Abstract

This paper reports a photonic chirp rates estimator for the piecewise linear frequency modulated waveforms (PLFMWs). The estimator is based on the photonic self-fractional Fourier transform (FrFT) by utilizing the input PLFMW as the transform kernel. In this way, the self-FrFT operation can be finished with short latency time and the chirp rates of all LFM sub-pulses can be retrieved according to their fractional frequencies. In experiment, the chirp rates estimation of a four-stage PLFMW is performed. The measurement range from −964.47 GHz/µs to 50.76 GHz/µs with resolution of 0.0518 GHz/µs is demonstrated for the experimental system. And the absolute measurement error within ±0.06 GHz/µs and the relative measurement error less than 2% is also obtained.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Qazi and A. Fam, “Good code sets based on Piecewise Linear FM,” in Radar Conference (IEEE, 2012), pp. 0522–0527.
  2. F. Qazi and A. Fam, “Discrete frequency-coding waveform sets based on piecewise linear FM,” in Radar Conference (IEEE, 2014), pp. 0469–0473.
  3. F. Qazi, “Triangular FM Based Discrete Frequency-Coding Waveform Sets,” in Military Communications Conference (IEEE, 2014), pp. 766–771.
  4. C. Gao, K. Teh, and A. Liu, “Frequency coding waveform with segment LFM,” in Synthetic Aperture Radar 5th Asia-Pacific Conference (IEEE, 2015), pp. 507–510.
  5. R. Jeevanmai and N. D. Rani, “Sidelobe reduction using frequency modulated pulse compression techniques in radar,” Int. J. Latest Trends Eng. Tech. 7(3), 171–179 (2013).
  6. Y. Chan, M. Chua, and V. Koo, “Sidelobes reduction using simple two and tri-stages nonlinear frequency modulation (NLFM),” Prog. Electromagn. Res. 98, 33–52 (2009).
    [Crossref]
  7. C. Gao, K. Teh, A. Liu, and H. Sun, “Piecewise LFM waveform for MIMO radar,” IEEE Trans. Aerosp. Electron. Syst. 52(2), 590–602 (2016).
    [Crossref]
  8. G. Chang, A. Liu, C. Yu, Y. Ji, Y. Wang, and J. Zhang, “Orthogonal waveform with multiple diversities for MIMO radar,” IEEE Sens. J. 18(11), 4462–4476 (2018).
    [Crossref]
  9. W. Wang, “Large time-bandwidth product MIMO radar waveform design based on chirp rate diversity,” IEEE Sens. J. 15(2), 1027–1034 (2015).
    [Crossref]
  10. M. A. Khan, R. K. Rao, and X. Wang, “Performance of Multiuser MIMO Communication System using Chirp Modulation,” in International Symposium on Performance Evaluation of Computer and Telecommunication Systems (IEEE, 2013), pp. 115–119.
  11. M. Roberton and E. R. Brown, “Integrated radar and communications based on chirped spread-spectrum techniques,” in MTT-S International Microwave Symposium Digest (IEEE, 2003), pp. 611–614.
  12. D. Gaglione, C. Clemente, C. V. Ilioudis, A. R. Persico, I. K. Proudler, and J. J. Soraghan, “Fractional Fourier Based Waveform for a Joint Radar-Communication System,” in Radar Conference (IEEE, 2016), pp. 1–6.
  13. S. Pan and J. Yao, “Photonics-based broadband microwave measurement,” J. Lightwave Technol. 35(16), 3498–3513 (2017).
    [Crossref]
  14. B. Zhang, X. Wang, and S. Pan, “Photonics-based instantaneous multi-parameter measurement of a linear frequency modulation microwave signal,” J. Lightwave Technol. 36(13), 2589–2596 (2018).
    [Crossref]
  15. M. Pelusi, F. Luan, T. D. Vo, M. R. Lamont, S. J. Madden, D. A. Bulla, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyzer with terahertz bandwidth,” Nat. Photonics 3(3), 139–143 (2009).
    [Crossref]
  16. M. Drummond, P. Monteiro, and R. Nogueira, “Photonic RF instantaneous frequency measurement system by means of a polarization domain interferometer,” Opt. Express 17(7), 5433–5438 (2009).
    [Crossref]
  17. S. Pan, J. Fu, and J. Yao, “Photonic approach to the simultaneous measurement of the frequency, amplitude, pulse width, and time of arrival of a microwave signal,” Opt. Lett. 37(1), 7–9 (2012).
    [Crossref]
  18. X. Zou, W. Pan, B. Luo, and L. Yan, “Photonic instantaneous frequency measurement using a single laser source and two quadrature optical filters,” IEEE Photonics Technol. Lett. 23(1), 39–41 (2011).
    [Crossref]
  19. S. Pan and J. Yao, “Instantaneous microwave frequency measurement using a photonic microwave filter pair,” IEEE Photonics Technol. Lett. 22(19), 1437–1439 (2010).
    [Crossref]
  20. L. Almeida, “The fractional Fourier transform and time-frequency representations,” IEEE Trans. Signal Process. 42(11), 3084–3091 (1994).
    [Crossref]
  21. R. Tao, X. Li, and Y. Li, “Time-delay estimation of chirp signals in the fractional Fourier domain,” IEEE Trans. Signal Process. 57(7), 2852–2855 (2009).
    [Crossref]
  22. L. Qi, R. Tao, and S. Zhou, “Detection and parameter estimation of multicomponent LFM signal based on the fractional Fourier transform,” Sci China Ser F 47(2), 184–198 (2004).
    [Crossref]
  23. X. Xia, “Discrete chirp-Fourier transform and its application to chirp rate estimation,” IEEE Trans. Signal Process. 48(11), 3122–3133 (2000).
    [Crossref]
  24. A. Serbes, “On the estimation of LFM signal parameters: analytical formulation,” IEEE Trans. Aerosp. Electron. Syst. 54(2), 848–860 (2018).
    [Crossref]
  25. A. Serbes and A. Omair, “A fast and accurate chirp rate estimation algorithm based on the fractional Fourier transform,” in 25th European Signal Processing Conference (IEEE, 2017), pp. 1145–1149.
  26. A. W. Lohmann and D. Mendlovic, “Fractional Fourier transform: photonic implementation,” Appl. Opt. 33(32), 7661–7664 (1994).
    [Crossref]
  27. C. Cuadrado-Laborde, A. Carrascosa, A. Díez, J. L. Cruz, and M. V. Andres, “Photonic fractional Fourier transformer with a single dispersive device,” Opt. Express 21(7), 8558–8563 (2013).
    [Crossref]
  28. C. Schnébelin and H. G. Chatellus, “Agile photonic fractional Fourier transformation of optical and RF signals,” Optica 4(8), 907–910 (2017).
    [Crossref]
  29. B. Hraimel, “Optical single-sideband modulation with tunable optical carrier to sideband ratio in radio over fiber systems,” J. Lightwave Technol. 29(5), 775–781 (2011).
    [Crossref]

