On the Diversity-Multiplexing Tradeoff in MIMO Wireless Channels at Finite SNRs

In this paper a new framework to characterize the trade off between diversity and multiplexing gains of Multi Input Multi Output (MIMO) wireless systems at finite Signal to Noise Ratios (SNRs) is presented By suitable definitions of non asymptotic diversity and multiplexing gains we extract a useful tool to investigate the performance of space time schemes at finite SNRs Exact results on the diversity multiplexing tradeoff (DMT) are derived for Multi Input Single Output (MISO) Single Input Multi Output (SIMO) and 2 x 2 MIMO channels We show that our outcomes coincide with the Zheng and Tse s results at high SNRs When the new definitions of non asymptotic diversity and multiplexing gains are used the resulted DMT converges to its asymptotic value at realistic SNRs Furthermore using these definitions enables the diversity gain to represent the outage probability with reasonable accuracy