Lower Bound for Finite-SNR DMT With Position Estimation Errors in MIMO Channels

The finite signal-to-noise ratio (SNR) situation for the diversity-multiplexing tradeoff (DMT) of multiple-input-multiple-output (MIMO) systems has become a fundamental research topic in wireless communications. In this letter, the impact of position estimation errors of the receiver on the finite-SNR DMT of the MIMO system is investigated. Formulas of the biased Cramér-Rao bound and the mean-square error lower bound of the biased finite-SNR DMT are proposed when the DMT value is influenced by the position estimation error of the receiver induced by a biased position estimator. Furthermore, based on the developed formulas, the case of the DMT over the Rayleigh fading channel and the position estimation errors raised by a radar is analyzed.