2018 (3)

G. Chang, A. Liu, C. Yu, Y. Ji, Y. Wang, and J. Zhang, “Orthogonal waveform with multiple diversities for MIMO radar,” IEEE Sens. J. 18(11), 4462–4476 (2018).
[Crossref]

B. Zhang, X. Wang, and S. Pan, “Photonics-based instantaneous multi-parameter measurement of a linear frequency modulation microwave signal,” J. Lightwave Technol. 36(13), 2589–2596 (2018).
[Crossref]

A. Serbes, “On the estimation of LFM signal parameters: analytical formulation,” IEEE Trans. Aerosp. Electron. Syst. 54(2), 848–860 (2018).
[Crossref]

2017 (2)

2016 (1)

C. Gao, K. Teh, A. Liu, and H. Sun, “Piecewise LFM waveform for MIMO radar,” IEEE Trans. Aerosp. Electron. Syst. 52(2), 590–602 (2016).
[Crossref]

2015 (1)

W. Wang, “Large time-bandwidth product MIMO radar waveform design based on chirp rate diversity,” IEEE Sens. J. 15(2), 1027–1034 (2015).
[Crossref]

2013 (2)

R. Jeevanmai and N. D. Rani, “Sidelobe reduction using frequency modulated pulse compression techniques in radar,” Int. J. Latest Trends Eng. Tech. 7(3), 171–179 (2013).

