Quadrature Frequency-Group Radar and its center estimation algorithms for small Vibrational Displacement

Figures

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  Figure 1. The QCW radar architecture.

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  Figure 2. Complex plot representation of ri(t): ri(t) due to the displacement x(t) is located in the thick arc.

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  Figure 3. The QFG radar architecture: (a) SFCW-type and (b) OFDM-type.

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  Figure 4. Received signal power (Transmission signal power is assumed to 1 mW): (a) 24 GHz band and (b) 2.4 GHz band.

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  Figure 5. Multiple arcs of the QFG radar for Δx = 1 mm: (a) Δf = 30 MHz and (b) Δf = 20 MHz.

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  Figure 6. Arc length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{\Delta }}{\vartheta }_{x}(m)$$\end{document}Δϑx(m) is almost constant with respect to m: (a) 24 GHz band and (b) 2.4 GHz band.

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  Figure 7. Examples at fc = 24 GHz, M = 4: (a) Δf = 30 MHz for Δx = 1 mm, (b) Δf = 40 MHz for Δx = 1 mm (c) Δf = 30 MHz for Δx = 0.1 mm, and (d) Δf = 5 MHz for Δx = 0.1 mm.

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  Figure 8. Circumcenter method: (a) If area \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{\Delta }}S > \epsilon $$\end{document}ΔS>ϵ, the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\widehat{DC}}_{I},{\widehat{DC}}_{Q})$$\end{document}(DC^I,DC^Q) is the circumcenter of the triangle S. (b) Flowchart.

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  Figure 9. Pratt method: (a) Gathered data points and (b) Flowchart.

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  Figure 10. Arcs of the QFG radar for different fc (Real center of the arcs are C (1, 1)): (a) fc = 400 MHz (b) fc = 2.4 GHz (c) fc = 10 GHz, and (d) fc = 24 GHz.

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  Figure 11. Normalized error for different carrier frequency bands for Δf = 20 MHz: (a) the QFG radar and (b) the QCW radar.

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  Figure 12. The effect of SNR on the error performance of circumcenter method.