Abstract

A novel scheme of microwave photonic generation of binary digitally modulated signals is proposed and experimentally demonstrated, which can simultaneously generate 2ASK, 2PSK and 2FSK. By dynamically manipulating an optical frequency comb, different modulation formats can be switched. Moreover, the bit rate and carrier frequency of the generated RF signals can be tuned.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  6. C. Wang and J. P. Yao, “Microwave and millimeter-wave arbitrary waveform generation and processing using fiber-optics-based techniques,” in Proceedings of IEEE International conference on Broadband Network & Multimedia Technology (IEEE, 2009), pp. 909–912.
    [Crossref]
  7. J. Yao, “Photonic generation of microwave arbitrary waveforms,” Opt. Commun. 284(15), 3723–3736 (2011).
    [Crossref]
  8. P. Xiang, X. Zheng, H. Zhang, Y. Li, and Y. Chen, “A novel approach to photonic generation of RF binary digital modulation signals,” Opt. Express 21(1), 631–639 (2013).
    [Crossref] [PubMed]
  9. Y. Long, L. Zhou, and J. Wang, “Photonic-assisted microwave signal multiplication and modulation using a silicon Mach-Zehnder modulator,” Sci. Rep. 6(1), 20215 (2016).
    [Crossref] [PubMed]
  10. P. Ghelfi, F. Scotti, F. Laghezza, and A. Bogoni, “Phase coding of RF pulses in photonics-aided frequency-agile coherent radar systems,” IEEE J. Quantum Electron. 48(9), 1151–1157 (2012).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  22. P. Cao, X. Hu, L. Zhang, J. Wu, X. Jiang, and Y. Su, “Photonic generation of microwave frequency shift keying signal using a single-drive Mach-Zehnder modulator,” Opt. Express 22(12), 14433–14440 (2014).
    [Crossref] [PubMed]
  23. L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Photonic generation of microwave frequency shift keying signals,” IEEE Photonics Technol. Lett. 28(18), 1928–1931 (2016).
    [Crossref]

2016 (2)

Y. Long, L. Zhou, and J. Wang, “Photonic-assisted microwave signal multiplication and modulation using a silicon Mach-Zehnder modulator,” Sci. Rep. 6(1), 20215 (2016).
[Crossref] [PubMed]

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Photonic generation of microwave frequency shift keying signals,” IEEE Photonics Technol. Lett. 28(18), 1928–1931 (2016).
[Crossref]

2015 (1)

2014 (3)

2013 (8)

P. Xiang, X. Zheng, H. Zhang, Y. Li, and Y. Chen, “A novel approach to photonic generation of RF binary digital modulation signals,” Opt. Express 21(1), 631–639 (2013).
[Crossref] [PubMed]

Y. Zhang and S. Pan, “Generation of phase-coded microwave signals using a polarization-modulator-based photonic microwave phase shifter,” Opt. Lett. 38(5), 766–768 (2013).
[Crossref] [PubMed]

H. Y. Jiang, L. S. Yan, J. Ye, W. Pan, B. Luo, and X. Zou, “Photonic generation of phase-coded microwave signals with tunable carrier frequency,” Opt. Lett. 38(8), 1361–1363 (2013).
[Crossref] [PubMed]

Z. Tang, T. Zhang, F. Zhang, and S. Pan, “Photonic generation of a phase-coded microwave signal based on a single dual-drive Mach-Zehnder modulator,” Opt. Lett. 38(24), 5365–5368 (2013).
[Crossref] [PubMed]

W. Li, L. X. Wang, M. Li, H. Wang, and N. H. Zhu, “Photonic generation of binary phase-coded microwave signals with large frequency tunability using a dual-parallel Mach–Zehnder modulator,” IEEE Photonics J. 5(4), 5501507 (2013).
[Crossref]

L. Gao, X. Chen, and J. Yao, “Photonic generation of a phase-coded microwave waveform with ultrawide frequency tunable range,” IEEE Photonics Technol. Lett. 25(10), 899–902 (2013).
[Crossref]

