A unified performance analysis framework for differential detection in MIMO Rayleigh fading channels

In this paper, a unified framework for the analysis of differential detection (DD) schemes in time-variant multiple- input multiple-output Rayleigh fading channels is provided. The present results are very general in that they apply to transmission with differential phase-shift keying, unitary differential space- time modulation (DSTM), and block DSTM and reception with conventional DD (CDD), multiple-symbol DD (MSDD), decision- feedback DD (DFDD), and (differentially) coherent detection (CD). New result for general quadratic forms of Gaussian random variables are derived which allows us to obtain elegant closed-form expressions for the pairwise error probabilities (PEPs) of the dominant error events of the considered detectors. Furthermore, it is shown that a unified treatment of all considered detectors is possible with a properly defined effective signal- to-noise ratio (ESNR) and a useful connection between MSDD and minimum-mean-squared-error (MMSE) interpolation is established. Interesting novel results obtained from this analysis include: (i) DSTM constellations designed for CDD and CD are also optimum for MSDD and DFDD; (ii) the error floor entailed by MSDD and DFDD in time-variant fading decreases exponentially with the observation window size N; and (iii) in time-variant fading with effective normalized fading bandwidth B_h,effT MSDD with N rarr infin suffers only from an SNR loss of (1-2B_h,effT) compared to CD, whereas DFDD suffers from a diversity loss of (1-2B_h,effT).