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

• Published in: IEEE transactions on communications 2008-11, Vol.56 (11), p.1972-1981
• Main Authors: Pauli, V., Schober, R., Lampe, L.
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; Channels; Closed-form solution; Constellations; Detectors; Differential phase shift keying; differential space time modulation; Error detection; Exact sciences and technology; Exact solutions; Fading; Feedback; Information, signal and communications theory; MIMO; MIMO fading channels; Modulation, demodulation; Organization, operation and development plans; Performance analysis; Permissible error; Phase detection; Phase modulation; Quadratic forms; Radiocommunications; Random variables; Signal and communications theory; Studies; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments)
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2008.060692

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,eff T MSDD with N &#x02192 ∞ suffers only from an SNR loss of (1 -2B h,eff T) compared to CD, whereas DFDD suffers from a diversity loss of (1 - 2B h,eff T).