Abstract

This paper reviews the foundations of the Kramers–Kronig (KK) receiver, a recently proposed scheme designed to reconstruct a complex-valued signal from the measurement of its intensity in the context of fiber-optic communications. We provide a comprehensive characterization of the signal properties that are required for the proper operation of the KK receiver and discuss the most relevant implementation requirements, such as the need for digital up-sampling, the implications of receiver imperfections, line chromatic dispersion, optical filtering, and polarization multiplexing.

© 2019 Optical Society of America

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Corrections

Antonio Mecozzi, Cristian Antonelli, and Mark Shtaif, "Kramers–Kronig receivers: erratum," Adv. Opt. Photon. 11, 826-827 (2019)
https://www.osapublishing.org/aop/abstract.cfm?uri=aop-11-4-826

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References

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  1. F. Derr, “Coherent optical QPSK intradyne system: concept and digital receiver realization,” J. Lightwave Technol. 10, 1290–1296 (1992).
    [Crossref]
  2. A. J. Lowery and J. Armstrong, “Orthogonal-frequency-division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express 14, 2079–2084 (2006).
    [Crossref]
  3. A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing, 2nd ed. (Prentice Hall, 1999).
  4. A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers-Kronig coherent receiver,” Optica 3, 1220–1227 (2016).
    [Crossref]
  5. A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers-Kronig receivers: supplementary material,” figshare (2019), https://doi.org/10.6084/m9.figshare.7982966 .
  6. C. Antonelli, A. Mecozzi, and M. Shtaif, “Kramers-Kronig PAM transceiver and two-sided polarization-multiplexed Kramers-Kronig transceiver,” J. Lightwave Technol. 36, 468–475 (2018).
    [Crossref]
  7. A. Mecozzi and M. Shtaif, “Coherent detection with an incoherent local oscillator,” Opt. Express 26, 33970–33981 (2018).
    [Crossref]
  8. A simple example is when the first root Za,1 is replaced by 1/Za,1* and A is replaced by A/Za,1*. The effect of this transformation on Eqs. (6) and (7) is Za˜(Z)=A/Za,1*(−1/Za,1*)∏k=2M−1(−Za,k)(Z−1Za,1*)∏k=2M−1(Z−Za,k), and Za˜*(Z)=A*/Za,1ZM−1(Z−Za,1)∏k=2M−1(Z−1Za,k*). It is easy to check that ZIaa(Z)=Za˜(Z)Za˜*(Z), showing that the intensity remains unchanged.
  9. P. Duren, W. Hengartner, and R. S. Laugesen, “The argument principle for harmonic functions,” Am. Math. Monthly 103(5), 411–415 (1996).
    [Crossref]
  10. We used in Eq. (15) that ln(S)=ln|S|+i arg(S) and that ∮Za(C)d log|S|=0.
  11. Zeros on the unit circle can always be considered the limit case of zeros outside the unit circle.
  12. Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Joint optimisation of resampling rate and carrier-to-signal power ratio in direct-detection Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (2017).
  13. W.-R. Peng, X. Wu, K.-M. Feng, V. R. Arbab, B. Shamee, J.-Y. Yang, L. C. Christen, A. E. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission employing an iterative estimation and cancellation technique,” Opt. Express 17, 9099–9111 (2009).
    [Crossref]
  14. S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s discrete-multitone transmission over 80-km SSMF using single-sideband modulation with novel interference-cancellation scheme,” in European Conference on Optical Communication (ECOC) (2015).
  15. K. Zou, Y. Zhu, F. Zhang, and Z. Chen, “Spectrally efficient terabit optical transmission with Nyquist 64-QAM half-cycle subcarrier modulation and direct detection,” Opt. Lett. 41, 2767–2770 (2016).
    [Crossref]
  16. Z. Li, M. S. Erkilinç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photon. Technol. Lett. 28, 2838–2841 (2016).
    [Crossref]
  17. Z. Li, M. S. Erkilinç, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Comparison of digital signal-signal beat interference compensation techniques in direct-detection subcarrier modulation systems,” Opt. Express 24, 29176–29189 (2016).
    [Crossref]
  18. L. Blech, Y. Eldar, C. Antonelli, A. Mecozzi, and M. Shtaif, “The enhanced Kramers Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.7.
  19. Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “SSBI mitigation and the Kramers-Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35, 1887–1893 (2017).
    [Crossref]
  20. Various flavors of these iterative methods have been proposed, including that reported in Appendix B of [4]. The method reported here is the simplest but, in general, not the most efficient, and it is used only for the purpose of discussion.
  21. A. Yekani, S. Amiralizadeh, and L. A. Rusch, “Analytical study of optical SSB-DMT with IMDD,” J. Lightwave Technol. 36, 666–674 (2018).
    [Crossref]
  22. Note that this equation implies Faa(−M)=0.
  23. We use the definition of the DFT where the factor 1/(2M) is placed in the definition of the DFT instead of the inverse DFT. This choice slightly simplifies the derivation and the final result. It is also interesting to note that, with Iaa(t) periodic with period T, Eq. (37) is the numerical approximation by the trapezoidal rule, with M+1 points and integration step T/(2M), of the integral at right-hand side of Eq. (34).
  24. Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Spectrally efficient 168  Gb/s/λ WDM 64-QAM single-sideband Nyquist-subcarrier modulation with Kramers-Kronig direct-detection receivers,” J. Lightwave Technol. 36, 1340–1346 (2018).
    [Crossref]
  25. T. Bo and H. Kim, “Kramers-Kronig receiver operable without digital upsampling,” Opt. Express 26, 13810–13818 (2018).
    [Crossref]
  26. T. Bo and H. Kim, “Kramers-Kronig receiver without digital upsampling,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.2.
  27. The difference with respect to Eq. (44) is that here the inverse DFT of the coefficients La,DFT(k,1) returns the waveform a(t) sampled at rate 2B, whereas the inverse DFT of those given by Eq. (44) returns a(t) sampled at rate B.
  28. The positivity of I(t) is required for every t∈[0,T), and it is not sufficient that only the 2M samples are positive. In practice, the validity of the condition I(t)>0 should be checked after sufficient oversampling.
  29. This is because (a) the reality of I(t) implies the condition ZI(Z)=[ZI(1/Z*)]* and hence, if Zk is a zero of ZI(Z), also 1/Zk* must be a zero, and (b) the condition that I(t) is always positive implies that there is no zero Zk¯ for which Zk¯=1/Zk¯* (they would be on the unit circle and correspond to real zeros of I(t)), and hence each of the 2(M−1) zeros of ZI(Z) must have its distinct inverse conjugate counterpart.
  30. If I(t) changes sign, Eq. (57) cannot be derived from the condition ZI(Z)=[ZI(1/Z*)]*. Assume I(t)=2 cos(Ωt). We have ZI(Z)=−i(Z+i)(1/Z+i), which does not have the form of Eq. (57) because both zeros (which correspond to the two real zeros of the cosine) are on the unit circle. In this case, each one of the two zeros coincides with its complex conjugate, so that ZI(Z)=[ZI(1/Z*)]* automatically holds.
  31. L. R. Kahn, “Compatible single sideband,” Proc. IRE 49, 1503–1527 (1961).
    [Crossref]
  32. M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
    [Crossref]
  33. M. Schuster, B. Spinnler, C. A. Bunge, and K. Petermann, “Spectrally efficient OFDM-transmission with compatible single-sideband modulation for direct detection,” in 33rd European Conference and Exhibition of Optical Communication (2007).
  34. Z. Xu, M. O’Sullivan, and R. Hui, “OFDM system implementation using compatible SSB modulation with a dual-electrode MZM,” Opt. Lett. 35, 1221–1223 (2010).
    [Crossref]
  35. Y. Zhang, M. O’Sullivan, and R. Hui, “Theoretical and experimental investigation of compatible SSB modulation for single channel long-distance optical OFDM transmission,” Opt. Express 18, 16751–16764 (2010).
    [Crossref]
  36. X. Chen, S. Chandrasekhar, S. Olsson, A. Adamiecki, and P. Winzer, “Impact of O/E front-end frequency response on Kramers-Kronig receivers and its compensation,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.5.
  37. G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photon. 1, 279–307 (2009).
    [Crossref]
  38. In this section we will proceed with the convention that the spectrum vanishes below the cutoff frequency.
  39. Of course, if the trajectory of a(t) encircles the origin, the component in phase with the carrier drops below zero, but there are instances where the signal does not encircle the origin although the component in-phase with the carrier drops below zero, but these are unlikely.
  40. L. G. Guerrero, H. Shams, I. Fatadin, M. J. Fice, M. Naftaly, A. J. Seeds, and C. C. Renaud, “Spectrally efficient SSB signals for W-band links enabled by Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Th2A.61.
  41. S. T. Le and K. Schuh, “Experimental verification of equalization enhanced phase noise in Kramers-Kronig transmissions,” in Optical Fiber Communication Conference (OFC) (Optical Society of America, 2019), paper Tu2B.2.
  42. W. Shieh and K.-P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16, 15718–15727 (2008).
    [Crossref]
  43. After the two orthogonal polarization components are detected independently, they are jointly processed digitally so as to deal with a possible polarization rotation as well as other polarization distortions caused by the fiber-optic channel.
  44. In order to see that, note that there is no way to avoid the possibility that one of the polarization eigenstates of the beam splitter is orthogonal to the polarization of the overall CW tone.
  45. C. Antonelli, A. Mecozzi, M. Shtaif, X. Chen, S. Chandrasekhar, and P. J. Winzer, “Polarization multiplexing with the Kramers-Kronig receiver,” J. Lightwave Technol. 35, 5418–5424 (2017).
    [Crossref]
  46. P. Dong, X. Chen, K. Kim, S. Chandrasekhar, Y.-K. Chen, and J. H. Sinsky, “128-Gb/s 100-km transmission with direct detection using silicon photonic Stokes vector receiver and I/Q modulator,” Opt. Express 24, 14208–14214 (2016).
    [Crossref]
  47. T. M. Hoang, M. Y. S. Sowailem, Q. Zhuge, Z. Xing, M. Morsy-Osman, E. El-Fiky, S. Fan, M. Xiang, and D. V. Plant, “Single wavelength 480  Gb/s direct detection over 80  km SSMF enabled by stokes vector Kramers-Kronig transceiver,” Opt. Express 25, 33534–33542 (2017).
    [Crossref]
  48. Y. Zhu, M. Jiang, and F. Zhang, “Direct detection of polarization multiplexed single sideband signals with orthogonal offset carriers,” Opt. Express 26, 15887–15898 (2018).
    [Crossref]
  49. Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Digital linearization of direct-detection transceivers for spectrally efficient 100  Gb/s/λ WDM metro networking,” J. Lightwave Technol. 36, 27–36 (2018).
    [Crossref]
  50. Z. Li, M. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. Thomsen, P. Bayvel, and R. Killey, “DSP for single-sideband direct-detection systems,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.5.
  51. Z. Li, L. Galdino, T. Xu, M. Erkilinç, K. Shi, E. Sillekens, B. Thomsen, P. Bayvel, and R. Killey, “Performance of digital back-propagation in Kramers-Kronig direct-detection receivers,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.4.
  52. Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “168  Gb/s direct-detection 64-QAM SSB Nyquist-SCM transmission over 80  km uncompensated SSMF at 4.54  b/s/Hz net ISD using a Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).
  53. X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, J. Sinsky, A. Mecozzi, M. Shtaif, and P. Winzer, “218-Gb/s single-wavelength, single-polarization, single-photodiode transmission over 125-km of standard singlemode fiber using Kramers-Kronig detection,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2017), paper Th5B.6.
  54. X. Chen, S. Chandrasekhar, and P. Winzer, “Frequency-resolved measurements of signal, noise, and signal-signal beat interference in self-coherent direct-detection receivers,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.6.
  55. X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, A. Mecozzi, M. Shtaif, and P. Winzer, “4 × 240  Gb/s dense WDM and PDM Kramers-Kronig detection with 125-km SSMF transmission,” in European Conference on Optical Communication (ECOC) (2017).
  56. X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode Kramers-Kronig detection of 440-gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (IPC) Part II (2017).
  57. R. Rios-Muller, J. Estaran, J. Renaudier, and G. Charlet, “Dual polarization in-phase and quadrature high speed submarine transmission with only two photodiodes, ADCs, MZMs and DACs,” in IEEE Photonics Conference (IPC) Part II (2017).
  58. I. Sackey, C. Schmidt-Langhorst, R. Emmerich, R. Elschner, T. Kato, T. Tanimura, S. Watanabe, T. Hoshida, and C. Schubert, “Distributed aggregation and reception of a 400-Gb/s net rate superchannel in a single-photodiode 110-GHz Kramers-Kronig receiver,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2018), paper Th4C.7.
  59. C. Füllner, S. Wolf, J. N. Kemal, J. Lutz, L. Altenhain, R. Schmid, W. Freude, C. Koos, and S. Randel, “Transmission of 80-GBd 16-QAM over 300  km and Kramers-Kronig reception using a low-complexity FIR Hilbert filter approximation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.3.
  60. T. Harter, C. Füllner, J. N. Kemal, S. Ummethala, M. Brosi, E. Bründermann, W. Freude, S. Randel, and C. Koos, “110-m THz wireless transmission at 100  Gbit/s using a Kramers-Kronig Schottky barrier diode receiver,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.7.
  61. Q. Zhang, B. Zheng, and C. Shu, “Kramers-Kronig detection with Brillouin-amplified virtual carrier,” Opt. Lett. 43, 1367–1370 (2018).
    [Crossref]
  62. Q. Zhang and C. Shu, “Carrier regeneration assisted Kramers-Kronig detection of an independent sideband signal,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2018), paper STu3C.2.
  63. Q. Zhang and C. Shu, “Kramers-Kronig detection of polarization multiplexing signals by a single-ended photodiode,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W2A.55.
  64. Y. Tong, Q. Zhang, X. Wu, C.-W. Chow, C. Shu, and H. K. Tsang, “Integrated germanium-on-silicon Franz-Keldysh vector modulator used with a Kramers-Kronig receiver,” Opt. Lett. 43, 4333–4336 (2018).
    [Crossref]
  65. T. Hoang, Q. Zhuge, Z. Xing, M. Sowailem, M. Morsy-Osman, M. Xiang, E. El-Fiky, S. Fan, and D. V. Plant, “Direct detection optical transmission systems employing Stokes vector Kramers-Kronig transceivers,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.2.
  66. S. Fan, Q. Zhuge, M. Y. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, Y. Li, J. Wu, and D. V. Plant, “Single wavelength twin-SSB direct detection system based on Kramers-Kronig receiver and time-interleaved OFDM frame,” Opt. Commun. 425, 133–140 (2018).
    [Crossref]
  67. S. Fan, Q. Zhuge, M. Y. S. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, M. Qiu, Y. Li, J. Wu, and D. V. Plant, “Twin-SSB direct detection transmission over 80km SSMF using Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).
  68. S. Fan, Q. Zhuge, Z. Xing, K. Zhang, T. M. Hoang, M. Morsy-Osman, M. Y. S. Sowailem, Y. Li, J. Wu, and D. V. Plant, “264  Gb/s twin-SSB-KK direct detection transmission enabled by MIMO processing,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.5.
  69. M. Presi, G. Cossu, G. Contestabile, E. Ciaramella, C. Antonelli, A. Mecozzi, and M. Shtaif, “Transmission in 125-km SMF with 3.9  bit/s/Hz spectral efficiency using a single-drive MZM and a direct-detection Kramers-Kronig receiver without optical CD compensation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.3.
  70. M. Zhu, J. Zhang, X. Yi, H. Ying, X. Li, M. Luo, Y. Song, X. Huang, and K. Qiu, “Optical single side-band Nyquist PAM-4 transmission using dual-drive MZM modulation and direct detection,” Opt. Express 26, 6629–6638 (2018).
    [Crossref]
  71. M. Zhu, J. Zhang, H. Ying, X. Li, M. Luo, X. Huang, Y. Song, F. Li, X. Yi, and K. Qiu, “56-Gb/s optical SSB PAM-4 transmission over 800-km SSMF using DDMZM transmitter and simplified direct detection Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper M2C.5.
  72. D. Li, Q. Yu, L. Deng, L. Huo, S. Fu, M. Tang, M. Cheng, M. Zhang, and D. Liu, “Bidirectional long-reach PON using Kramers-Kronig-based receiver for Rayleigh backscattering noise and SSBI interference elimination,” Opt. Express 26, 19020–19036 (2018).
    [Crossref]
  73. L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers-Kronig detection over 80-km SSMF,” IEEE Photon. J. 9, 1–9 (2017).
    [Crossref]
  74. L. Shu, J. Li, Z. Wan, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “56-Gb/s single-photodiode 16QAM transmission over 140-km SSMF using Kramers-Kronig detection,” in Asia Communications and Photonics Conference (Optical Society of America, 2017), paper M2B.2.
  75. Y. Zhu, K. Zou, X. Ruan, and F. Zhang, “Single carrier 400G transmission with single-ended heterodyne detection,” IEEE Photon. Technol. Lett. 29, 1788–1791 (2017).
    [Crossref]
  76. Y. Zhu, M. Jiang, X. Ruan, Z. Chen, C. Li, and F. Zhang, “6.4  Tb/s (32 × 200  Gb/s) WDM direct-detection transmission with twin-SSB modulation and Kramers-Kronig receiver,” Opt. Commun. 415, 64–69 (2018).
    [Crossref]
  77. Y. Zhu, M. Jiang, X. Ruan, C. Li, and F. Zhang, “16×112  Gb/s single-sideband PAM4 WDM transmission over 80km SSMF with Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.2.
  78. Z. Wu, H. Jiang, X. Feng, and S. Gao, “Demonstration of cost-effective single-photodetector coherent receiver for free-space optical communications,” in Asia Communications and Photonics Conference (Optical Society of America, 2017), paper M3G.4.
  79. T. Zuo, S. Zhang, L. Liu, W. Cheng, and X. Xu, “Single-lane 100  Gb/s 4-PAM transmission over 80  km SSMF based on K-K scheme and integrated 10G TOSA,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.6.
  80. S. van der Heide, J. van Weerdenburg, M. Bigot-Astruc, A. Amezcua-Correa, J. Antonio-Lopez, J. C. Alvarado-Zacarias, H. de Waardt, T. Koonen, P. Sillard, R. Amezcua-Correa, and C. Okonkwo, “Single carrier 1  Tbit/s mode-multiplexed transmission over graded-index 50  μm core multi-mode fiber employing Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Tu1G.3.
  81. S. Ohlendorf, R. Joy, S. Pachnicke, and W. Rosenkranz, “Flexible PAM in DWDM transmission with Kramers-Kronig DSP,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.6.
  82. C. Li, M. Luo, Q. You, and X. Li, “114-Gb/s PDM-DMT transmission over 100-km SSMF with high phase noise tolerance using Kramers-Kronig detection and digital carrier regeneration,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.4.
  83. R. S. Luìs, G. Rademacher, B. J. Puttnam, S. Shinada, H. Furukawa, R. Maruyama, K. Aikawa, and N. Wada, “A coherent Kramers-Kronig receiver for 3-mode few-mode fiber transmission,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.3.
  84. D. Kong, E. P. da Silva, Y. Sasaki, K. Aikawa, F. D. Ros, M. Galili, T. Morioka, L. K. Oxenløwe, and H. Hu, “Kramers-Kronig detection with adaptive rates for 909.5  Tbit/s dense SDM and WDM data channels,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.5.

