Finite-SNR Diversity-Multiplexing Tradeoff for Rayleigh MIMO Channels

In this paper, exact diversity-multiplexing tradeoff (DMT) at finite signal to noise ratio (SNR) for multipleinput multiple-output (MIMO) systems with dual antennas at the transmitter (2 × N_r) and/or at the receiver (N_t × 2) is derived over Rayleigh fading channels. We derive the outage probability of the mutual information between transmitted and received signals versus SNR. It is shown that at realistic SNRs, achievable diversity gains are significantly lower than asymptotic values. While space-time codes (STCs) for MIMO systems are conventionally designed to achieve the asymptotic DMT frontier, this finite-SNR DMT could provide a new insight to design STCs for practical MIMO systems optimized at operational SNRs.