Finite-SNR Diversity-Multiplexing Tradeoff for OFDM Channels

The diversity-multiplexing tradeoff, which relates the transmission reliability and efficiency, is an important performance metric in wireless communications. So far only an asymptotic tradeoff result has been obtained for OFDM channels, and such result is only valid for high SNRs. To characterize the outage performance of OFDM systems in realistic SNRs, a finite-SNR framework that analyzes and describes the diversity-multiplexing tradeoff will be proposed in this paper. New upper and lower bounds on outage probabilities will be derived by using the method of integral round a contour, Laurent series, and the properties of Meijer's G-function and Gamma function. The finite-SNR diversity gain, as a function of the multiplexing gain and SNR, will also be computed by Meijer's G-function. We will then show that the finite-SNR diversity-multiplexing tradeoff will converge to the corresponding asymptotic results as SNR tends to infinity. As a result, the finite-SNR diversity-multiplexing tradeoff can be used to estimate the additional SNR required to decrease the outage probability by a specified amount for a given multiplexing gain.