2018 (13)

C. Antonelli, A. Mecozzi, and M. Shtaif, “Kramers-Kronig PAM transceiver and two-sided polarization-multiplexed Kramers-Kronig transceiver,” J. Lightwave Technol. 36, 468–475 (2018).
[Crossref]

A. Mecozzi and M. Shtaif, “Coherent detection with an incoherent local oscillator,” Opt. Express 26, 33970–33981 (2018).
[Crossref]

A. Yekani, S. Amiralizadeh, and L. A. Rusch, “Analytical study of optical SSB-DMT with IMDD,” J. Lightwave Technol. 36, 666–674 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Spectrally efficient 168  Gb/s/λ WDM 64-QAM single-sideband Nyquist-subcarrier modulation with Kramers-Kronig direct-detection receivers,” J. Lightwave Technol. 36, 1340–1346 (2018).
[Crossref]

T. Bo and H. Kim, “Kramers-Kronig receiver operable without digital upsampling,” Opt. Express 26, 13810–13818 (2018).
[Crossref]

Y. Zhu, M. Jiang, and F. Zhang, “Direct detection of polarization multiplexed single sideband signals with orthogonal offset carriers,” Opt. Express 26, 15887–15898 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Digital linearization of direct-detection transceivers for spectrally efficient 100  Gb/s/λ WDM metro networking,” J. Lightwave Technol. 36, 27–36 (2018).
[Crossref]

Q. Zhang, B. Zheng, and C. Shu, “Kramers-Kronig detection with Brillouin-amplified virtual carrier,” Opt. Lett. 43, 1367–1370 (2018).
[Crossref]

Y. Tong, Q. Zhang, X. Wu, C.-W. Chow, C. Shu, and H. K. Tsang, “Integrated germanium-on-silicon Franz-Keldysh vector modulator used with a Kramers-Kronig receiver,” Opt. Lett. 43, 4333–4336 (2018).
[Crossref]

S. Fan, Q. Zhuge, M. Y. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, Y. Li, J. Wu, and D. V. Plant, “Single wavelength twin-SSB direct detection system based on Kramers-Kronig receiver and time-interleaved OFDM frame,” Opt. Commun. 425, 133–140 (2018).
[Crossref]

M. Zhu, J. Zhang, X. Yi, H. Ying, X. Li, M. Luo, Y. Song, X. Huang, and K. Qiu, “Optical single side-band Nyquist PAM-4 transmission using dual-drive MZM modulation and direct detection,” Opt. Express 26, 6629–6638 (2018).
[Crossref]

D. Li, Q. Yu, L. Deng, L. Huo, S. Fu, M. Tang, M. Cheng, M. Zhang, and D. Liu, “Bidirectional long-reach PON using Kramers-Kronig-based receiver for Rayleigh backscattering noise and SSBI interference elimination,” Opt. Express 26, 19020–19036 (2018).
[Crossref]

Y. Zhu, M. Jiang, X. Ruan, Z. Chen, C. Li, and F. Zhang, “6.4  Tb/s (32 × 200  Gb/s) WDM direct-detection transmission with twin-SSB modulation and Kramers-Kronig receiver,” Opt. Commun. 415, 64–69 (2018).
[Crossref]

2017 (5)

2016 (5)

2010 (2)

2009 (2)

2008 (2)

W. Shieh and K.-P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16, 15718–15727 (2008).
[Crossref]

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

2006 (1)

1996 (1)

P. Duren, W. Hengartner, and R. S. Laugesen, “The argument principle for harmonic functions,” Am. Math. Monthly 103(5), 411–415 (1996).
[Crossref]

1992 (1)

F. Derr, “Coherent optical QPSK intradyne system: concept and digital receiver realization,” J. Lightwave Technol. 10, 1290–1296 (1992).
[Crossref]

1961 (1)

L. R. Kahn, “Compatible single sideband,” Proc. IRE 49, 1503–1527 (1961).
[Crossref]

Adamiecki, A.

X. Chen, S. Chandrasekhar, S. Olsson, A. Adamiecki, and P. Winzer, “Impact of O/E front-end frequency response on Kramers-Kronig receivers and its compensation,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.5.

Aikawa, K.

R. S. Luìs, G. Rademacher, B. J. Puttnam, S. Shinada, H. Furukawa, R. Maruyama, K. Aikawa, and N. Wada, “A coherent Kramers-Kronig receiver for 3-mode few-mode fiber transmission,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.3.

D. Kong, E. P. da Silva, Y. Sasaki, K. Aikawa, F. D. Ros, M. Galili, T. Morioka, L. K. Oxenløwe, and H. Hu, “Kramers-Kronig detection with adaptive rates for 909.5  Tbit/s dense SDM and WDM data channels,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.5.

Altenhain, L.

C. Füllner, S. Wolf, J. N. Kemal, J. Lutz, L. Altenhain, R. Schmid, W. Freude, C. Koos, and S. Randel, “Transmission of 80-GBd 16-QAM over 300  km and Kramers-Kronig reception using a low-complexity FIR Hilbert filter approximation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.3.

Alvarado-Zacarias, J. C.

S. van der Heide, J. van Weerdenburg, M. Bigot-Astruc, A. Amezcua-Correa, J. Antonio-Lopez, J. C. Alvarado-Zacarias, H. de Waardt, T. Koonen, P. Sillard, R. Amezcua-Correa, and C. Okonkwo, “Single carrier 1  Tbit/s mode-multiplexed transmission over graded-index 50  μm core multi-mode fiber employing Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Tu1G.3.

Amezcua-Correa, A.

S. van der Heide, J. van Weerdenburg, M. Bigot-Astruc, A. Amezcua-Correa, J. Antonio-Lopez, J. C. Alvarado-Zacarias, H. de Waardt, T. Koonen, P. Sillard, R. Amezcua-Correa, and C. Okonkwo, “Single carrier 1  Tbit/s mode-multiplexed transmission over graded-index 50  μm core multi-mode fiber employing Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Tu1G.3.

Amezcua-Correa, R.

S. van der Heide, J. van Weerdenburg, M. Bigot-Astruc, A. Amezcua-Correa, J. Antonio-Lopez, J. C. Alvarado-Zacarias, H. de Waardt, T. Koonen, P. Sillard, R. Amezcua-Correa, and C. Okonkwo, “Single carrier 1  Tbit/s mode-multiplexed transmission over graded-index 50  μm core multi-mode fiber employing Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Tu1G.3.

Amiralizadeh, S.

Antonelli, C.

C. Antonelli, A. Mecozzi, and M. Shtaif, “Kramers-Kronig PAM transceiver and two-sided polarization-multiplexed Kramers-Kronig transceiver,” J. Lightwave Technol. 36, 468–475 (2018).
[Crossref]

C. Antonelli, A. Mecozzi, M. Shtaif, X. Chen, S. Chandrasekhar, and P. J. Winzer, “Polarization multiplexing with the Kramers-Kronig receiver,” J. Lightwave Technol. 35, 5418–5424 (2017).
[Crossref]

A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers-Kronig coherent receiver,” Optica 3, 1220–1227 (2016).
[Crossref]

M. Presi, G. Cossu, G. Contestabile, E. Ciaramella, C. Antonelli, A. Mecozzi, and M. Shtaif, “Transmission in 125-km SMF with 3.9  bit/s/Hz spectral efficiency using a single-drive MZM and a direct-detection Kramers-Kronig receiver without optical CD compensation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.3.