Y. Chen, A. Wen, and J. Yao, “Photonic generation of frequency tunable binary phase-coded microwave waveforms,” IEEE Photonics Technol. Lett. 25(23), 2319–2322 (2013).
[Crossref]

Z. Li, W. Li, H. Chi, X. Zhang, and J. Yao, “Photonic generation of phase-coded microwave signal with large frequency tenability,” IEEE Photonics Technol. Lett. 23(11), 712–714 (2013).
[Crossref]

2012 (2)

P. Ghelfi, F. Scotti, F. Laghezza, and A. Bogoni, “Phase coding of RF pulses in photonics-aided frequency-agile coherent radar systems,” IEEE J. Quantum Electron. 48(9), 1151–1157 (2012).
[Crossref]

P. Ghelfi, F. Scotti, F. Laghezza, and A. Bogoni, “Photonic generation of phase-modulated RF signals for pulse compression techniques in coherent radars,” J. Lightwave Technol. 30(11), 1638–1644 (2012).
[Crossref]

2011 (1)

J. Yao, “Photonic generation of microwave arbitrary waveforms,” Opt. Commun. 284(15), 3723–3736 (2011).
[Crossref]

2009 (1)

2007 (1)

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

2006 (1)

2003 (1)

C. Jason, H. Yan, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photonics Technol. Lett. 15(4), 581–583 (2003).
[Crossref]

2002 (1)

Bogoni, A.

P. Ghelfi, F. Scotti, F. Laghezza, and A. Bogoni, “Phase coding of RF pulses in photonics-aided frequency-agile coherent radar systems,” IEEE J. Quantum Electron. 48(9), 1151–1157 (2012).
[Crossref]

P. Ghelfi, F. Scotti, F. Laghezza, and A. Bogoni, “Photonic generation of phase-modulated RF signals for pulse compression techniques in coherent radars,” J. Lightwave Technol. 30(11), 1638–1644 (2012).
[Crossref]

Cao, P.

Capmany, J.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Chen, D.

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Photonic generation of microwave frequency shift keying signals,” IEEE Photonics Technol. Lett. 28(18), 1928–1931 (2016).
[Crossref]

Chen, X.

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Photonic generation of microwave frequency shift keying signals,” IEEE Photonics Technol. Lett. 28(18), 1928–1931 (2016).
[Crossref]

L. Gao, X. Chen, and J. Yao, “Photonic generation of a phase-coded microwave waveform with ultrawide frequency tunable range,” IEEE Photonics Technol. Lett. 25(10), 899–902 (2013).
[Crossref]

Chen, Y.

Chi, H.

Z. Li, W. Li, H. Chi, X. Zhang, and J. Yao, “Photonic generation of phase-coded microwave signal with large frequency tenability,” IEEE Photonics Technol. Lett. 23(11), 712–714 (2013).
[Crossref]

Gao, B.

Gao, L.

L. Gao, X. Chen, and J. Yao, “Photonic generation of a phase-coded microwave waveform with ultrawide frequency tunable range,” IEEE Photonics Technol. Lett. 25(10), 899–902 (2013).
[Crossref]

Ge, X.

Ghelfi, P.

P. Ghelfi, F. Scotti, F. Laghezza, and A. Bogoni, “Phase coding of RF pulses in photonics-aided frequency-agile coherent radar systems,” IEEE J. Quantum Electron. 48(9), 1151–1157 (2012).
[Crossref]

P. Ghelfi, F. Scotti, F. Laghezza, and A. Bogoni, “Photonic generation of phase-modulated RF signals for pulse compression techniques in coherent radars,” J. Lightwave Technol. 30(11), 1638–1644 (2012).
[Crossref]

Hu, X.

Huang, L.

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Photonic generation of microwave frequency shift keying signals,” IEEE Photonics Technol. Lett. 28(18), 1928–1931 (2016).
[Crossref]

Jalali, B.

C. Jason, H. Yan, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photonics Technol. Lett. 15(4), 581–583 (2003).
[Crossref]

Jason, C.

C. Jason, H. Yan, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photonics Technol. Lett. 15(4), 581–583 (2003).
[Crossref]

Jiang, H. Y.

