Finite-SNR diversity-multiplexing tradeoff for spatially correlated Rayleigh MIMO channels

In this paper, we derive the exact expression of the finite-signal to noise ratio (SNR) diversity-multiplexing tradeoff (DMT) for Rayleigh fading multiple-input multiple-output (MIMO) channels with dual correlated antennas at the transmitter (2×N_r) and/or at the receiver (N_t ×2). We first derive the exact outage probability versus SNR. While finite-SNR DMT and outage probabilities are usually only estimated, we show that the numerical results of our derived outage probability and finite-SNR DMT are identical to those obtained using Monte Carlo simulations. Furthermore, it is shown that achievable diversity gains at realistic SNRs are significantly lower than asymptotic values and that the DMT degrades as the spatial correlation increases. 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 realistic SNRs and propagation environments.