C. Cuadrado-Laborde, A. Carrascosa, A. Díez, J. L. Cruz, and M. V. Andres, “Photonic fractional Fourier transformer with a single dispersive device,” Opt. Express 21(7), 8558–8563 (2013).
[Crossref]

2012 (1)

2011 (2)

X. Zou, W. Pan, B. Luo, and L. Yan, “Photonic instantaneous frequency measurement using a single laser source and two quadrature optical filters,” IEEE Photonics Technol. Lett. 23(1), 39–41 (2011).
[Crossref]

B. Hraimel, “Optical single-sideband modulation with tunable optical carrier to sideband ratio in radio over fiber systems,” J. Lightwave Technol. 29(5), 775–781 (2011).
[Crossref]

2010 (1)

S. Pan and J. Yao, “Instantaneous microwave frequency measurement using a photonic microwave filter pair,” IEEE Photonics Technol. Lett. 22(19), 1437–1439 (2010).
[Crossref]

2009 (4)

R. Tao, X. Li, and Y. Li, “Time-delay estimation of chirp signals in the fractional Fourier domain,” IEEE Trans. Signal Process. 57(7), 2852–2855 (2009).
[Crossref]

Y. Chan, M. Chua, and V. Koo, “Sidelobes reduction using simple two and tri-stages nonlinear frequency modulation (NLFM),” Prog. Electromagn. Res. 98, 33–52 (2009).
[Crossref]

M. Pelusi, F. Luan, T. D. Vo, M. R. Lamont, S. J. Madden, D. A. Bulla, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyzer with terahertz bandwidth,” Nat. Photonics 3(3), 139–143 (2009).
[Crossref]

M. Drummond, P. Monteiro, and R. Nogueira, “Photonic RF instantaneous frequency measurement system by means of a polarization domain interferometer,” Opt. Express 17(7), 5433–5438 (2009).
[Crossref]

2004 (1)

L. Qi, R. Tao, and S. Zhou, “Detection and parameter estimation of multicomponent LFM signal based on the fractional Fourier transform,” Sci China Ser F 47(2), 184–198 (2004).
[Crossref]

2000 (1)

X. Xia, “Discrete chirp-Fourier transform and its application to chirp rate estimation,” IEEE Trans. Signal Process. 48(11), 3122–3133 (2000).
[Crossref]

1994 (2)

A. W. Lohmann and D. Mendlovic, “Fractional Fourier transform: photonic implementation,” Appl. Opt. 33(32), 7661–7664 (1994).
[Crossref]

L. Almeida, “The fractional Fourier transform and time-frequency representations,” IEEE Trans. Signal Process. 42(11), 3084–3091 (1994).
[Crossref]

Almeida, L.

L. Almeida, “The fractional Fourier transform and time-frequency representations,” IEEE Trans. Signal Process. 42(11), 3084–3091 (1994).
[Crossref]

Andres, M. V.

Brown, E. R.

M. Roberton and E. R. Brown, “Integrated radar and communications based on chirped spread-spectrum techniques,” in MTT-S International Microwave Symposium Digest (IEEE, 2003), pp. 611–614.

Bulla, D. A.

M. Pelusi, F. Luan, T. D. Vo, M. R. Lamont, S. J. Madden, D. A. Bulla, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyzer with terahertz bandwidth,” Nat. Photonics 3(3), 139–143 (2009).
[Crossref]

Carrascosa, A.

Chan, Y.

Y. Chan, M. Chua, and V. Koo, “Sidelobes reduction using simple two and tri-stages nonlinear frequency modulation (NLFM),” Prog. Electromagn. Res. 98, 33–52 (2009).
[Crossref]

Chang, G.

G. Chang, A. Liu, C. Yu, Y. Ji, Y. Wang, and J. Zhang, “Orthogonal waveform with multiple diversities for MIMO radar,” IEEE Sens. J. 18(11), 4462–4476 (2018).
[Crossref]

Chatellus, H. G.

Choi, D. Y.

M. Pelusi, F. Luan, T. D. Vo, M. R. Lamont, S. J. Madden, D. A. Bulla, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyzer with terahertz bandwidth,” Nat. Photonics 3(3), 139–143 (2009).
[Crossref]

Chua, M.