Jiang, X.

Laghezza, F.

P. Ghelfi, F. Scotti, F. Laghezza, and A. Bogoni, “Photonic generation of phase-modulated RF signals for pulse compression techniques in coherent radars,” J. Lightwave Technol. 30(11), 1638–1644 (2012).
[Crossref]

P. Ghelfi, F. Scotti, F. Laghezza, and A. Bogoni, “Phase coding of RF pulses in photonics-aided frequency-agile coherent radar systems,” IEEE J. Quantum Electron. 48(9), 1151–1157 (2012).
[Crossref]

Leaird, D. E.

Li, M.

W. Li, L. X. Wang, M. Li, H. Wang, and N. H. Zhu, “Photonic generation of binary phase-coded microwave signals with large frequency tunability using a dual-parallel Mach–Zehnder modulator,” IEEE Photonics J. 5(4), 5501507 (2013).
[Crossref]

Li, W.

W. Li, W. T. Wang, W. H. Sun, L. X. Wang, and N. H. Zhu, “Photonic generation of arbitrarily phase-modulated microwave signals based on a single DDMZM,” Opt. Express 22(7), 7446–7457 (2014).
[Crossref] [PubMed]

W. Li, L. X. Wang, M. Li, H. Wang, and N. H. Zhu, “Photonic generation of binary phase-coded microwave signals with large frequency tunability using a dual-parallel Mach–Zehnder modulator,” IEEE Photonics J. 5(4), 5501507 (2013).
[Crossref]

Z. Li, W. Li, H. Chi, X. Zhang, and J. Yao, “Photonic generation of phase-coded microwave signal with large frequency tenability,” IEEE Photonics Technol. Lett. 23(11), 712–714 (2013).
[Crossref]

Li, Y.

Li, Z.

Z. Li, W. Li, H. Chi, X. Zhang, and J. Yao, “Photonic generation of phase-coded microwave signal with large frequency tenability,” IEEE Photonics Technol. Lett. 23(11), 712–714 (2013).
[Crossref]

Long, Y.

Y. Long, L. Zhou, and J. Wang, “Photonic-assisted microwave signal multiplication and modulation using a silicon Mach-Zehnder modulator,” Sci. Rep. 6(1), 20215 (2016).
[Crossref] [PubMed]

Luo, B.

McKinney, J. D.

Novak, D.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Pan, S.

Pan, W.

Pu, T.

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Photonic generation of microwave frequency shift keying signals,” IEEE Photonics Technol. Lett. 28(18), 1928–1931 (2016).
[Crossref]

Scotti, F.

P. Ghelfi, F. Scotti, F. Laghezza, and A. Bogoni, “Photonic generation of phase-modulated RF signals for pulse compression techniques in coherent radars,” J. Lightwave Technol. 30(11), 1638–1644 (2012).
[Crossref]

P. Ghelfi, F. Scotti, F. Laghezza, and A. Bogoni, “Phase coding of RF pulses in photonics-aided frequency-agile coherent radar systems,” IEEE J. Quantum Electron. 48(9), 1151–1157 (2012).
[Crossref]

Seeds, A. J.

Su, Y.

Sun, W. H.

Tang, Z.

Tao, J.

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Photonic generation of microwave frequency shift keying signals,” IEEE Photonics Technol. Lett. 28(18), 1928–1931 (2016).
[Crossref]

Wang, C.

C. Wang and J. P. Yao, “Microwave and millimeter-wave arbitrary waveform generation and processing using fiber-optics-based techniques,” in Proceedings of IEEE International conference on Broadband Network & Multimedia Technology (IEEE, 2009), pp. 909–912.
[Crossref]

Wang, H.

W. Li, L. X. Wang, M. Li, H. Wang, and N. H. Zhu, “Photonic generation of binary phase-coded microwave signals with large frequency tunability using a dual-parallel Mach–Zehnder modulator,” IEEE Photonics J. 5(4), 5501507 (2013).
[Crossref]

Wang, J.

