Finite-SNR diversity-multiplexing tradeoff of space-time codes

A novel framework is presented to characterize the tradeoff between diversity and multiplexing of space-time codes at finite signal-to-noise ratios (SNR). The diversity gain of a space-time code is defined by the slope at a particular SNR of the outage probability versus SNR curve for a multiplexing gain defined by the ratio of the system spectral efficiency to the capacity of an additive white Gaussian noise (AWGN) channel. The finite-SNR diversity-multiplexing tradeoff is evaluated for orthogonal space-time block codes and spatial multiplexing with horizontal encoding. The tradeoff curves provide a characterization of achievable diversity and multiplexing gains for a given space-time code at SNR encountered in practice. It is seen that the achievable diversity gains at finite SNR are significantly lower than the asymptotic values given in the literature.