Y. Chan, M. Chua, and V. Koo, “Sidelobes reduction using simple two and tri-stages nonlinear frequency modulation (NLFM),” Prog. Electromagn. Res. 98, 33–52 (2009).
[Crossref]

Clemente, C.

D. Gaglione, C. Clemente, C. V. Ilioudis, A. R. Persico, I. K. Proudler, and J. J. Soraghan, “Fractional Fourier Based Waveform for a Joint Radar-Communication System,” in Radar Conference (IEEE, 2016), pp. 1–6.

Cruz, J. L.

Cuadrado-Laborde, C.

Díez, A.

Drummond, M.

Eggleton, B. J.

M. Pelusi, F. Luan, T. D. Vo, M. R. Lamont, S. J. Madden, D. A. Bulla, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyzer with terahertz bandwidth,” Nat. Photonics 3(3), 139–143 (2009).
[Crossref]

Fam, A.

F. Qazi and A. Fam, “Good code sets based on Piecewise Linear FM,” in Radar Conference (IEEE, 2012), pp. 0522–0527.

F. Qazi and A. Fam, “Discrete frequency-coding waveform sets based on piecewise linear FM,” in Radar Conference (IEEE, 2014), pp. 0469–0473.

Fu, J.

Gaglione, D.

D. Gaglione, C. Clemente, C. V. Ilioudis, A. R. Persico, I. K. Proudler, and J. J. Soraghan, “Fractional Fourier Based Waveform for a Joint Radar-Communication System,” in Radar Conference (IEEE, 2016), pp. 1–6.

Gao, C.

C. Gao, K. Teh, A. Liu, and H. Sun, “Piecewise LFM waveform for MIMO radar,” IEEE Trans. Aerosp. Electron. Syst. 52(2), 590–602 (2016).
[Crossref]

C. Gao, K. Teh, and A. Liu, “Frequency coding waveform with segment LFM,” in Synthetic Aperture Radar 5th Asia-Pacific Conference (IEEE, 2015), pp. 507–510.

Hraimel, B.

Ilioudis, C. V.

D. Gaglione, C. Clemente, C. V. Ilioudis, A. R. Persico, I. K. Proudler, and J. J. Soraghan, “Fractional Fourier Based Waveform for a Joint Radar-Communication System,” in Radar Conference (IEEE, 2016), pp. 1–6.

Jeevanmai, R.

R. Jeevanmai and N. D. Rani, “Sidelobe reduction using frequency modulated pulse compression techniques in radar,” Int. J. Latest Trends Eng. Tech. 7(3), 171–179 (2013).

Ji, Y.

G. Chang, A. Liu, C. Yu, Y. Ji, Y. Wang, and J. Zhang, “Orthogonal waveform with multiple diversities for MIMO radar,” IEEE Sens. J. 18(11), 4462–4476 (2018).
[Crossref]

Khan, M. A.

M. A. Khan, R. K. Rao, and X. Wang, “Performance of Multiuser MIMO Communication System using Chirp Modulation,” in International Symposium on Performance Evaluation of Computer and Telecommunication Systems (IEEE, 2013), pp. 115–119.

Koo, V.

Y. Chan, M. Chua, and V. Koo, “Sidelobes reduction using simple two and tri-stages nonlinear frequency modulation (NLFM),” Prog. Electromagn. Res. 98, 33–52 (2009).
[Crossref]

Lamont, M. R.

M. Pelusi, F. Luan, T. D. Vo, M. R. Lamont, S. J. Madden, D. A. Bulla, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyzer with terahertz bandwidth,” Nat. Photonics 3(3), 139–143 (2009).
[Crossref]

Li, X.

R. Tao, X. Li, and Y. Li, “Time-delay estimation of chirp signals in the fractional Fourier domain,” IEEE Trans. Signal Process. 57(7), 2852–2855 (2009).
[Crossref]

Li, Y.

R. Tao, X. Li, and Y. Li, “Time-delay estimation of chirp signals in the fractional Fourier domain,” IEEE Trans. Signal Process. 57(7), 2852–2855 (2009).
[Crossref]

Liu, A.