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, A. Mecozzi, M. Shtaif, and P. Winzer, “4 × 240  Gb/s dense WDM and PDM Kramers-Kronig detection with 125-km SSMF transmission,” in European Conference on Optical Communication (ECOC) (2017).

X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode Kramers-Kronig detection of 440-gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (IPC) Part II (2017).

L. Blech, Y. Eldar, C. Antonelli, A. Mecozzi, and M. Shtaif, “The enhanced Kramers Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.7.

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, J. Sinsky, A. Mecozzi, M. Shtaif, and P. Winzer, “218-Gb/s single-wavelength, single-polarization, single-photodiode transmission over 125-km of standard singlemode fiber using Kramers-Kronig detection,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2017), paper Th5B.6.

Antonio-Lopez, J.

S. van der Heide, J. van Weerdenburg, M. Bigot-Astruc, A. Amezcua-Correa, J. Antonio-Lopez, J. C. Alvarado-Zacarias, H. de Waardt, T. Koonen, P. Sillard, R. Amezcua-Correa, and C. Okonkwo, “Single carrier 1  Tbit/s mode-multiplexed transmission over graded-index 50  μm core multi-mode fiber employing Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Tu1G.3.

Arbab, V. R.

Armstrong, J.

Bayvel, P.

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Digital linearization of direct-detection transceivers for spectrally efficient 100  Gb/s/λ WDM metro networking,” J. Lightwave Technol. 36, 27–36 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Spectrally efficient 168  Gb/s/λ WDM 64-QAM single-sideband Nyquist-subcarrier modulation with Kramers-Kronig direct-detection receivers,” J. Lightwave Technol. 36, 1340–1346 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “SSBI mitigation and the Kramers-Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35, 1887–1893 (2017).
[Crossref]

Z. Li, M. S. Erkilinç, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Comparison of digital signal-signal beat interference compensation techniques in direct-detection subcarrier modulation systems,” Opt. Express 24, 29176–29189 (2016).
[Crossref]

Z. Li, M. S. Erkilinç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photon. Technol. Lett. 28, 2838–2841 (2016).
[Crossref]

Z. Li, L. Galdino, T. Xu, M. Erkilinç, K. Shi, E. Sillekens, B. Thomsen, P. Bayvel, and R. Killey, “Performance of digital back-propagation in Kramers-Kronig direct-detection receivers,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.4.

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “168  Gb/s direct-detection 64-QAM SSB Nyquist-SCM transmission over 80  km uncompensated SSMF at 4.54  b/s/Hz net ISD using a Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

Z. Li, M. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. Thomsen, P. Bayvel, and R. Killey, “DSP for single-sideband direct-detection systems,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.5.

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Joint optimisation of resampling rate and carrier-to-signal power ratio in direct-detection Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (2017).

Bigot-Astruc, M.

S. van der Heide, J. van Weerdenburg, M. Bigot-Astruc, A. Amezcua-Correa, J. Antonio-Lopez, J. C. Alvarado-Zacarias, H. de Waardt, T. Koonen, P. Sillard, R. Amezcua-Correa, and C. Okonkwo, “Single carrier 1  Tbit/s mode-multiplexed transmission over graded-index 50  μm core multi-mode fiber employing Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Tu1G.3.

Blech, L.

L. Blech, Y. Eldar, C. Antonelli, A. Mecozzi, and M. Shtaif, “The enhanced Kramers Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.7.

Bo, T.

T. Bo and H. Kim, “Kramers-Kronig receiver operable without digital upsampling,” Opt. Express 26, 13810–13818 (2018).
[Crossref]

T. Bo and H. Kim, “Kramers-Kronig receiver without digital upsampling,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.2.

Breyer, F.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

Brosi, M.

T. Harter, C. Füllner, J. N. Kemal, S. Ummethala, M. Brosi, E. Bründermann, W. Freude, S. Randel, and C. Koos, “110-m THz wireless transmission at 100  Gbit/s using a Kramers-Kronig Schottky barrier diode receiver,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.7.

Bründermann, E.

T. Harter, C. Füllner, J. N. Kemal, S. Ummethala, M. Brosi, E. Bründermann, W. Freude, S. Randel, and C. Koos, “110-m THz wireless transmission at 100  Gbit/s using a Kramers-Kronig Schottky barrier diode receiver,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.7.

Buck, J. R.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing, 2nd ed. (Prentice Hall, 1999).

Bunge, C. A.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

M. Schuster, B. Spinnler, C. A. Bunge, and K. Petermann, “Spectrally efficient OFDM-transmission with compatible single-sideband modulation for direct detection,” in 33rd European Conference and Exhibition of Optical Communication (2007).

Chandrasekhar, S.

C. Antonelli, A. Mecozzi, M. Shtaif, X. Chen, S. Chandrasekhar, and P. J. Winzer, “Polarization multiplexing with the Kramers-Kronig receiver,” J. Lightwave Technol. 35, 5418–5424 (2017).
[Crossref]

P. Dong, X. Chen, K. Kim, S. Chandrasekhar, Y.-K. Chen, and J. H. Sinsky, “128-Gb/s 100-km transmission with direct detection using silicon photonic Stokes vector receiver and I/Q modulator,” Opt. Express 24, 14208–14214 (2016).
[Crossref]

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, J. Sinsky, A. Mecozzi, M. Shtaif, and P. Winzer, “218-Gb/s single-wavelength, single-polarization, single-photodiode transmission over 125-km of standard singlemode fiber using Kramers-Kronig detection,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2017), paper Th5B.6.

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s discrete-multitone transmission over 80-km SSMF using single-sideband modulation with novel interference-cancellation scheme,” in European Conference on Optical Communication (ECOC) (2015).

X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode Kramers-Kronig detection of 440-gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (IPC) Part II (2017).

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, A. Mecozzi, M. Shtaif, and P. Winzer, “4 × 240  Gb/s dense WDM and PDM Kramers-Kronig detection with 125-km SSMF transmission,” in European Conference on Optical Communication (ECOC) (2017).

X. Chen, S. Chandrasekhar, and P. Winzer, “Frequency-resolved measurements of signal, noise, and signal-signal beat interference in self-coherent direct-detection receivers,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.6.

X. Chen, S. Chandrasekhar, S. Olsson, A. Adamiecki, and P. Winzer, “Impact of O/E front-end frequency response on Kramers-Kronig receivers and its compensation,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.5.

Charlet, G.

R. Rios-Muller, J. Estaran, J. Renaudier, and G. Charlet, “Dual polarization in-phase and quadrature high speed submarine transmission with only two photodiodes, ADCs, MZMs and DACs,” in IEEE Photonics Conference (IPC) Part II (2017).

Chen, X.

C. Antonelli, A. Mecozzi, M. Shtaif, X. Chen, S. Chandrasekhar, and P. J. Winzer, “Polarization multiplexing with the Kramers-Kronig receiver,” J. Lightwave Technol. 35, 5418–5424 (2017).
[Crossref]

P. Dong, X. Chen, K. Kim, S. Chandrasekhar, Y.-K. Chen, and J. H. Sinsky, “128-Gb/s 100-km transmission with direct detection using silicon photonic Stokes vector receiver and I/Q modulator,” Opt. Express 24, 14208–14214 (2016).
[Crossref]

X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode Kramers-Kronig detection of 440-gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (IPC) Part II (2017).

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, A. Mecozzi, M. Shtaif, and P. Winzer, “4 × 240  Gb/s dense WDM and PDM Kramers-Kronig detection with 125-km SSMF transmission,” in European Conference on Optical Communication (ECOC) (2017).

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, J. Sinsky, A. Mecozzi, M. Shtaif, and P. Winzer, “218-Gb/s single-wavelength, single-polarization, single-photodiode transmission over 125-km of standard singlemode fiber using Kramers-Kronig detection,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2017), paper Th5B.6.

X. Chen, S. Chandrasekhar, and P. Winzer, “Frequency-resolved measurements of signal, noise, and signal-signal beat interference in self-coherent direct-detection receivers,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.6.

X. Chen, S. Chandrasekhar, S. Olsson, A. Adamiecki, and P. Winzer, “Impact of O/E front-end frequency response on Kramers-Kronig receivers and its compensation,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.5.

Chen, Y.-K.

Chen, Z.

Y. Zhu, M. Jiang, X. Ruan, Z. Chen, C. Li, and F. Zhang, “6.4  Tb/s (32 × 200  Gb/s) WDM direct-detection transmission with twin-SSB modulation and Kramers-Kronig receiver,” Opt. Commun. 415, 64–69 (2018).
[Crossref]

K. Zou, Y. Zhu, F. Zhang, and Z. Chen, “Spectrally efficient terabit optical transmission with Nyquist 64-QAM half-cycle subcarrier modulation and direct detection,” Opt. Lett. 41, 2767–2770 (2016).
[Crossref]

Cheng, M.

Cheng, W.

T. Zuo, S. Zhang, L. Liu, W. Cheng, and X. Xu, “Single-lane 100  Gb/s 4-PAM transmission over 80  km SSMF based on K-K scheme and integrated 10G TOSA,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.6.

Chi, S.

Cho, J.

X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode Kramers-Kronig detection of 440-gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (IPC) Part II (2017).

Chow, C.-W.

Christen, L. C.

Ciaramella, E.

M. Presi, G. Cossu, G. Contestabile, E. Ciaramella, C. Antonelli, A. Mecozzi, and M. Shtaif, “Transmission in 125-km SMF with 3.9  bit/s/Hz spectral efficiency using a single-drive MZM and a direct-detection Kramers-Kronig receiver without optical CD compensation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.3.

Contestabile, G.

M. Presi, G. Cossu, G. Contestabile, E. Ciaramella, C. Antonelli, A. Mecozzi, and M. Shtaif, “Transmission in 125-km SMF with 3.9  bit/s/Hz spectral efficiency using a single-drive MZM and a direct-detection Kramers-Kronig receiver without optical CD compensation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.3.

Cossu, G.

M. Presi, G. Cossu, G. Contestabile, E. Ciaramella, C. Antonelli, A. Mecozzi, and M. Shtaif, “Transmission in 125-km SMF with 3.9  bit/s/Hz spectral efficiency using a single-drive MZM and a direct-detection Kramers-Kronig receiver without optical CD compensation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.3.

da Silva, E. P.

D. Kong, E. P. da Silva, Y. Sasaki, K. Aikawa, F. D. Ros, M. Galili, T. Morioka, L. K. Oxenløwe, and H. Hu, “Kramers-Kronig detection with adaptive rates for 909.5  Tbit/s dense SDM and WDM data channels,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.5.

Dai, Y.

L. Shu, J. Li, Z. Wan, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “56-Gb/s single-photodiode 16QAM transmission over 140-km SSMF using Kramers-Kronig detection,” in Asia Communications and Photonics Conference (Optical Society of America, 2017), paper M2B.2.

de Waardt, H.

S. van der Heide, J. van Weerdenburg, M. Bigot-Astruc, A. Amezcua-Correa, J. Antonio-Lopez, J. C. Alvarado-Zacarias, H. de Waardt, T. Koonen, P. Sillard, R. Amezcua-Correa, and C. Okonkwo, “Single carrier 1  Tbit/s mode-multiplexed transmission over graded-index 50  μm core multi-mode fiber employing Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Tu1G.3.

Deng, L.

Derr, F.

F. Derr, “Coherent optical QPSK intradyne system: concept and digital receiver realization,” J. Lightwave Technol. 10, 1290–1296 (1992).
[Crossref]

Dong, P.

Duren, P.

P. Duren, W. Hengartner, and R. S. Laugesen, “The argument principle for harmonic functions,” Am. Math. Monthly 103(5), 411–415 (1996).
[Crossref]

Eldar, Y.

L. Blech, Y. Eldar, C. Antonelli, A. Mecozzi, and M. Shtaif, “The enhanced Kramers Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.7.

El-Fiky, E.

T. M. Hoang, M. Y. S. Sowailem, Q. Zhuge, Z. Xing, M. Morsy-Osman, E. El-Fiky, S. Fan, M. Xiang, and D. V. Plant, “Single wavelength 480  Gb/s direct detection over 80  km SSMF enabled by stokes vector Kramers-Kronig transceiver,” Opt. Express 25, 33534–33542 (2017).
[Crossref]

T. Hoang, Q. Zhuge, Z. Xing, M. Sowailem, M. Morsy-Osman, M. Xiang, E. El-Fiky, S. Fan, and D. V. Plant, “Direct detection optical transmission systems employing Stokes vector Kramers-Kronig transceivers,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.2.

Elschner, R.

I. Sackey, C. Schmidt-Langhorst, R. Emmerich, R. Elschner, T. Kato, T. Tanimura, S. Watanabe, T. Hoshida, and C. Schubert, “Distributed aggregation and reception of a 400-Gb/s net rate superchannel in a single-photodiode 110-GHz Kramers-Kronig receiver,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2018), paper Th4C.7.

Emmerich, R.

I. Sackey, C. Schmidt-Langhorst, R. Emmerich, R. Elschner, T. Kato, T. Tanimura, S. Watanabe, T. Hoshida, and C. Schubert, “Distributed aggregation and reception of a 400-Gb/s net rate superchannel in a single-photodiode 110-GHz Kramers-Kronig receiver,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2018), paper Th4C.7.

Erkilinç, M.

