Comparisons of Two Real-Valued MIMO Signal Models and Their Associated ZF-SIC Detectors over the Rayleigh Fading Channel

Two real MIMO models, the new lattice representation and the conventional real model, have been proposed in literature as equivalent models to the same complex MIMO model. To learn which one shares more information with the complex model, we show in this paper that the matrices produced by singular value decomposition and QR-decomposition of the complex and new real channel matrices for the complex and new real models, respectively, are fully related. Also, the new real zero-forcing successive interference cancellation (ZF-SIC) detector is shown to find the same solution as the complex ZF-SIC detector. Comparisons of the two real ZF-SIC detectors based on the two real models are therefore equivalent to the comparisons of the complex and conventional real ZF-SIC detectors. Plenty comparisons of the two real ZF-SIC detectors over the Rayleigh fading channel are reported, including the average joint error probability at finite signal-to-noise ratio (SNR), outage probability at different layers, average error probability at high SNR, and the scenario with optimal transmit power allocation. These comparisons provide much understanding about the complex and two real models as well as their associated detectors.