G. Chang, A. Liu, C. Yu, Y. Ji, Y. Wang, and J. Zhang, “Orthogonal waveform with multiple diversities for MIMO radar,” IEEE Sens. J. 18(11), 4462–4476 (2018).
[Crossref]

C. Gao, K. Teh, A. Liu, and H. Sun, “Piecewise LFM waveform for MIMO radar,” IEEE Trans. Aerosp. Electron. Syst. 52(2), 590–602 (2016).
[Crossref]

C. Gao, K. Teh, and A. Liu, “Frequency coding waveform with segment LFM,” in Synthetic Aperture Radar 5th Asia-Pacific Conference (IEEE, 2015), pp. 507–510.

Lohmann, A. W.

Luan, F.

M. Pelusi, F. Luan, T. D. Vo, M. R. Lamont, S. J. Madden, D. A. Bulla, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyzer with terahertz bandwidth,” Nat. Photonics 3(3), 139–143 (2009).
[Crossref]

Luo, B.

X. Zou, W. Pan, B. Luo, and L. Yan, “Photonic instantaneous frequency measurement using a single laser source and two quadrature optical filters,” IEEE Photonics Technol. Lett. 23(1), 39–41 (2011).
[Crossref]

Luther-Davies, B.

M. Pelusi, F. Luan, T. D. Vo, M. R. Lamont, S. J. Madden, D. A. Bulla, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyzer with terahertz bandwidth,” Nat. Photonics 3(3), 139–143 (2009).
[Crossref]

Madden, S. J.

M. Pelusi, F. Luan, T. D. Vo, M. R. Lamont, S. J. Madden, D. A. Bulla, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyzer with terahertz bandwidth,” Nat. Photonics 3(3), 139–143 (2009).
[Crossref]

Mendlovic, D.

Monteiro, P.

Nogueira, R.

Omair, A.

A. Serbes and A. Omair, “A fast and accurate chirp rate estimation algorithm based on the fractional Fourier transform,” in 25th European Signal Processing Conference (IEEE, 2017), pp. 1145–1149.

Pan, S.

Pan, W.

X. Zou, W. Pan, B. Luo, and L. Yan, “Photonic instantaneous frequency measurement using a single laser source and two quadrature optical filters,” IEEE Photonics Technol. Lett. 23(1), 39–41 (2011).
[Crossref]

Pelusi, M.

M. Pelusi, F. Luan, T. D. Vo, M. R. Lamont, S. J. Madden, D. A. Bulla, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyzer with terahertz bandwidth,” Nat. Photonics 3(3), 139–143 (2009).
[Crossref]

Persico, A. R.

D. Gaglione, C. Clemente, C. V. Ilioudis, A. R. Persico, I. K. Proudler, and J. J. Soraghan, “Fractional Fourier Based Waveform for a Joint Radar-Communication System,” in Radar Conference (IEEE, 2016), pp. 1–6.

Proudler, I. K.

D. Gaglione, C. Clemente, C. V. Ilioudis, A. R. Persico, I. K. Proudler, and J. J. Soraghan, “Fractional Fourier Based Waveform for a Joint Radar-Communication System,” in Radar Conference (IEEE, 2016), pp. 1–6.

Qazi, F.

F. Qazi and A. Fam, “Good code sets based on Piecewise Linear FM,” in Radar Conference (IEEE, 2012), pp. 0522–0527.

F. Qazi, “Triangular FM Based Discrete Frequency-Coding Waveform Sets,” in Military Communications Conference (IEEE, 2014), pp. 766–771.

F. Qazi and A. Fam, “Discrete frequency-coding waveform sets based on piecewise linear FM,” in Radar Conference (IEEE, 2014), pp. 0469–0473.

Qi, L.

L. Qi, R. Tao, and S. Zhou, “Detection and parameter estimation of multicomponent LFM signal based on the fractional Fourier transform,” Sci China Ser F 47(2), 184–198 (2004).
[Crossref]

Rani, N. D.

R. Jeevanmai and N. D. Rani, “Sidelobe reduction using frequency modulated pulse compression techniques in radar,” Int. J. Latest Trends Eng. Tech. 7(3), 171–179 (2013).

Rao, R. K.

M. A. Khan, R. K. Rao, and X. Wang, “Performance of Multiuser MIMO Communication System using Chirp Modulation,” in International Symposium on Performance Evaluation of Computer and Telecommunication Systems (IEEE, 2013), pp. 115–119.

Roberton, M.

