condition number of the relay channel is found.