Z. Li, M. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. Thomsen, P. Bayvel, and R. Killey, “DSP for single-sideband direct-detection systems,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.5.

Z. Li, L. Galdino, T. Xu, M. Erkilinç, K. Shi, E. Sillekens, B. Thomsen, P. Bayvel, and R. Killey, “Performance of digital back-propagation in Kramers-Kronig direct-detection receivers,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.4.

Erkilinç, M. S.

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Spectrally efficient 168  Gb/s/λ WDM 64-QAM single-sideband Nyquist-subcarrier modulation with Kramers-Kronig direct-detection receivers,” J. Lightwave Technol. 36, 1340–1346 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Digital linearization of direct-detection transceivers for spectrally efficient 100  Gb/s/λ WDM metro networking,” J. Lightwave Technol. 36, 27–36 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “SSBI mitigation and the Kramers-Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35, 1887–1893 (2017).
[Crossref]

Z. Li, M. S. Erkilinç, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Comparison of digital signal-signal beat interference compensation techniques in direct-detection subcarrier modulation systems,” Opt. Express 24, 29176–29189 (2016).
[Crossref]

Z. Li, M. S. Erkilinç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photon. Technol. Lett. 28, 2838–2841 (2016).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “168  Gb/s direct-detection 64-QAM SSB Nyquist-SCM transmission over 80  km uncompensated SSMF at 4.54  b/s/Hz net ISD using a Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Joint optimisation of resampling rate and carrier-to-signal power ratio in direct-detection Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (2017).

Estaran, J.

R. Rios-Muller, J. Estaran, J. Renaudier, and G. Charlet, “Dual polarization in-phase and quadrature high speed submarine transmission with only two photodiodes, ADCs, MZMs and DACs,” in IEEE Photonics Conference (IPC) Part II (2017).

Fan, S.

S. Fan, Q. Zhuge, M. Y. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, Y. Li, J. Wu, and D. V. Plant, “Single wavelength twin-SSB direct detection system based on Kramers-Kronig receiver and time-interleaved OFDM frame,” Opt. Commun. 425, 133–140 (2018).
[Crossref]

T. M. Hoang, M. Y. S. Sowailem, Q. Zhuge, Z. Xing, M. Morsy-Osman, E. El-Fiky, S. Fan, M. Xiang, and D. V. Plant, “Single wavelength 480  Gb/s direct detection over 80  km SSMF enabled by stokes vector Kramers-Kronig transceiver,” Opt. Express 25, 33534–33542 (2017).
[Crossref]

T. Hoang, Q. Zhuge, Z. Xing, M. Sowailem, M. Morsy-Osman, M. Xiang, E. El-Fiky, S. Fan, and D. V. Plant, “Direct detection optical transmission systems employing Stokes vector Kramers-Kronig transceivers,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.2.

S. Fan, Q. Zhuge, M. Y. S. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, M. Qiu, Y. Li, J. Wu, and D. V. Plant, “Twin-SSB direct detection transmission over 80km SSMF using Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

S. Fan, Q. Zhuge, Z. Xing, K. Zhang, T. M. Hoang, M. Morsy-Osman, M. Y. S. Sowailem, Y. Li, J. Wu, and D. V. Plant, “264  Gb/s twin-SSB-KK direct detection transmission enabled by MIMO processing,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.5.

Fan, Y.

L. Shu, J. Li, Z. Wan, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “56-Gb/s single-photodiode 16QAM transmission over 140-km SSMF using Kramers-Kronig detection,” in Asia Communications and Photonics Conference (Optical Society of America, 2017), paper M2B.2.

Fatadin, I.

L. G. Guerrero, H. Shams, I. Fatadin, M. J. Fice, M. Naftaly, A. J. Seeds, and C. C. Renaud, “Spectrally efficient SSB signals for W-band links enabled by Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Th2A.61.

Feng, K.-M.

Feng, X.

Z. Wu, H. Jiang, X. Feng, and S. Gao, “Demonstration of cost-effective single-photodetector coherent receiver for free-space optical communications,” in Asia Communications and Photonics Conference (Optical Society of America, 2017), paper M3G.4.

Fice, M. J.

L. G. Guerrero, H. Shams, I. Fatadin, M. J. Fice, M. Naftaly, A. J. Seeds, and C. C. Renaud, “Spectrally efficient SSB signals for W-band links enabled by Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Th2A.61.

Freude, W.

T. Harter, C. Füllner, J. N. Kemal, S. Ummethala, M. Brosi, E. Bründermann, W. Freude, S. Randel, and C. Koos, “110-m THz wireless transmission at 100  Gbit/s using a Kramers-Kronig Schottky barrier diode receiver,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.7.

C. Füllner, S. Wolf, J. N. Kemal, J. Lutz, L. Altenhain, R. Schmid, W. Freude, C. Koos, and S. Randel, “Transmission of 80-GBd 16-QAM over 300  km and Kramers-Kronig reception using a low-complexity FIR Hilbert filter approximation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.3.

Fu, S.

D. Li, Q. Yu, L. Deng, L. Huo, S. Fu, M. Tang, M. Cheng, M. Zhang, and D. Liu, “Bidirectional long-reach PON using Kramers-Kronig-based receiver for Rayleigh backscattering noise and SSBI interference elimination,” Opt. Express 26, 19020–19036 (2018).
[Crossref]

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers-Kronig detection over 80-km SSMF,” IEEE Photon. J. 9, 1–9 (2017).
[Crossref]

Füllner, C.

C. Füllner, S. Wolf, J. N. Kemal, J. Lutz, L. Altenhain, R. Schmid, W. Freude, C. Koos, and S. Randel, “Transmission of 80-GBd 16-QAM over 300  km and Kramers-Kronig reception using a low-complexity FIR Hilbert filter approximation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.3.

T. Harter, C. Füllner, J. N. Kemal, S. Ummethala, M. Brosi, E. Bründermann, W. Freude, S. Randel, and C. Koos, “110-m THz wireless transmission at 100  Gbit/s using a Kramers-Kronig Schottky barrier diode receiver,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.7.

Furukawa, H.

R. S. Luìs, G. Rademacher, B. J. Puttnam, S. Shinada, H. Furukawa, R. Maruyama, K. Aikawa, and N. Wada, “A coherent Kramers-Kronig receiver for 3-mode few-mode fiber transmission,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.3.

Galdino, L.

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Spectrally efficient 168  Gb/s/λ WDM 64-QAM single-sideband Nyquist-subcarrier modulation with Kramers-Kronig direct-detection receivers,” J. Lightwave Technol. 36, 1340–1346 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Digital linearization of direct-detection transceivers for spectrally efficient 100  Gb/s/λ WDM metro networking,” J. Lightwave Technol. 36, 27–36 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “SSBI mitigation and the Kramers-Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35, 1887–1893 (2017).
[Crossref]

Z. Li, M. S. Erkilinç, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Comparison of digital signal-signal beat interference compensation techniques in direct-detection subcarrier modulation systems,” Opt. Express 24, 29176–29189 (2016).
[Crossref]

Z. Li, M. S. Erkilinç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photon. Technol. Lett. 28, 2838–2841 (2016).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Joint optimisation of resampling rate and carrier-to-signal power ratio in direct-detection Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (2017).

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “168  Gb/s direct-detection 64-QAM SSB Nyquist-SCM transmission over 80  km uncompensated SSMF at 4.54  b/s/Hz net ISD using a Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

Z. Li, L. Galdino, T. Xu, M. Erkilinç, K. Shi, E. Sillekens, B. Thomsen, P. Bayvel, and R. Killey, “Performance of digital back-propagation in Kramers-Kronig direct-detection receivers,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.4.

Z. Li, M. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. Thomsen, P. Bayvel, and R. Killey, “DSP for single-sideband direct-detection systems,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.5.

Galili, M.

D. Kong, E. P. da Silva, Y. Sasaki, K. Aikawa, F. D. Ros, M. Galili, T. Morioka, L. K. Oxenløwe, and H. Hu, “Kramers-Kronig detection with adaptive rates for 909.5  Tbit/s dense SDM and WDM data channels,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.5.

Gao, F.

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers-Kronig detection over 80-km SSMF,” IEEE Photon. J. 9, 1–9 (2017).
[Crossref]

Gao, S.

Z. Wu, H. Jiang, X. Feng, and S. Gao, “Demonstration of cost-effective single-photodetector coherent receiver for free-space optical communications,” in Asia Communications and Photonics Conference (Optical Society of America, 2017), paper M3G.4.

Guerrero, L. G.

L. G. Guerrero, H. Shams, I. Fatadin, M. J. Fice, M. Naftaly, A. J. Seeds, and C. C. Renaud, “Spectrally efficient SSB signals for W-band links enabled by Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Th2A.61.

Harter, T.

T. Harter, C. Füllner, J. N. Kemal, S. Ummethala, M. Brosi, E. Bründermann, W. Freude, S. Randel, and C. Koos, “110-m THz wireless transmission at 100  Gbit/s using a Kramers-Kronig Schottky barrier diode receiver,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.7.

Hengartner, W.

P. Duren, W. Hengartner, and R. S. Laugesen, “The argument principle for harmonic functions,” Am. Math. Monthly 103(5), 411–415 (1996).
[Crossref]

Ho, K.-P.

Hoang, T.

T. Hoang, Q. Zhuge, Z. Xing, M. Sowailem, M. Morsy-Osman, M. Xiang, E. El-Fiky, S. Fan, and D. V. Plant, “Direct detection optical transmission systems employing Stokes vector Kramers-Kronig transceivers,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.2.

Hoang, T. M.

S. Fan, Q. Zhuge, M. Y. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, Y. Li, J. Wu, and D. V. Plant, “Single wavelength twin-SSB direct detection system based on Kramers-Kronig receiver and time-interleaved OFDM frame,” Opt. Commun. 425, 133–140 (2018).
[Crossref]

T. M. Hoang, M. Y. S. Sowailem, Q. Zhuge, Z. Xing, M. Morsy-Osman, E. El-Fiky, S. Fan, M. Xiang, and D. V. Plant, “Single wavelength 480  Gb/s direct detection over 80  km SSMF enabled by stokes vector Kramers-Kronig transceiver,” Opt. Express 25, 33534–33542 (2017).
[Crossref]

S. Fan, Q. Zhuge, M. Y. S. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, M. Qiu, Y. Li, J. Wu, and D. V. Plant, “Twin-SSB direct detection transmission over 80km SSMF using Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

S. Fan, Q. Zhuge, Z. Xing, K. Zhang, T. M. Hoang, M. Morsy-Osman, M. Y. S. Sowailem, Y. Li, J. Wu, and D. V. Plant, “264  Gb/s twin-SSB-KK direct detection transmission enabled by MIMO processing,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.5.

Hoshida, T.

I. Sackey, C. Schmidt-Langhorst, R. Emmerich, R. Elschner, T. Kato, T. Tanimura, S. Watanabe, T. Hoshida, and C. Schubert, “Distributed aggregation and reception of a 400-Gb/s net rate superchannel in a single-photodiode 110-GHz Kramers-Kronig receiver,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2018), paper Th4C.7.

Hu, H.

D. Kong, E. P. da Silva, Y. Sasaki, K. Aikawa, F. D. Ros, M. Galili, T. Morioka, L. K. Oxenløwe, and H. Hu, “Kramers-Kronig detection with adaptive rates for 909.5  Tbit/s dense SDM and WDM data channels,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.5.

Huang, X.

M. Zhu, J. Zhang, X. Yi, H. Ying, X. Li, M. Luo, Y. Song, X. Huang, and K. Qiu, “Optical single side-band Nyquist PAM-4 transmission using dual-drive MZM modulation and direct detection,” Opt. Express 26, 6629–6638 (2018).
[Crossref]

M. Zhu, J. Zhang, H. Ying, X. Li, M. Luo, X. Huang, Y. Song, F. Li, X. Yi, and K. Qiu, “56-Gb/s optical SSB PAM-4 transmission over 800-km SSMF using DDMZM transmitter and simplified direct detection Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper M2C.5.

Hui, R.

Huo, L.

Jiang, H.

Z. Wu, H. Jiang, X. Feng, and S. Gao, “Demonstration of cost-effective single-photodetector coherent receiver for free-space optical communications,” in Asia Communications and Photonics Conference (Optical Society of America, 2017), paper M3G.4.

Jiang, M.

Y. Zhu, M. Jiang, X. Ruan, Z. Chen, C. Li, and F. Zhang, “6.4  Tb/s (32 × 200  Gb/s) WDM direct-detection transmission with twin-SSB modulation and Kramers-Kronig receiver,” Opt. Commun. 415, 64–69 (2018).
[Crossref]

Y. Zhu, M. Jiang, and F. Zhang, “Direct detection of polarization multiplexed single sideband signals with orthogonal offset carriers,” Opt. Express 26, 15887–15898 (2018).
[Crossref]

Y. Zhu, M. Jiang, X. Ruan, C. Li, and F. Zhang, “16×112  Gb/s single-sideband PAM4 WDM transmission over 80km SSMF with Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.2.

Joy, R.

S. Ohlendorf, R. Joy, S. Pachnicke, and W. Rosenkranz, “Flexible PAM in DWDM transmission with Kramers-Kronig DSP,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.6.

Kahn, L. R.

L. R. Kahn, “Compatible single sideband,” Proc. IRE 49, 1503–1527 (1961).
[Crossref]

Kato, T.