Y. Long, L. Zhou, and J. Wang, “Photonic-assisted microwave signal multiplication and modulation using a silicon Mach-Zehnder modulator,” Sci. Rep. 6(1), 20215 (2016).
[Crossref] [PubMed]

Wang, L. X.

W. Li, W. T. Wang, W. H. Sun, L. X. Wang, and N. H. Zhu, “Photonic generation of arbitrarily phase-modulated microwave signals based on a single DDMZM,” Opt. Express 22(7), 7446–7457 (2014).
[Crossref] [PubMed]

W. Li, L. X. Wang, M. Li, H. Wang, and N. H. Zhu, “Photonic generation of binary phase-coded microwave signals with large frequency tunability using a dual-parallel Mach–Zehnder modulator,” IEEE Photonics J. 5(4), 5501507 (2013).
[Crossref]

Wang, P.

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Photonic generation of microwave frequency shift keying signals,” IEEE Photonics Technol. Lett. 28(18), 1928–1931 (2016).
[Crossref]

Wang, W. T.

Weiner, A. M.

Wen, A.

Y. Chen, A. Wen, Y. Chen, and X. Wu, “Photonic generation of binary and quaternary phase-coded microwave waveforms with an ultra-wide frequency tunable range,” Opt. Express 22(13), 15618–15625 (2014).
[Crossref] [PubMed]

Y. Chen, A. Wen, and J. Yao, “Photonic generation of frequency tunable binary phase-coded microwave waveforms,” IEEE Photonics Technol. Lett. 25(23), 2319–2322 (2013).
[Crossref]

Williams, K. J.

Wu, J.

Wu, X.

Xiang, P.

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Photonic generation of microwave frequency shift keying signals,” IEEE Photonics Technol. Lett. 28(18), 1928–1931 (2016).
[Crossref]

P. Xiang, X. Zheng, H. Zhang, Y. Li, and Y. Chen, “A novel approach to photonic generation of RF binary digital modulation signals,” Opt. Express 21(1), 631–639 (2013).
[Crossref] [PubMed]

Yan, H.

C. Jason, H. Yan, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photonics Technol. Lett. 15(4), 581–583 (2003).
[Crossref]

Yan, L. S.

Yao, J.

Z. Li, W. Li, H. Chi, X. Zhang, and J. Yao, “Photonic generation of phase-coded microwave signal with large frequency tenability,” IEEE Photonics Technol. Lett. 23(11), 712–714 (2013).
[Crossref]

Y. Chen, A. Wen, and J. Yao, “Photonic generation of frequency tunable binary phase-coded microwave waveforms,” IEEE Photonics Technol. Lett. 25(23), 2319–2322 (2013).
[Crossref]

L. Gao, X. Chen, and J. Yao, “Photonic generation of a phase-coded microwave waveform with ultrawide frequency tunable range,” IEEE Photonics Technol. Lett. 25(10), 899–902 (2013).
[Crossref]

J. Yao, “Photonic generation of microwave arbitrary waveforms,” Opt. Commun. 284(15), 3723–3736 (2011).
[Crossref]

J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009).
[Crossref]

Yao, J. P.

C. Wang and J. P. Yao, “Microwave and millimeter-wave arbitrary waveform generation and processing using fiber-optics-based techniques,” in Proceedings of IEEE International conference on Broadband Network & Multimedia Technology (IEEE, 2009), pp. 909–912.
[Crossref]

Ye, J.

Zhang, F.

Zhang, H.

Zhang, L.

Zhang, T.

Zhang, X.

Z. Li, W. Li, H. Chi, X. Zhang, and J. Yao, “Photonic generation of phase-coded microwave signal with large frequency tenability,” IEEE Photonics Technol. Lett. 23(11), 712–714 (2013).
[Crossref]

Zhang, Y.

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Photonic generation of microwave frequency shift keying signals,” IEEE Photonics Technol. Lett. 28(18), 1928–1931 (2016).
[Crossref]

Y. Zhang and S. Pan, “Generation of phase-coded microwave signals using a polarization-modulator-based photonic microwave phase shifter,” Opt. Lett. 38(5), 766–768 (2013).
[Crossref] [PubMed]

Zheng, X.

