Compare Beamforming with Multiplexing for Mimo Relay Network in the Low SNR Regime

Given a multiple-antenna source and a multiple-antenna destination, a multiple-antenna relay between the source and the destination is desirable under useful circumstances. In this paper, a spatial multiplexing scheme and a cooperative beamforming scheme have been proposed for a non-regenerative MIMO relay system. In the spatial multiplexing scheme, the MIMO relay channel can be decomposed into several parallel channels each with the source to relay channel gain and the relay to destination channel gain. In the cooperative beamforming scheme, the transmitter uses all of its antennas to transmit one signal instead of multiplexing different signals simultaneously. It can be proved that the capacity of the spatial multiplexing scheme is smaller than that of the cooperative beamforming scheme in the low SNR regime. It is shown that for asymptotically large number of relays, the capacity of the spatial multiplexing scheme is converging to that of the beamforming scheme.