I. Sackey, C. Schmidt-Langhorst, R. Emmerich, R. Elschner, T. Kato, T. Tanimura, S. Watanabe, T. Hoshida, and C. Schubert, “Distributed aggregation and reception of a 400-Gb/s net rate superchannel in a single-photodiode 110-GHz Kramers-Kronig receiver,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2018), paper Th4C.7.

Kemal, J. N.

C. Füllner, S. Wolf, J. N. Kemal, J. Lutz, L. Altenhain, R. Schmid, W. Freude, C. Koos, and S. Randel, “Transmission of 80-GBd 16-QAM over 300  km and Kramers-Kronig reception using a low-complexity FIR Hilbert filter approximation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.3.

T. Harter, C. Füllner, J. N. Kemal, S. Ummethala, M. Brosi, E. Bründermann, W. Freude, S. Randel, and C. Koos, “110-m THz wireless transmission at 100  Gbit/s using a Kramers-Kronig Schottky barrier diode receiver,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.7.

Killey, R.

Z. Li, M. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. Thomsen, P. Bayvel, and R. Killey, “DSP for single-sideband direct-detection systems,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.5.

Z. Li, L. Galdino, T. Xu, M. Erkilinç, K. Shi, E. Sillekens, B. Thomsen, P. Bayvel, and R. Killey, “Performance of digital back-propagation in Kramers-Kronig direct-detection receivers,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.4.

Killey, R. I.

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Spectrally efficient 168  Gb/s/λ WDM 64-QAM single-sideband Nyquist-subcarrier modulation with Kramers-Kronig direct-detection receivers,” J. Lightwave Technol. 36, 1340–1346 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Digital linearization of direct-detection transceivers for spectrally efficient 100  Gb/s/λ WDM metro networking,” J. Lightwave Technol. 36, 27–36 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “SSBI mitigation and the Kramers-Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35, 1887–1893 (2017).
[Crossref]

Z. Li, M. S. Erkilinç, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Comparison of digital signal-signal beat interference compensation techniques in direct-detection subcarrier modulation systems,” Opt. Express 24, 29176–29189 (2016).
[Crossref]

Z. Li, M. S. Erkilinç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photon. Technol. Lett. 28, 2838–2841 (2016).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “168  Gb/s direct-detection 64-QAM SSB Nyquist-SCM transmission over 80  km uncompensated SSMF at 4.54  b/s/Hz net ISD using a Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Joint optimisation of resampling rate and carrier-to-signal power ratio in direct-detection Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (2017).

Kim, H.

T. Bo and H. Kim, “Kramers-Kronig receiver operable without digital upsampling,” Opt. Express 26, 13810–13818 (2018).
[Crossref]

T. Bo and H. Kim, “Kramers-Kronig receiver without digital upsampling,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.2.

Kim, K.

Kong, D.

D. Kong, E. P. da Silva, Y. Sasaki, K. Aikawa, F. D. Ros, M. Galili, T. Morioka, L. K. Oxenløwe, and H. Hu, “Kramers-Kronig detection with adaptive rates for 909.5  Tbit/s dense SDM and WDM data channels,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.5.

Koonen, T.

S. van der Heide, J. van Weerdenburg, M. Bigot-Astruc, A. Amezcua-Correa, J. Antonio-Lopez, J. C. Alvarado-Zacarias, H. de Waardt, T. Koonen, P. Sillard, R. Amezcua-Correa, and C. Okonkwo, “Single carrier 1  Tbit/s mode-multiplexed transmission over graded-index 50  μm core multi-mode fiber employing Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Tu1G.3.

Koos, C.

T. Harter, C. Füllner, J. N. Kemal, S. Ummethala, M. Brosi, E. Bründermann, W. Freude, S. Randel, and C. Koos, “110-m THz wireless transmission at 100  Gbit/s using a Kramers-Kronig Schottky barrier diode receiver,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.7.

C. Füllner, S. Wolf, J. N. Kemal, J. Lutz, L. Altenhain, R. Schmid, W. Freude, C. Koos, and S. Randel, “Transmission of 80-GBd 16-QAM over 300  km and Kramers-Kronig reception using a low-complexity FIR Hilbert filter approximation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.3.

Laugesen, R. S.

P. Duren, W. Hengartner, and R. S. Laugesen, “The argument principle for harmonic functions,” Am. Math. Monthly 103(5), 411–415 (1996).
[Crossref]

Le, S. T.

S. T. Le and K. Schuh, “Experimental verification of equalization enhanced phase noise in Kramers-Kronig transmissions,” in Optical Fiber Communication Conference (OFC) (Optical Society of America, 2019), paper Tu2B.2.

Lee, S. C. J.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

Li, C.

Y. Zhu, M. Jiang, X. Ruan, Z. Chen, C. Li, and F. Zhang, “6.4  Tb/s (32 × 200  Gb/s) WDM direct-detection transmission with twin-SSB modulation and Kramers-Kronig receiver,” Opt. Commun. 415, 64–69 (2018).
[Crossref]

Y. Zhu, M. Jiang, X. Ruan, C. Li, and F. Zhang, “16×112  Gb/s single-sideband PAM4 WDM transmission over 80km SSMF with Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.2.

C. Li, M. Luo, Q. You, and X. Li, “114-Gb/s PDM-DMT transmission over 100-km SSMF with high phase noise tolerance using Kramers-Kronig detection and digital carrier regeneration,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.4.

Li, D.

Li, F.

M. Zhu, J. Zhang, H. Ying, X. Li, M. Luo, X. Huang, Y. Song, F. Li, X. Yi, and K. Qiu, “56-Gb/s optical SSB PAM-4 transmission over 800-km SSMF using DDMZM transmitter and simplified direct detection Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper M2C.5.

Li, G.

Li, J.

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers-Kronig detection over 80-km SSMF,” IEEE Photon. J. 9, 1–9 (2017).
[Crossref]

L. Shu, J. Li, Z. Wan, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “56-Gb/s single-photodiode 16QAM transmission over 140-km SSMF using Kramers-Kronig detection,” in Asia Communications and Photonics Conference (Optical Society of America, 2017), paper M2B.2.

Li, X.

M. Zhu, J. Zhang, X. Yi, H. Ying, X. Li, M. Luo, Y. Song, X. Huang, and K. Qiu, “Optical single side-band Nyquist PAM-4 transmission using dual-drive MZM modulation and direct detection,” Opt. Express 26, 6629–6638 (2018).
[Crossref]

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers-Kronig detection over 80-km SSMF,” IEEE Photon. J. 9, 1–9 (2017).
[Crossref]

M. Zhu, J. Zhang, H. Ying, X. Li, M. Luo, X. Huang, Y. Song, F. Li, X. Yi, and K. Qiu, “56-Gb/s optical SSB PAM-4 transmission over 800-km SSMF using DDMZM transmitter and simplified direct detection Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper M2C.5.

C. Li, M. Luo, Q. You, and X. Li, “114-Gb/s PDM-DMT transmission over 100-km SSMF with high phase noise tolerance using Kramers-Kronig detection and digital carrier regeneration,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.4.

Li, Y.

S. Fan, Q. Zhuge, M. Y. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, Y. Li, J. Wu, and D. V. Plant, “Single wavelength twin-SSB direct detection system based on Kramers-Kronig receiver and time-interleaved OFDM frame,” Opt. Commun. 425, 133–140 (2018).
[Crossref]

S. Fan, Q. Zhuge, M. Y. S. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, M. Qiu, Y. Li, J. Wu, and D. V. Plant, “Twin-SSB direct detection transmission over 80km SSMF using Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

S. Fan, Q. Zhuge, Z. Xing, K. Zhang, T. M. Hoang, M. Morsy-Osman, M. Y. S. Sowailem, Y. Li, J. Wu, and D. V. Plant, “264  Gb/s twin-SSB-KK direct detection transmission enabled by MIMO processing,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.5.

Li, Z.

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Spectrally efficient 168  Gb/s/λ WDM 64-QAM single-sideband Nyquist-subcarrier modulation with Kramers-Kronig direct-detection receivers,” J. Lightwave Technol. 36, 1340–1346 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Digital linearization of direct-detection transceivers for spectrally efficient 100  Gb/s/λ WDM metro networking,” J. Lightwave Technol. 36, 27–36 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “SSBI mitigation and the Kramers-Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35, 1887–1893 (2017).
[Crossref]

Z. Li, M. S. Erkilinç, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Comparison of digital signal-signal beat interference compensation techniques in direct-detection subcarrier modulation systems,” Opt. Express 24, 29176–29189 (2016).
[Crossref]

Z. Li, M. S. Erkilinç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photon. Technol. Lett. 28, 2838–2841 (2016).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Joint optimisation of resampling rate and carrier-to-signal power ratio in direct-detection Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (2017).

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “168  Gb/s direct-detection 64-QAM SSB Nyquist-SCM transmission over 80  km uncompensated SSMF at 4.54  b/s/Hz net ISD using a Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

Z. Li, L. Galdino, T. Xu, M. Erkilinç, K. Shi, E. Sillekens, B. Thomsen, P. Bayvel, and R. Killey, “Performance of digital back-propagation in Kramers-Kronig direct-detection receivers,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.4.

Z. Li, M. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. Thomsen, P. Bayvel, and R. Killey, “DSP for single-sideband direct-detection systems,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.5.

Liu, D.

Liu, L.

T. Zuo, S. Zhang, L. Liu, W. Cheng, and X. Xu, “Single-lane 100  Gb/s 4-PAM transmission over 80  km SSMF based on K-K scheme and integrated 10G TOSA,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.6.

Lowery, A. J.

Luìs, R. S.

R. S. Luìs, G. Rademacher, B. J. Puttnam, S. Shinada, H. Furukawa, R. Maruyama, K. Aikawa, and N. Wada, “A coherent Kramers-Kronig receiver for 3-mode few-mode fiber transmission,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.3.

Luo, M.

M. Zhu, J. Zhang, X. Yi, H. Ying, X. Li, M. Luo, Y. Song, X. Huang, and K. Qiu, “Optical single side-band Nyquist PAM-4 transmission using dual-drive MZM modulation and direct detection,” Opt. Express 26, 6629–6638 (2018).
[Crossref]

C. Li, M. Luo, Q. You, and X. Li, “114-Gb/s PDM-DMT transmission over 100-km SSMF with high phase noise tolerance using Kramers-Kronig detection and digital carrier regeneration,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.4.

M. Zhu, J. Zhang, H. Ying, X. Li, M. Luo, X. Huang, Y. Song, F. Li, X. Yi, and K. Qiu, “56-Gb/s optical SSB PAM-4 transmission over 800-km SSMF using DDMZM transmitter and simplified direct detection Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper M2C.5.

Lutz, J.

C. Füllner, S. Wolf, J. N. Kemal, J. Lutz, L. Altenhain, R. Schmid, W. Freude, C. Koos, and S. Randel, “Transmission of 80-GBd 16-QAM over 300  km and Kramers-Kronig reception using a low-complexity FIR Hilbert filter approximation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.3.

Maher, R.

Z. Li, M. S. Erkilinç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photon. Technol. Lett. 28, 2838–2841 (2016).
[Crossref]

Maruyama, R.

R. S. Luìs, G. Rademacher, B. J. Puttnam, S. Shinada, H. Furukawa, R. Maruyama, K. Aikawa, and N. Wada, “A coherent Kramers-Kronig receiver for 3-mode few-mode fiber transmission,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.3.

Mecozzi, A.

A. Mecozzi and M. Shtaif, “Coherent detection with an incoherent local oscillator,” Opt. Express 26, 33970–33981 (2018).
[Crossref]

C. Antonelli, A. Mecozzi, and M. Shtaif, “Kramers-Kronig PAM transceiver and two-sided polarization-multiplexed Kramers-Kronig transceiver,” J. Lightwave Technol. 36, 468–475 (2018).
[Crossref]

C. Antonelli, A. Mecozzi, M. Shtaif, X. Chen, S. Chandrasekhar, and P. J. Winzer, “Polarization multiplexing with the Kramers-Kronig receiver,” J. Lightwave Technol. 35, 5418–5424 (2017).
[Crossref]

A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers-Kronig coherent receiver,” Optica 3, 1220–1227 (2016).
[Crossref]

M. Presi, G. Cossu, G. Contestabile, E. Ciaramella, C. Antonelli, A. Mecozzi, and M. Shtaif, “Transmission in 125-km SMF with 3.9  bit/s/Hz spectral efficiency using a single-drive MZM and a direct-detection Kramers-Kronig receiver without optical CD compensation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.3.

X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode Kramers-Kronig detection of 440-gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (IPC) Part II (2017).

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, A. Mecozzi, M. Shtaif, and P. Winzer, “4 × 240  Gb/s dense WDM and PDM Kramers-Kronig detection with 125-km SSMF transmission,” in European Conference on Optical Communication (ECOC) (2017).

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, J. Sinsky, A. Mecozzi, M. Shtaif, and P. Winzer, “218-Gb/s single-wavelength, single-polarization, single-photodiode transmission over 125-km of standard singlemode fiber using Kramers-Kronig detection,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2017), paper Th5B.6.

L. Blech, Y. Eldar, C. Antonelli, A. Mecozzi, and M. Shtaif, “The enhanced Kramers Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.7.

Morioka, T.

D. Kong, E. P. da Silva, Y. Sasaki, K. Aikawa, F. D. Ros, M. Galili, T. Morioka, L. K. Oxenløwe, and H. Hu, “Kramers-Kronig detection with adaptive rates for 909.5  Tbit/s dense SDM and WDM data channels,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.5.