Zhou, L.

Y. Long, L. Zhou, and J. Wang, “Photonic-assisted microwave signal multiplication and modulation using a silicon Mach-Zehnder modulator,” Sci. Rep. 6(1), 20215 (2016).
[Crossref] [PubMed]

Zhu, N. H.

W. Li, W. T. Wang, W. H. Sun, L. X. Wang, and N. H. Zhu, “Photonic generation of arbitrarily phase-modulated microwave signals based on a single DDMZM,” Opt. Express 22(7), 7446–7457 (2014).
[Crossref] [PubMed]

W. Li, L. X. Wang, M. Li, H. Wang, and N. H. Zhu, “Photonic generation of binary phase-coded microwave signals with large frequency tunability using a dual-parallel Mach–Zehnder modulator,” IEEE Photonics J. 5(4), 5501507 (2013).
[Crossref]

Zou, X.

IEEE J. Quantum Electron. (1)

P. Ghelfi, F. Scotti, F. Laghezza, and A. Bogoni, “Phase coding of RF pulses in photonics-aided frequency-agile coherent radar systems,” IEEE J. Quantum Electron. 48(9), 1151–1157 (2012).
[Crossref]

IEEE Photonics J. (1)

W. Li, L. X. Wang, M. Li, H. Wang, and N. H. Zhu, “Photonic generation of binary phase-coded microwave signals with large frequency tunability using a dual-parallel Mach–Zehnder modulator,” IEEE Photonics J. 5(4), 5501507 (2013).
[Crossref]

IEEE Photonics Technol. Lett. (5)

L. Gao, X. Chen, and J. Yao, “Photonic generation of a phase-coded microwave waveform with ultrawide frequency tunable range,” IEEE Photonics Technol. Lett. 25(10), 899–902 (2013).
[Crossref]

C. Jason, H. Yan, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photonics Technol. Lett. 15(4), 581–583 (2003).
[Crossref]

Y. Chen, A. Wen, and J. Yao, “Photonic generation of frequency tunable binary phase-coded microwave waveforms,” IEEE Photonics Technol. Lett. 25(23), 2319–2322 (2013).
[Crossref]

Z. Li, W. Li, H. Chi, X. Zhang, and J. Yao, “Photonic generation of phase-coded microwave signal with large frequency tenability,” IEEE Photonics Technol. Lett. 23(11), 712–714 (2013).
[Crossref]

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Photonic generation of microwave frequency shift keying signals,” IEEE Photonics Technol. Lett. 28(18), 1928–1931 (2016).
[Crossref]

J. Lightwave Technol. (3)

Nat. Photonics (1)

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Opt. Commun. (1)

J. Yao, “Photonic generation of microwave arbitrary waveforms,” Opt. Commun. 284(15), 3723–3736 (2011).
[Crossref]

Opt. Express (5)

Opt. Lett. (4)

Sci. Rep. (1)

Y. Long, L. Zhou, and J. Wang, “Photonic-assisted microwave signal multiplication and modulation using a silicon Mach-Zehnder modulator,” Sci. Rep. 6(1), 20215 (2016).
[Crossref] [PubMed]

Other (1)