M. Roberton and E. R. Brown, “Integrated radar and communications based on chirped spread-spectrum techniques,” in MTT-S International Microwave Symposium Digest (IEEE, 2003), pp. 611–614.

Schnébelin, C.

Serbes, A.

A. Serbes, “On the estimation of LFM signal parameters: analytical formulation,” IEEE Trans. Aerosp. Electron. Syst. 54(2), 848–860 (2018).
[Crossref]

A. Serbes and A. Omair, “A fast and accurate chirp rate estimation algorithm based on the fractional Fourier transform,” in 25th European Signal Processing Conference (IEEE, 2017), pp. 1145–1149.

Soraghan, J. J.

D. Gaglione, C. Clemente, C. V. Ilioudis, A. R. Persico, I. K. Proudler, and J. J. Soraghan, “Fractional Fourier Based Waveform for a Joint Radar-Communication System,” in Radar Conference (IEEE, 2016), pp. 1–6.

Sun, H.

C. Gao, K. Teh, A. Liu, and H. Sun, “Piecewise LFM waveform for MIMO radar,” IEEE Trans. Aerosp. Electron. Syst. 52(2), 590–602 (2016).
[Crossref]

Tao, R.

R. Tao, X. Li, and Y. Li, “Time-delay estimation of chirp signals in the fractional Fourier domain,” IEEE Trans. Signal Process. 57(7), 2852–2855 (2009).
[Crossref]

L. Qi, R. Tao, and S. Zhou, “Detection and parameter estimation of multicomponent LFM signal based on the fractional Fourier transform,” Sci China Ser F 47(2), 184–198 (2004).
[Crossref]

Teh, K.

C. Gao, K. Teh, A. Liu, and H. Sun, “Piecewise LFM waveform for MIMO radar,” IEEE Trans. Aerosp. Electron. Syst. 52(2), 590–602 (2016).
[Crossref]

C. Gao, K. Teh, and A. Liu, “Frequency coding waveform with segment LFM,” in Synthetic Aperture Radar 5th Asia-Pacific Conference (IEEE, 2015), pp. 507–510.

Vo, T. D.

M. Pelusi, F. Luan, T. D. Vo, M. R. Lamont, S. J. Madden, D. A. Bulla, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyzer with terahertz bandwidth,” Nat. Photonics 3(3), 139–143 (2009).
[Crossref]

Wang, W.

W. Wang, “Large time-bandwidth product MIMO radar waveform design based on chirp rate diversity,” IEEE Sens. J. 15(2), 1027–1034 (2015).
[Crossref]

Wang, X.

B. Zhang, X. Wang, and S. Pan, “Photonics-based instantaneous multi-parameter measurement of a linear frequency modulation microwave signal,” J. Lightwave Technol. 36(13), 2589–2596 (2018).
[Crossref]

M. A. Khan, R. K. Rao, and X. Wang, “Performance of Multiuser MIMO Communication System using Chirp Modulation,” in International Symposium on Performance Evaluation of Computer and Telecommunication Systems (IEEE, 2013), pp. 115–119.

Wang, Y.

G. Chang, A. Liu, C. Yu, Y. Ji, Y. Wang, and J. Zhang, “Orthogonal waveform with multiple diversities for MIMO radar,” IEEE Sens. J. 18(11), 4462–4476 (2018).
[Crossref]

Xia, X.

X. Xia, “Discrete chirp-Fourier transform and its application to chirp rate estimation,” IEEE Trans. Signal Process. 48(11), 3122–3133 (2000).
[Crossref]

Yan, L.

X. Zou, W. Pan, B. Luo, and L. Yan, “Photonic instantaneous frequency measurement using a single laser source and two quadrature optical filters,” IEEE Photonics Technol. Lett. 23(1), 39–41 (2011).
[Crossref]

Yao, J.

Yu, C.

G. Chang, A. Liu, C. Yu, Y. Ji, Y. Wang, and J. Zhang, “Orthogonal waveform with multiple diversities for MIMO radar,” IEEE Sens. J. 18(11), 4462–4476 (2018).
[Crossref]

Zhang, B.

Zhang, J.

G. Chang, A. Liu, C. Yu, Y. Ji, Y. Wang, and J. Zhang, “Orthogonal waveform with multiple diversities for MIMO radar,” IEEE Sens. J. 18(11), 4462–4476 (2018).
[Crossref]

Zhou, S.