Morsy-Osman, M.

S. Fan, Q. Zhuge, M. Y. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, Y. Li, J. Wu, and D. V. Plant, “Single wavelength twin-SSB direct detection system based on Kramers-Kronig receiver and time-interleaved OFDM frame,” Opt. Commun. 425, 133–140 (2018).
[Crossref]

T. M. Hoang, M. Y. S. Sowailem, Q. Zhuge, Z. Xing, M. Morsy-Osman, E. El-Fiky, S. Fan, M. Xiang, and D. V. Plant, “Single wavelength 480  Gb/s direct detection over 80  km SSMF enabled by stokes vector Kramers-Kronig transceiver,” Opt. Express 25, 33534–33542 (2017).
[Crossref]

T. Hoang, Q. Zhuge, Z. Xing, M. Sowailem, M. Morsy-Osman, M. Xiang, E. El-Fiky, S. Fan, and D. V. Plant, “Direct detection optical transmission systems employing Stokes vector Kramers-Kronig transceivers,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.2.

S. Fan, Q. Zhuge, Z. Xing, K. Zhang, T. M. Hoang, M. Morsy-Osman, M. Y. S. Sowailem, Y. Li, J. Wu, and D. V. Plant, “264  Gb/s twin-SSB-KK direct detection transmission enabled by MIMO processing,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.5.

S. Fan, Q. Zhuge, M. Y. S. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, M. Qiu, Y. Li, J. Wu, and D. V. Plant, “Twin-SSB direct detection transmission over 80km SSMF using Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

Naftaly, M.

L. G. Guerrero, H. Shams, I. Fatadin, M. J. Fice, M. Naftaly, A. J. Seeds, and C. C. Renaud, “Spectrally efficient SSB signals for W-band links enabled by Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Th2A.61.

O’Sullivan, M.

Ohlendorf, S.

S. Ohlendorf, R. Joy, S. Pachnicke, and W. Rosenkranz, “Flexible PAM in DWDM transmission with Kramers-Kronig DSP,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.6.

Okonkwo, C.

S. van der Heide, J. van Weerdenburg, M. Bigot-Astruc, A. Amezcua-Correa, J. Antonio-Lopez, J. C. Alvarado-Zacarias, H. de Waardt, T. Koonen, P. Sillard, R. Amezcua-Correa, and C. Okonkwo, “Single carrier 1  Tbit/s mode-multiplexed transmission over graded-index 50  μm core multi-mode fiber employing Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Tu1G.3.

Olsson, S.

X. Chen, S. Chandrasekhar, S. Olsson, A. Adamiecki, and P. Winzer, “Impact of O/E front-end frequency response on Kramers-Kronig receivers and its compensation,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.5.

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing, 2nd ed. (Prentice Hall, 1999).

Oxenløwe, L. K.

D. Kong, E. P. da Silva, Y. Sasaki, K. Aikawa, F. D. Ros, M. Galili, T. Morioka, L. K. Oxenløwe, and H. Hu, “Kramers-Kronig detection with adaptive rates for 909.5  Tbit/s dense SDM and WDM data channels,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.5.

Pachnicke, S.

S. Ohlendorf, R. Joy, S. Pachnicke, and W. Rosenkranz, “Flexible PAM in DWDM transmission with Kramers-Kronig DSP,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.6.

Peng, W.-R.

Petermann, K.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

M. Schuster, B. Spinnler, C. A. Bunge, and K. Petermann, “Spectrally efficient OFDM-transmission with compatible single-sideband modulation for direct detection,” in 33rd European Conference and Exhibition of Optical Communication (2007).

Pilori, D.

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s discrete-multitone transmission over 80-km SSMF using single-sideband modulation with novel interference-cancellation scheme,” in European Conference on Optical Communication (ECOC) (2015).

Plant, D. V.

S. Fan, Q. Zhuge, M. Y. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, Y. Li, J. Wu, and D. V. Plant, “Single wavelength twin-SSB direct detection system based on Kramers-Kronig receiver and time-interleaved OFDM frame,” Opt. Commun. 425, 133–140 (2018).
[Crossref]

T. M. Hoang, M. Y. S. Sowailem, Q. Zhuge, Z. Xing, M. Morsy-Osman, E. El-Fiky, S. Fan, M. Xiang, and D. V. Plant, “Single wavelength 480  Gb/s direct detection over 80  km SSMF enabled by stokes vector Kramers-Kronig transceiver,” Opt. Express 25, 33534–33542 (2017).
[Crossref]

S. Fan, Q. Zhuge, M. Y. S. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, M. Qiu, Y. Li, J. Wu, and D. V. Plant, “Twin-SSB direct detection transmission over 80km SSMF using Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

S. Fan, Q. Zhuge, Z. Xing, K. Zhang, T. M. Hoang, M. Morsy-Osman, M. Y. S. Sowailem, Y. Li, J. Wu, and D. V. Plant, “264  Gb/s twin-SSB-KK direct detection transmission enabled by MIMO processing,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.5.

T. Hoang, Q. Zhuge, Z. Xing, M. Sowailem, M. Morsy-Osman, M. Xiang, E. El-Fiky, S. Fan, and D. V. Plant, “Direct detection optical transmission systems employing Stokes vector Kramers-Kronig transceivers,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.2.

Presi, M.

M. Presi, G. Cossu, G. Contestabile, E. Ciaramella, C. Antonelli, A. Mecozzi, and M. Shtaif, “Transmission in 125-km SMF with 3.9  bit/s/Hz spectral efficiency using a single-drive MZM and a direct-detection Kramers-Kronig receiver without optical CD compensation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.3.

Puttnam, B. J.

R. S. Luìs, G. Rademacher, B. J. Puttnam, S. Shinada, H. Furukawa, R. Maruyama, K. Aikawa, and N. Wada, “A coherent Kramers-Kronig receiver for 3-mode few-mode fiber transmission,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.3.

Qiu, K.

M. Zhu, J. Zhang, X. Yi, H. Ying, X. Li, M. Luo, Y. Song, X. Huang, and K. Qiu, “Optical single side-band Nyquist PAM-4 transmission using dual-drive MZM modulation and direct detection,” Opt. Express 26, 6629–6638 (2018).
[Crossref]

M. Zhu, J. Zhang, H. Ying, X. Li, M. Luo, X. Huang, Y. Song, F. Li, X. Yi, and K. Qiu, “56-Gb/s optical SSB PAM-4 transmission over 800-km SSMF using DDMZM transmitter and simplified direct detection Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper M2C.5.

Qiu, M.

S. Fan, Q. Zhuge, M. Y. S. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, M. Qiu, Y. Li, J. Wu, and D. V. Plant, “Twin-SSB direct detection transmission over 80km SSMF using Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

Rademacher, G.

R. S. Luìs, G. Rademacher, B. J. Puttnam, S. Shinada, H. Furukawa, R. Maruyama, K. Aikawa, and N. Wada, “A coherent Kramers-Kronig receiver for 3-mode few-mode fiber transmission,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.3.

Randel, S.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s discrete-multitone transmission over 80-km SSMF using single-sideband modulation with novel interference-cancellation scheme,” in European Conference on Optical Communication (ECOC) (2015).

T. Harter, C. Füllner, J. N. Kemal, S. Ummethala, M. Brosi, E. Bründermann, W. Freude, S. Randel, and C. Koos, “110-m THz wireless transmission at 100  Gbit/s using a Kramers-Kronig Schottky barrier diode receiver,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.7.

C. Füllner, S. Wolf, J. N. Kemal, J. Lutz, L. Altenhain, R. Schmid, W. Freude, C. Koos, and S. Randel, “Transmission of 80-GBd 16-QAM over 300  km and Kramers-Kronig reception using a low-complexity FIR Hilbert filter approximation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.3.

Raybon, G.

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, A. Mecozzi, M. Shtaif, and P. Winzer, “4 × 240  Gb/s dense WDM and PDM Kramers-Kronig detection with 125-km SSMF transmission,” in European Conference on Optical Communication (ECOC) (2017).

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s discrete-multitone transmission over 80-km SSMF using single-sideband modulation with novel interference-cancellation scheme,” in European Conference on Optical Communication (ECOC) (2015).

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, J. Sinsky, A. Mecozzi, M. Shtaif, and P. Winzer, “218-Gb/s single-wavelength, single-polarization, single-photodiode transmission over 125-km of standard singlemode fiber using Kramers-Kronig detection,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2017), paper Th5B.6.

Renaud, C. C.

L. G. Guerrero, H. Shams, I. Fatadin, M. J. Fice, M. Naftaly, A. J. Seeds, and C. C. Renaud, “Spectrally efficient SSB signals for W-band links enabled by Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Th2A.61.

Renaudier, J.

R. Rios-Muller, J. Estaran, J. Renaudier, and G. Charlet, “Dual polarization in-phase and quadrature high speed submarine transmission with only two photodiodes, ADCs, MZMs and DACs,” in IEEE Photonics Conference (IPC) Part II (2017).

Rios-Muller, R.

R. Rios-Muller, J. Estaran, J. Renaudier, and G. Charlet, “Dual polarization in-phase and quadrature high speed submarine transmission with only two photodiodes, ADCs, MZMs and DACs,” in IEEE Photonics Conference (IPC) Part II (2017).

Ros, F. D.

D. Kong, E. P. da Silva, Y. Sasaki, K. Aikawa, F. D. Ros, M. Galili, T. Morioka, L. K. Oxenløwe, and H. Hu, “Kramers-Kronig detection with adaptive rates for 909.5  Tbit/s dense SDM and WDM data channels,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.5.

Rosenkranz, W.

S. Ohlendorf, R. Joy, S. Pachnicke, and W. Rosenkranz, “Flexible PAM in DWDM transmission with Kramers-Kronig DSP,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.6.

Ruan, X.

Y. Zhu, M. Jiang, X. Ruan, Z. Chen, C. Li, and F. Zhang, “6.4  Tb/s (32 × 200  Gb/s) WDM direct-detection transmission with twin-SSB modulation and Kramers-Kronig receiver,” Opt. Commun. 415, 64–69 (2018).
[Crossref]

Y. Zhu, K. Zou, X. Ruan, and F. Zhang, “Single carrier 400G transmission with single-ended heterodyne detection,” IEEE Photon. Technol. Lett. 29, 1788–1791 (2017).
[Crossref]

Y. Zhu, M. Jiang, X. Ruan, C. Li, and F. Zhang, “16×112  Gb/s single-sideband PAM4 WDM transmission over 80km SSMF with Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.2.

Rusch, L. A.

Sackey, I.

I. Sackey, C. Schmidt-Langhorst, R. Emmerich, R. Elschner, T. Kato, T. Tanimura, S. Watanabe, T. Hoshida, and C. Schubert, “Distributed aggregation and reception of a 400-Gb/s net rate superchannel in a single-photodiode 110-GHz Kramers-Kronig receiver,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2018), paper Th4C.7.

Sasaki, Y.

D. Kong, E. P. da Silva, Y. Sasaki, K. Aikawa, F. D. Ros, M. Galili, T. Morioka, L. K. Oxenløwe, and H. Hu, “Kramers-Kronig detection with adaptive rates for 909.5  Tbit/s dense SDM and WDM data channels,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.5.

Schafer, R. W.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing, 2nd ed. (Prentice Hall, 1999).

Schmid, R.

C. Füllner, S. Wolf, J. N. Kemal, J. Lutz, L. Altenhain, R. Schmid, W. Freude, C. Koos, and S. Randel, “Transmission of 80-GBd 16-QAM over 300  km and Kramers-Kronig reception using a low-complexity FIR Hilbert filter approximation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.3.

Schmidt-Langhorst, C.

I. Sackey, C. Schmidt-Langhorst, R. Emmerich, R. Elschner, T. Kato, T. Tanimura, S. Watanabe, T. Hoshida, and C. Schubert, “Distributed aggregation and reception of a 400-Gb/s net rate superchannel in a single-photodiode 110-GHz Kramers-Kronig receiver,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2018), paper Th4C.7.

Schubert, C.

I. Sackey, C. Schmidt-Langhorst, R. Emmerich, R. Elschner, T. Kato, T. Tanimura, S. Watanabe, T. Hoshida, and C. Schubert, “Distributed aggregation and reception of a 400-Gb/s net rate superchannel in a single-photodiode 110-GHz Kramers-Kronig receiver,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2018), paper Th4C.7.

Schuh, K.

S. T. Le and K. Schuh, “Experimental verification of equalization enhanced phase noise in Kramers-Kronig transmissions,” in Optical Fiber Communication Conference (OFC) (Optical Society of America, 2019), paper Tu2B.2.

Schuster, M.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

M. Schuster, B. Spinnler, C. A. Bunge, and K. Petermann, “Spectrally efficient OFDM-transmission with compatible single-sideband modulation for direct detection,” in 33rd European Conference and Exhibition of Optical Communication (2007).

Seeds, A. J.

L. G. Guerrero, H. Shams, I. Fatadin, M. J. Fice, M. Naftaly, A. J. Seeds, and C. C. Renaud, “Spectrally efficient SSB signals for W-band links enabled by Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Th2A.61.

Shamee, B.

Shams, H.

L. G. Guerrero, H. Shams, I. Fatadin, M. J. Fice, M. Naftaly, A. J. Seeds, and C. C. Renaud, “Spectrally efficient SSB signals for W-band links enabled by Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Th2A.61.

