Finite-SNR Performance Analysis of Space–Time Coding in Correlated Ricean MIMO Channels

The performance analysis and the subsequent design of space-time codes (STC) in multiantenna channels commonly assume an infinite signal-to-noise ratio (SNR). This assumption has been shown to be justified in uncorrelated Rayleigh-fading channels. By contrast, this correspondence investigates STC in all SNR regimes and in the broad class of space-time correlated Ricean fading multiple-input-multiple-output (MIMO) channels. For rank-deficient codes, it is proven analytically that the error probability is significantly affected by spatial correlations and coherent components, irrespective of the SNR range and the temporal correlation. For full-rank codes, the performance and the code design are shown to be affected by spatial correlations and/or coherent paths only at finite SNR in slow fading channels, whereas in time-varying channels, they are affected in all SNR regimes. Hence, there is no guarantee that STC designed for independent and indentically distributed (i.i.d.) Rayleigh-fading channels perform adequately in space-time correlated Rayleigh/Ricean channels. Simulation examples confirm the conclusions drawn from the analytical derivations. They further illustrate that the use of a high SNR assumption does not allow to accurately estimate the behavior of STC in practical scenarios and should, thus, be used with care.