Diversity and multiplexing tradeoff of beamforming for MIMO channels

This work derives a tight upper bound on the diversity and spatial multiplexing gain for MIMO systems when the transmitter has perfect channel knowledge, generalizing the pioneering work of Zheng and Tse developed in the context of no channel state information at the transmit side. This result is obtained looking at the channel performance limits when both the SNR and the transmission rate tend to infinity, such that the relation between the rate and the capacity is constant. This result is then particularized for the optimal single beamforming scheme illustrating the performance loss incurred by any coding scheme based on this structure in the diversity versus rate tradeoff.