Finite-signal-to-noise ratio diversity-multiplexing-rate trade-off in limited feedback beamforming systems with imperfect channel state information

The problem of diversity-multiplexing-rate trade-off (DMRT) in limited feedback beamforming systems is addressed here. A major difference from previous works is that the authors consider the trade-off in finite-signal-to-noise ratio (SNR) regime. Under this condition, the feedback rate has a great impact on the conventional diversity-multiplexing relationship. Hence, the release of the trade-off among diversity, multiplexing and feedback rate has a practical benefit to the design and adoption of space-time signals in limited feedback beamforming systems. Asymptotical analysis shows that the obtained trade-off is consistent with the conventional one when feedback rate equals to zero and the SNR approaches infinity. Furthermore, considering the channel dynamics, the authors investigate the effect of imperfect channel state information (CSI) caused by channel estimation error and feedback delay on the DMRT. It is found that in the presence of imperfect CSI, besides the system parameters, such as the number of transmit and receive antennas, maximum diversity order and multiplexing gain are also limited by SNR and correlation coefficient between the obtained CSI and the real CSI. Finally, our theoretical claims are validated by the numerical results.