L. Qi, R. Tao, and S. Zhou, “Detection and parameter estimation of multicomponent LFM signal based on the fractional Fourier transform,” Sci China Ser F 47(2), 184–198 (2004).
[Crossref]

Zou, X.

X. Zou, W. Pan, B. Luo, and L. Yan, “Photonic instantaneous frequency measurement using a single laser source and two quadrature optical filters,” IEEE Photonics Technol. Lett. 23(1), 39–41 (2011).
[Crossref]

Appl. Opt. (1)

IEEE Photonics Technol. Lett. (2)

X. Zou, W. Pan, B. Luo, and L. Yan, “Photonic instantaneous frequency measurement using a single laser source and two quadrature optical filters,” IEEE Photonics Technol. Lett. 23(1), 39–41 (2011).
[Crossref]

S. Pan and J. Yao, “Instantaneous microwave frequency measurement using a photonic microwave filter pair,” IEEE Photonics Technol. Lett. 22(19), 1437–1439 (2010).
[Crossref]

IEEE Sens. J. (2)

G. Chang, A. Liu, C. Yu, Y. Ji, Y. Wang, and J. Zhang, “Orthogonal waveform with multiple diversities for MIMO radar,” IEEE Sens. J. 18(11), 4462–4476 (2018).
[Crossref]

W. Wang, “Large time-bandwidth product MIMO radar waveform design based on chirp rate diversity,” IEEE Sens. J. 15(2), 1027–1034 (2015).
[Crossref]

IEEE Trans. Aerosp. Electron. Syst. (2)

A. Serbes, “On the estimation of LFM signal parameters: analytical formulation,” IEEE Trans. Aerosp. Electron. Syst. 54(2), 848–860 (2018).
[Crossref]

C. Gao, K. Teh, A. Liu, and H. Sun, “Piecewise LFM waveform for MIMO radar,” IEEE Trans. Aerosp. Electron. Syst. 52(2), 590–602 (2016).
[Crossref]

IEEE Trans. Signal Process. (3)

X. Xia, “Discrete chirp-Fourier transform and its application to chirp rate estimation,” IEEE Trans. Signal Process. 48(11), 3122–3133 (2000).
[Crossref]

L. Almeida, “The fractional Fourier transform and time-frequency representations,” IEEE Trans. Signal Process. 42(11), 3084–3091 (1994).
[Crossref]

R. Tao, X. Li, and Y. Li, “Time-delay estimation of chirp signals in the fractional Fourier domain,” IEEE Trans. Signal Process. 57(7), 2852–2855 (2009).
[Crossref]

Int. J. Latest Trends Eng. Tech. (1)

R. Jeevanmai and N. D. Rani, “Sidelobe reduction using frequency modulated pulse compression techniques in radar,” Int. J. Latest Trends Eng. Tech. 7(3), 171–179 (2013).

J. Lightwave Technol. (3)

Nat. Photonics (1)

M. Pelusi, F. Luan, T. D. Vo, M. R. Lamont, S. J. Madden, D. A. Bulla, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyzer with terahertz bandwidth,” Nat. Photonics 3(3), 139–143 (2009).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Optica (1)

Prog. Electromagn. Res. (1)

Y. Chan, M. Chua, and V. Koo, “Sidelobes reduction using simple two and tri-stages nonlinear frequency modulation (NLFM),” Prog. Electromagn. Res. 98, 33–52 (2009).
[Crossref]

Sci China Ser F (1)

L. Qi, R. Tao, and S. Zhou, “Detection and parameter estimation of multicomponent LFM signal based on the fractional Fourier transform,” Sci China Ser F 47(2), 184–198 (2004).
[Crossref]

Other (8)

M. A. Khan, R. K. Rao, and X. Wang, “Performance of Multiuser MIMO Communication System using Chirp Modulation,” in International Symposium on Performance Evaluation of Computer and Telecommunication Systems (IEEE, 2013), pp. 115–119.

M. Roberton and E. R. Brown, “Integrated radar and communications based on chirped spread-spectrum techniques,” in MTT-S International Microwave Symposium Digest (IEEE, 2003), pp. 611–614.