Shi, K.

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Spectrally efficient 168  Gb/s/λ WDM 64-QAM single-sideband Nyquist-subcarrier modulation with Kramers-Kronig direct-detection receivers,” J. Lightwave Technol. 36, 1340–1346 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Digital linearization of direct-detection transceivers for spectrally efficient 100  Gb/s/λ WDM metro networking,” J. Lightwave Technol. 36, 27–36 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “SSBI mitigation and the Kramers-Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35, 1887–1893 (2017).
[Crossref]

Z. Li, M. S. Erkilinç, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Comparison of digital signal-signal beat interference compensation techniques in direct-detection subcarrier modulation systems,” Opt. Express 24, 29176–29189 (2016).
[Crossref]

Z. Li, M. S. Erkilinç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photon. Technol. Lett. 28, 2838–2841 (2016).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Joint optimisation of resampling rate and carrier-to-signal power ratio in direct-detection Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (2017).

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “168  Gb/s direct-detection 64-QAM SSB Nyquist-SCM transmission over 80  km uncompensated SSMF at 4.54  b/s/Hz net ISD using a Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

Z. Li, M. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. Thomsen, P. Bayvel, and R. Killey, “DSP for single-sideband direct-detection systems,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.5.

Z. Li, L. Galdino, T. Xu, M. Erkilinç, K. Shi, E. Sillekens, B. Thomsen, P. Bayvel, and R. Killey, “Performance of digital back-propagation in Kramers-Kronig direct-detection receivers,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.4.

Shieh, W.

Shinada, S.

R. S. Luìs, G. Rademacher, B. J. Puttnam, S. Shinada, H. Furukawa, R. Maruyama, K. Aikawa, and N. Wada, “A coherent Kramers-Kronig receiver for 3-mode few-mode fiber transmission,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.3.

Shtaif, M.

C. Antonelli, A. Mecozzi, and M. Shtaif, “Kramers-Kronig PAM transceiver and two-sided polarization-multiplexed Kramers-Kronig transceiver,” J. Lightwave Technol. 36, 468–475 (2018).
[Crossref]

A. Mecozzi and M. Shtaif, “Coherent detection with an incoherent local oscillator,” Opt. Express 26, 33970–33981 (2018).
[Crossref]

C. Antonelli, A. Mecozzi, M. Shtaif, X. Chen, S. Chandrasekhar, and P. J. Winzer, “Polarization multiplexing with the Kramers-Kronig receiver,” J. Lightwave Technol. 35, 5418–5424 (2017).
[Crossref]

A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers-Kronig coherent receiver,” Optica 3, 1220–1227 (2016).
[Crossref]

M. Presi, G. Cossu, G. Contestabile, E. Ciaramella, C. Antonelli, A. Mecozzi, and M. Shtaif, “Transmission in 125-km SMF with 3.9  bit/s/Hz spectral efficiency using a single-drive MZM and a direct-detection Kramers-Kronig receiver without optical CD compensation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.3.

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, J. Sinsky, A. Mecozzi, M. Shtaif, and P. Winzer, “218-Gb/s single-wavelength, single-polarization, single-photodiode transmission over 125-km of standard singlemode fiber using Kramers-Kronig detection,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2017), paper Th5B.6.

L. Blech, Y. Eldar, C. Antonelli, A. Mecozzi, and M. Shtaif, “The enhanced Kramers Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.7.

X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode Kramers-Kronig detection of 440-gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (IPC) Part II (2017).

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, A. Mecozzi, M. Shtaif, and P. Winzer, “4 × 240  Gb/s dense WDM and PDM Kramers-Kronig detection with 125-km SSMF transmission,” in European Conference on Optical Communication (ECOC) (2017).

Shu, C.

Q. Zhang, B. Zheng, and C. Shu, “Kramers-Kronig detection with Brillouin-amplified virtual carrier,” Opt. Lett. 43, 1367–1370 (2018).
[Crossref]

Y. Tong, Q. Zhang, X. Wu, C.-W. Chow, C. Shu, and H. K. Tsang, “Integrated germanium-on-silicon Franz-Keldysh vector modulator used with a Kramers-Kronig receiver,” Opt. Lett. 43, 4333–4336 (2018).
[Crossref]

Q. Zhang and C. Shu, “Carrier regeneration assisted Kramers-Kronig detection of an independent sideband signal,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2018), paper STu3C.2.

Q. Zhang and C. Shu, “Kramers-Kronig detection of polarization multiplexing signals by a single-ended photodiode,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W2A.55.

Shu, L.

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers-Kronig detection over 80-km SSMF,” IEEE Photon. J. 9, 1–9 (2017).
[Crossref]

L. Shu, J. Li, Z. Wan, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “56-Gb/s single-photodiode 16QAM transmission over 140-km SSMF using Kramers-Kronig detection,” in Asia Communications and Photonics Conference (Optical Society of America, 2017), paper M2B.2.

Sillard, P.

S. van der Heide, J. van Weerdenburg, M. Bigot-Astruc, A. Amezcua-Correa, J. Antonio-Lopez, J. C. Alvarado-Zacarias, H. de Waardt, T. Koonen, P. Sillard, R. Amezcua-Correa, and C. Okonkwo, “Single carrier 1  Tbit/s mode-multiplexed transmission over graded-index 50  μm core multi-mode fiber employing Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Tu1G.3.

Sillekens, E.

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Digital linearization of direct-detection transceivers for spectrally efficient 100  Gb/s/λ WDM metro networking,” J. Lightwave Technol. 36, 27–36 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Spectrally efficient 168  Gb/s/λ WDM 64-QAM single-sideband Nyquist-subcarrier modulation with Kramers-Kronig direct-detection receivers,” J. Lightwave Technol. 36, 1340–1346 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “SSBI mitigation and the Kramers-Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35, 1887–1893 (2017).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Joint optimisation of resampling rate and carrier-to-signal power ratio in direct-detection Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (2017).

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “168  Gb/s direct-detection 64-QAM SSB Nyquist-SCM transmission over 80  km uncompensated SSMF at 4.54  b/s/Hz net ISD using a Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

Z. Li, L. Galdino, T. Xu, M. Erkilinç, K. Shi, E. Sillekens, B. Thomsen, P. Bayvel, and R. Killey, “Performance of digital back-propagation in Kramers-Kronig direct-detection receivers,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.4.

Z. Li, M. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. Thomsen, P. Bayvel, and R. Killey, “DSP for single-sideband direct-detection systems,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.5.

Sinsky, J.

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, J. Sinsky, A. Mecozzi, M. Shtaif, and P. Winzer, “218-Gb/s single-wavelength, single-polarization, single-photodiode transmission over 125-km of standard singlemode fiber using Kramers-Kronig detection,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2017), paper Th5B.6.

Sinsky, J. H.

Song, Y.

M. Zhu, J. Zhang, X. Yi, H. Ying, X. Li, M. Luo, Y. Song, X. Huang, and K. Qiu, “Optical single side-band Nyquist PAM-4 transmission using dual-drive MZM modulation and direct detection,” Opt. Express 26, 6629–6638 (2018).
[Crossref]

M. Zhu, J. Zhang, H. Ying, X. Li, M. Luo, X. Huang, Y. Song, F. Li, X. Yi, and K. Qiu, “56-Gb/s optical SSB PAM-4 transmission over 800-km SSMF using DDMZM transmitter and simplified direct detection Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper M2C.5.

Sowailem, M.

T. Hoang, Q. Zhuge, Z. Xing, M. Sowailem, M. Morsy-Osman, M. Xiang, E. El-Fiky, S. Fan, and D. V. Plant, “Direct detection optical transmission systems employing Stokes vector Kramers-Kronig transceivers,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.2.

Sowailem, M. Y.

S. Fan, Q. Zhuge, M. Y. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, Y. Li, J. Wu, and D. V. Plant, “Single wavelength twin-SSB direct detection system based on Kramers-Kronig receiver and time-interleaved OFDM frame,” Opt. Commun. 425, 133–140 (2018).
[Crossref]

Sowailem, M. Y. S.

T. M. Hoang, M. Y. S. Sowailem, Q. Zhuge, Z. Xing, M. Morsy-Osman, E. El-Fiky, S. Fan, M. Xiang, and D. V. Plant, “Single wavelength 480  Gb/s direct detection over 80  km SSMF enabled by stokes vector Kramers-Kronig transceiver,” Opt. Express 25, 33534–33542 (2017).
[Crossref]

S. Fan, Q. Zhuge, Z. Xing, K. Zhang, T. M. Hoang, M. Morsy-Osman, M. Y. S. Sowailem, Y. Li, J. Wu, and D. V. Plant, “264  Gb/s twin-SSB-KK direct detection transmission enabled by MIMO processing,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.5.

S. Fan, Q. Zhuge, M. Y. S. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, M. Qiu, Y. Li, J. Wu, and D. V. Plant, “Twin-SSB direct detection transmission over 80km SSMF using Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

Spinnler, B.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

M. Schuster, B. Spinnler, C. A. Bunge, and K. Petermann, “Spectrally efficient OFDM-transmission with compatible single-sideband modulation for direct detection,” in 33rd European Conference and Exhibition of Optical Communication (2007).

Tang, M.

Tanimura, T.

I. Sackey, C. Schmidt-Langhorst, R. Emmerich, R. Elschner, T. Kato, T. Tanimura, S. Watanabe, T. Hoshida, and C. Schubert, “Distributed aggregation and reception of a 400-Gb/s net rate superchannel in a single-photodiode 110-GHz Kramers-Kronig receiver,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2018), paper Th4C.7.

Thomsen, B.

Z. Li, M. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. Thomsen, P. Bayvel, and R. Killey, “DSP for single-sideband direct-detection systems,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.5.

Z. Li, L. Galdino, T. Xu, M. Erkilinç, K. Shi, E. Sillekens, B. Thomsen, P. Bayvel, and R. Killey, “Performance of digital back-propagation in Kramers-Kronig direct-detection receivers,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.4.

Thomsen, B. C.

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Digital linearization of direct-detection transceivers for spectrally efficient 100  Gb/s/λ WDM metro networking,” J. Lightwave Technol. 36, 27–36 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Spectrally efficient 168  Gb/s/λ WDM 64-QAM single-sideband Nyquist-subcarrier modulation with Kramers-Kronig direct-detection receivers,” J. Lightwave Technol. 36, 1340–1346 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “SSBI mitigation and the Kramers-Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35, 1887–1893 (2017).
[Crossref]

Z. Li, M. S. Erkilinç, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Comparison of digital signal-signal beat interference compensation techniques in direct-detection subcarrier modulation systems,” Opt. Express 24, 29176–29189 (2016).
[Crossref]

Z. Li, M. S. Erkilinç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photon. Technol. Lett. 28, 2838–2841 (2016).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “168  Gb/s direct-detection 64-QAM SSB Nyquist-SCM transmission over 80  km uncompensated SSMF at 4.54  b/s/Hz net ISD using a Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Joint optimisation of resampling rate and carrier-to-signal power ratio in direct-detection Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (2017).

Tong, Y.

Tsang, H. K.

Ummethala, S.

T. Harter, C. Füllner, J. N. Kemal, S. Ummethala, M. Brosi, E. Bründermann, W. Freude, S. Randel, and C. Koos, “110-m THz wireless transmission at 100  Gbit/s using a Kramers-Kronig Schottky barrier diode receiver,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.7.

van der Heide, S.

S. van der Heide, J. van Weerdenburg, M. Bigot-Astruc, A. Amezcua-Correa, J. Antonio-Lopez, J. C. Alvarado-Zacarias, H. de Waardt, T. Koonen, P. Sillard, R. Amezcua-Correa, and C. Okonkwo, “Single carrier 1  Tbit/s mode-multiplexed transmission over graded-index 50  μm core multi-mode fiber employing Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Tu1G.3.

van Weerdenburg, J.

S. van der Heide, J. van Weerdenburg, M. Bigot-Astruc, A. Amezcua-Correa, J. Antonio-Lopez, J. C. Alvarado-Zacarias, H. de Waardt, T. Koonen, P. Sillard, R. Amezcua-Correa, and C. Okonkwo, “Single carrier 1  Tbit/s mode-multiplexed transmission over graded-index 50  μm core multi-mode fiber employing Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Tu1G.3.

Wada, N.

R. S. Luìs, G. Rademacher, B. J. Puttnam, S. Shinada, H. Furukawa, R. Maruyama, K. Aikawa, and N. Wada, “A coherent Kramers-Kronig receiver for 3-mode few-mode fiber transmission,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.3.

Wan, Z.

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers-Kronig detection over 80-km SSMF,” IEEE Photon. J. 9, 1–9 (2017).
[Crossref]

L. Shu, J. Li, Z. Wan, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “56-Gb/s single-photodiode 16QAM transmission over 140-km SSMF using Kramers-Kronig detection,” in Asia Communications and Photonics Conference (Optical Society of America, 2017), paper M2B.2.

Watanabe, S.

I. Sackey, C. Schmidt-Langhorst, R. Emmerich, R. Elschner, T. Kato, T. Tanimura, S. Watanabe, T. Hoshida, and C. Schubert, “Distributed aggregation and reception of a 400-Gb/s net rate superchannel in a single-photodiode 110-GHz Kramers-Kronig receiver,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2018), paper Th4C.7.

Willner, A. E.

Winzer, P.