C. Wang and J. P. Yao, “Microwave and millimeter-wave arbitrary waveform generation and processing using fiber-optics-based techniques,” in Proceedings of IEEE International conference on Broadband Network & Multimedia Technology (IEEE, 2009), pp. 909–912.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Schematic diagram of multiple microwave binary modulated signals generation. A point: phase modulated signals; B point: output of the MZI in time domain; C point: output of the OTF with the different center wavelength and bandwidth; D point: detected microwave binary modulated signals; C1, C2 and C3 correspond to D1, D2 and D3 respectively. PM: phase modulator; MZI: Mach-Zehnder interferometer; OTF: optical tunable filter; PD: photodetector; s(t): the binary signal.
Fig. 2
Fig. 2 Experimental setup of the scheme. TLS: tunable light source; PC: polarization controller; IM: intensity modulator; EDFA: er-droped optical fiber amplifier; MG: microwave signal generator; PPG: pluse-pattern generator.
Fig. 3
Fig. 3 Measured optical spectra before and after the MZI when B = 12.8-Gb/s, fRF1 = 16-GHz and fRF2 = 35.2-GHz.
Fig. 4
Fig. 4 Experimental results for B = 12.8-Gb/s, fRF1 = 16-GHz, fRF2 = 35.2-GHz. (a) and (b) The MZI output signals for frequency tones at minimum and maximum points of MZI transmission curve; (c) 16-GHz 2ASK microwave modulated signal; (d) 2FSK signal with frequencies of 16-GHz and 35.2-GHz; (e) 35.2-GHz 2PSK signal.
Fig. 5
Fig. 5 Experimental results for B = 10.7-Gb/s, fRF1 = 24.075-GHz. (a) and (b) Complementary 24.075-GHz 2ASK signals; (c) 24.075-GHz 2PSK signal.
Fig. 6
Fig. 6 Experimental results for B = 10.7-Gb/s, fRF1 = 29.425-GHz. (a) and (b) 29.425-GHz 2ASK signals; (c) 29.425-GHz 2PSK signal.
Fig. 7
Fig. 7 Measured optical spectra before and after the MZI for B = 10.7-Gb/s, fRF1 = 5.35-GHz, fRF2 = 21.4-GHz.
Fig. 8
Fig. 8 Experimental results for B = 10.7-Gb/s. when fRF1 = 5.35-GHz, fRF2 = 21.4-GHz (a) 10.7-GHz and (b) 21.4-GHz 2ASK (OOK) signals; (c) The 2FSK signal with frequencies of 10.7-GHz and 21.4-GHz; (d) The 2FSK signal with frequencies of 32.1-GHz and 21.4-GHz when fRF1 = 16.05-GHz, fRF2 = 21.4-GHz.
Fig. 9
Fig. 9 Experimental result of 2FSK signal with carrier frequencies of 10.7-GHz and 21.4-GHz when the pattern of s´(t) is “1111000011011110” and B = 10.7-Gb/s.

Equations (12)

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E k p ( t ) = A k exp ( j 2 π f k t ) exp ( j γ s ( t ) )
h MZI ( t ) = [ δ ( t ) + δ ( t τ ) ] / 2
H MZI ( f ) = [ 1 + exp ( j f τ ) ] / 2
E k M ( t ) = E k p ( t ) * h MZI ( t ) = A k exp ( j f k t + j γ s ( t ) ] { 1 + exp [ - j f k τ j γ s ( t ) ] } / 2
E k M ( t ) = { A k exp [ j f k t + j γ s ( t ) ] f k = f i + 1 A k 2 exp [ j f k t + j γ s ( t ) ] f k = f i 0 f k = f i - 1 , o r i + 2
E k M ( t ) = { 0 f k = f i + 1 A k 2 exp [ j f k t + j γ s ( t ) ] f k = f i A k exp [ j f k t + j γ s ( t ) ] f k = f i - 1 , or i + 2
I ASK ( t ) = { 5 / 4 + cos [ 2 π ( f i + 1 f i ) t ] s ' ( t ) = 0 1 / 4 s ' ( t ) = 1
I FSK ( t ) = { 5 / 4 + cos ( | f i f i + 1 | t ) s ' ( t ) = 0 5 / 4 + cos ( | f i f i + 2 | t ) s ' ( t ) = 1
I PSK ( t ) = { 5 / 4 - cos ( f p t ) s ' ( t ) = 0 5 / 4 + cos ( f p t ) s ' ( t ) = 1
E ( t ) = ( 1 + J 0 ( β ) ) exp( j f c t ) + J 1 ( β ) exp[ j ( f c + f R F 1 ) t ] + J 1 ( β ) exp[ j ( f c f R F 1 ) t ]
f R F 1 = ξ + 1 2 n Δ f , n = 0 , 1 , 2...
f R F 2 f R F 1 = 1 2 Δ f + m Δ f , m = 0 , ± 1 , ± 2...

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