D. Gaglione, C. Clemente, C. V. Ilioudis, A. R. Persico, I. K. Proudler, and J. J. Soraghan, “Fractional Fourier Based Waveform for a Joint Radar-Communication System,” in Radar Conference (IEEE, 2016), pp. 1–6.

F. Qazi and A. Fam, “Good code sets based on Piecewise Linear FM,” in Radar Conference (IEEE, 2012), pp. 0522–0527.

F. Qazi and A. Fam, “Discrete frequency-coding waveform sets based on piecewise linear FM,” in Radar Conference (IEEE, 2014), pp. 0469–0473.

F. Qazi, “Triangular FM Based Discrete Frequency-Coding Waveform Sets,” in Military Communications Conference (IEEE, 2014), pp. 766–771.

C. Gao, K. Teh, and A. Liu, “Frequency coding waveform with segment LFM,” in Synthetic Aperture Radar 5th Asia-Pacific Conference (IEEE, 2015), pp. 507–510.

A. Serbes and A. Omair, “A fast and accurate chirp rate estimation algorithm based on the fractional Fourier transform,” in 25th European Signal Processing Conference (IEEE, 2017), pp. 1145–1149.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1. Illustration of the time delay property of FrFT
Fig. 2.
Fig. 2. The schematic diagram of the self-FrFT based PLFMW chirp rate estimator. PLFMW: piecewise linear frequency modulated waveform; E/O: electro-optic modulation; OC: optical coupler; PD: photodetector; FFT: fast Fourier transform.
Fig. 3.
Fig. 3. (a) Experimental configuration of the proposed chirp rate estimation system. (b) Detailed structure of the DPMZM. DPMZM: dual-parallel Mach-Zehnder modulator; AWG: arbitrary waveform generator; AMP: amplifier; DSO: digital storage oscilloscope; DSP: digital signal processing; CS-SSB: carrier suppressed single-sideband.
Fig. 4.
Fig. 4. (a) Generated four-stage PLFMW; (b) spectrogram of the generated PLFMW; (c) spectrum of the FrFTed PLFMW; (d) measured chirp rates; and (e) time-chirp rate distribution of the PLFMW.
Fig. 5.
Fig. 5. (a) Spectrogram of the generated two-stage PLFMW with approximate chirp rates and (b) Measured result
Fig. 6.
Fig. 6. Chirp rate measurement error performance. (a) Absolute error and (b) relative error.

Tables (1)

Tables Icon

Table 1. Parameters of the four-stage PLFMW

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

F α [ s ( t ) ] ( u ) = 1 -  j cot α 2 π exp ( j cot α 2 u 2 ) s ( t ) exp ( j cot α 2 t 2 ) exp ( j u csc α t ) d t ,
s ( t τ ) = r e c t ( t τ T ) exp j [ 2 π f 0 ( t τ ) + π k ( t τ ) 2 ] ,
| F α [ s ( t ) ] ( u ) | sinc[ T ( u csc α 2 π k τ 2 π f 0 ) / 2 ] .
u = 2 π ( k τ + f 0 ) sin α .
S o u t ( f ) =  -  [ s i n ( t τ ) exp ( j 2 π Δ f t ) ] s i n ( t ) exp ( j 2 π f t ) d t = exp j [ 2 π ( f i + Δ f ) ( t τ ) + π k i ( t τ ) 2 ] exp j ( 2 π f i t π k t 2 ) exp ( 2 π f t ) d t = ( T i  -  τ )sinc[( T i  -  τ ) π ( f ( Δ f k i τ ))] ,
s i n ( t ) = { r e c t ( t T 1 ) exp j ( 2 π f 1 t + π k 1 t 2 ) 0 < t T 1 r e c t ( t T 1 T 2 ) exp j ( 2 π f 2 t + π k 2 t 2 ) T 1 < t T 1  +  T 2 r e c t ( t i n 1 T i T n ) exp j ( 2 π f n t + π k n t 2 ) i n 1 T n 1 < t i n T n .
f i = Δ f k i τ .
k i = ( Δ f f i ) / τ .
k < Δ f / τ .
k > Δ f f s / 2 τ .
Δ f f s / 2 τ < k < Δ f τ .
Δ f = 1 T τ ,
Δ k = Δ f τ = 1 T τ τ 2 .

Metrics