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, A. Mecozzi, M. Shtaif, and P. Winzer, “4 × 240  Gb/s dense WDM and PDM Kramers-Kronig detection with 125-km SSMF transmission,” in European Conference on Optical Communication (ECOC) (2017).

X. Chen, S. Chandrasekhar, and P. Winzer, “Frequency-resolved measurements of signal, noise, and signal-signal beat interference in self-coherent direct-detection receivers,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.6.

X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode Kramers-Kronig detection of 440-gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (IPC) Part II (2017).

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s discrete-multitone transmission over 80-km SSMF using single-sideband modulation with novel interference-cancellation scheme,” in European Conference on Optical Communication (ECOC) (2015).

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, J. Sinsky, A. Mecozzi, M. Shtaif, and P. Winzer, “218-Gb/s single-wavelength, single-polarization, single-photodiode transmission over 125-km of standard singlemode fiber using Kramers-Kronig detection,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2017), paper Th5B.6.

X. Chen, S. Chandrasekhar, S. Olsson, A. Adamiecki, and P. Winzer, “Impact of O/E front-end frequency response on Kramers-Kronig receivers and its compensation,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.5.

Winzer, P. J.

Wolf, S.

C. Füllner, S. Wolf, J. N. Kemal, J. Lutz, L. Altenhain, R. Schmid, W. Freude, C. Koos, and S. Randel, “Transmission of 80-GBd 16-QAM over 300  km and Kramers-Kronig reception using a low-complexity FIR Hilbert filter approximation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.3.

Wu, J.

S. Fan, Q. Zhuge, M. Y. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, Y. Li, J. Wu, and D. V. Plant, “Single wavelength twin-SSB direct detection system based on Kramers-Kronig receiver and time-interleaved OFDM frame,” Opt. Commun. 425, 133–140 (2018).
[Crossref]

S. Fan, Q. Zhuge, M. Y. S. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, M. Qiu, Y. Li, J. Wu, and D. V. Plant, “Twin-SSB direct detection transmission over 80km SSMF using Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

S. Fan, Q. Zhuge, Z. Xing, K. Zhang, T. M. Hoang, M. Morsy-Osman, M. Y. S. Sowailem, Y. Li, J. Wu, and D. V. Plant, “264  Gb/s twin-SSB-KK direct detection transmission enabled by MIMO processing,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.5.

Wu, X.

Wu, Z.

Z. Wu, H. Jiang, X. Feng, and S. Gao, “Demonstration of cost-effective single-photodetector coherent receiver for free-space optical communications,” in Asia Communications and Photonics Conference (Optical Society of America, 2017), paper M3G.4.

Xiang, M.

T. M. Hoang, M. Y. S. Sowailem, Q. Zhuge, Z. Xing, M. Morsy-Osman, E. El-Fiky, S. Fan, M. Xiang, and D. V. Plant, “Single wavelength 480  Gb/s direct detection over 80  km SSMF enabled by stokes vector Kramers-Kronig transceiver,” Opt. Express 25, 33534–33542 (2017).
[Crossref]

T. Hoang, Q. Zhuge, Z. Xing, M. Sowailem, M. Morsy-Osman, M. Xiang, E. El-Fiky, S. Fan, and D. V. Plant, “Direct detection optical transmission systems employing Stokes vector Kramers-Kronig transceivers,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.2.

Xing, Z.

T. M. Hoang, M. Y. S. Sowailem, Q. Zhuge, Z. Xing, M. Morsy-Osman, E. El-Fiky, S. Fan, M. Xiang, and D. V. Plant, “Single wavelength 480  Gb/s direct detection over 80  km SSMF enabled by stokes vector Kramers-Kronig transceiver,” Opt. Express 25, 33534–33542 (2017).
[Crossref]

T. Hoang, Q. Zhuge, Z. Xing, M. Sowailem, M. Morsy-Osman, M. Xiang, E. El-Fiky, S. Fan, and D. V. Plant, “Direct detection optical transmission systems employing Stokes vector Kramers-Kronig transceivers,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.2.

S. Fan, Q. Zhuge, Z. Xing, K. Zhang, T. M. Hoang, M. Morsy-Osman, M. Y. S. Sowailem, Y. Li, J. Wu, and D. V. Plant, “264  Gb/s twin-SSB-KK direct detection transmission enabled by MIMO processing,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.5.

Xu, K.

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers-Kronig detection over 80-km SSMF,” IEEE Photon. J. 9, 1–9 (2017).
[Crossref]

L. Shu, J. Li, Z. Wan, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “56-Gb/s single-photodiode 16QAM transmission over 140-km SSMF using Kramers-Kronig detection,” in Asia Communications and Photonics Conference (Optical Society of America, 2017), paper M2B.2.

Xu, T.

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Digital linearization of direct-detection transceivers for spectrally efficient 100  Gb/s/λ WDM metro networking,” J. Lightwave Technol. 36, 27–36 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Spectrally efficient 168  Gb/s/λ WDM 64-QAM single-sideband Nyquist-subcarrier modulation with Kramers-Kronig direct-detection receivers,” J. Lightwave Technol. 36, 1340–1346 (2018).
[Crossref]

Z. Li, L. Galdino, T. Xu, M. Erkilinç, K. Shi, E. Sillekens, B. Thomsen, P. Bayvel, and R. Killey, “Performance of digital back-propagation in Kramers-Kronig direct-detection receivers,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.4.

Z. Li, M. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. Thomsen, P. Bayvel, and R. Killey, “DSP for single-sideband direct-detection systems,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.5.

Xu, X.

T. Zuo, S. Zhang, L. Liu, W. Cheng, and X. Xu, “Single-lane 100  Gb/s 4-PAM transmission over 80  km SSMF based on K-K scheme and integrated 10G TOSA,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.6.

Xu, Z.

Yang, J.-Y.

Yang, Q.

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers-Kronig detection over 80-km SSMF,” IEEE Photon. J. 9, 1–9 (2017).
[Crossref]

Yekani, A.

Yi, X.

M. Zhu, J. Zhang, X. Yi, H. Ying, X. Li, M. Luo, Y. Song, X. Huang, and K. Qiu, “Optical single side-band Nyquist PAM-4 transmission using dual-drive MZM modulation and direct detection,” Opt. Express 26, 6629–6638 (2018).
[Crossref]

M. Zhu, J. Zhang, H. Ying, X. Li, M. Luo, X. Huang, Y. Song, F. Li, X. Yi, and K. Qiu, “56-Gb/s optical SSB PAM-4 transmission over 800-km SSMF using DDMZM transmitter and simplified direct detection Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper M2C.5.

Yin, F.

L. Shu, J. Li, Z. Wan, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “56-Gb/s single-photodiode 16QAM transmission over 140-km SSMF using Kramers-Kronig detection,” in Asia Communications and Photonics Conference (Optical Society of America, 2017), paper M2B.2.

Ying, H.

M. Zhu, J. Zhang, X. Yi, H. Ying, X. Li, M. Luo, Y. Song, X. Huang, and K. Qiu, “Optical single side-band Nyquist PAM-4 transmission using dual-drive MZM modulation and direct detection,” Opt. Express 26, 6629–6638 (2018).
[Crossref]

M. Zhu, J. Zhang, H. Ying, X. Li, M. Luo, X. Huang, Y. Song, F. Li, X. Yi, and K. Qiu, “56-Gb/s optical SSB PAM-4 transmission over 800-km SSMF using DDMZM transmitter and simplified direct detection Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper M2C.5.

You, Q.

C. Li, M. Luo, Q. You, and X. Li, “114-Gb/s PDM-DMT transmission over 100-km SSMF with high phase noise tolerance using Kramers-Kronig detection and digital carrier regeneration,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.4.

Yu, Q.

Zhang, F.

Y. Zhu, M. Jiang, and F. Zhang, “Direct detection of polarization multiplexed single sideband signals with orthogonal offset carriers,” Opt. Express 26, 15887–15898 (2018).
[Crossref]

Y. Zhu, M. Jiang, X. Ruan, Z. Chen, C. Li, and F. Zhang, “6.4  Tb/s (32 × 200  Gb/s) WDM direct-detection transmission with twin-SSB modulation and Kramers-Kronig receiver,” Opt. Commun. 415, 64–69 (2018).
[Crossref]

S. Fan, Q. Zhuge, M. Y. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, Y. Li, J. Wu, and D. V. Plant, “Single wavelength twin-SSB direct detection system based on Kramers-Kronig receiver and time-interleaved OFDM frame,” Opt. Commun. 425, 133–140 (2018).
[Crossref]

Y. Zhu, K. Zou, X. Ruan, and F. Zhang, “Single carrier 400G transmission with single-ended heterodyne detection,” IEEE Photon. Technol. Lett. 29, 1788–1791 (2017).
[Crossref]

K. Zou, Y. Zhu, F. Zhang, and Z. Chen, “Spectrally efficient terabit optical transmission with Nyquist 64-QAM half-cycle subcarrier modulation and direct detection,” Opt. Lett. 41, 2767–2770 (2016).
[Crossref]

Y. Zhu, M. Jiang, X. Ruan, C. Li, and F. Zhang, “16×112  Gb/s single-sideband PAM4 WDM transmission over 80km SSMF with Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.2.

S. Fan, Q. Zhuge, M. Y. S. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, M. Qiu, Y. Li, J. Wu, and D. V. Plant, “Twin-SSB direct detection transmission over 80km SSMF using Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

Zhang, J.

M. Zhu, J. Zhang, X. Yi, H. Ying, X. Li, M. Luo, Y. Song, X. Huang, and K. Qiu, “Optical single side-band Nyquist PAM-4 transmission using dual-drive MZM modulation and direct detection,” Opt. Express 26, 6629–6638 (2018).
[Crossref]

M. Zhu, J. Zhang, H. Ying, X. Li, M. Luo, X. Huang, Y. Song, F. Li, X. Yi, and K. Qiu, “56-Gb/s optical SSB PAM-4 transmission over 800-km SSMF using DDMZM transmitter and simplified direct detection Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper M2C.5.

Zhang, K.

S. Fan, Q. Zhuge, Z. Xing, K. Zhang, T. M. Hoang, M. Morsy-Osman, M. Y. S. Sowailem, Y. Li, J. Wu, and D. V. Plant, “264  Gb/s twin-SSB-KK direct detection transmission enabled by MIMO processing,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.5.

Zhang, M.

Zhang, Q.

Y. Tong, Q. Zhang, X. Wu, C.-W. Chow, C. Shu, and H. K. Tsang, “Integrated germanium-on-silicon Franz-Keldysh vector modulator used with a Kramers-Kronig receiver,” Opt. Lett. 43, 4333–4336 (2018).
[Crossref]

Q. Zhang, B. Zheng, and C. Shu, “Kramers-Kronig detection with Brillouin-amplified virtual carrier,” Opt. Lett. 43, 1367–1370 (2018).
[Crossref]

Q. Zhang and C. Shu, “Kramers-Kronig detection of polarization multiplexing signals by a single-ended photodiode,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W2A.55.

Q. Zhang and C. Shu, “Carrier regeneration assisted Kramers-Kronig detection of an independent sideband signal,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2018), paper STu3C.2.

Zhang, S.

T. Zuo, S. Zhang, L. Liu, W. Cheng, and X. Xu, “Single-lane 100  Gb/s 4-PAM transmission over 80  km SSMF based on K-K scheme and integrated 10G TOSA,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.6.

Zhang, Y.

Zheng, B.

Zhou, Y.

L. Shu, J. Li, Z. Wan, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “56-Gb/s single-photodiode 16QAM transmission over 140-km SSMF using Kramers-Kronig detection,” in Asia Communications and Photonics Conference (Optical Society of America, 2017), paper M2B.2.

Zhu, M.

M. Zhu, J. Zhang, X. Yi, H. Ying, X. Li, M. Luo, Y. Song, X. Huang, and K. Qiu, “Optical single side-band Nyquist PAM-4 transmission using dual-drive MZM modulation and direct detection,” Opt. Express 26, 6629–6638 (2018).
[Crossref]

M. Zhu, J. Zhang, H. Ying, X. Li, M. Luo, X. Huang, Y. Song, F. Li, X. Yi, and K. Qiu, “56-Gb/s optical SSB PAM-4 transmission over 800-km SSMF using DDMZM transmitter and simplified direct detection Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper M2C.5.

Zhu, Y.

Y. Zhu, M. Jiang, X. Ruan, Z. Chen, C. Li, and F. Zhang, “6.4  Tb/s (32 × 200  Gb/s) WDM direct-detection transmission with twin-SSB modulation and Kramers-Kronig receiver,” Opt. Commun. 415, 64–69 (2018).
[Crossref]

Y. Zhu, M. Jiang, and F. Zhang, “Direct detection of polarization multiplexed single sideband signals with orthogonal offset carriers,” Opt. Express 26, 15887–15898 (2018).
[Crossref]

Y. Zhu, K. Zou, X. Ruan, and F. Zhang, “Single carrier 400G transmission with single-ended heterodyne detection,” IEEE Photon. Technol. Lett. 29, 1788–1791 (2017).
[Crossref]

K. Zou, Y. Zhu, F. Zhang, and Z. Chen, “Spectrally efficient terabit optical transmission with Nyquist 64-QAM half-cycle subcarrier modulation and direct detection,” Opt. Lett. 41, 2767–2770 (2016).
[Crossref]

Y. Zhu, M. Jiang, X. Ruan, C. Li, and F. Zhang, “16×112  Gb/s single-sideband PAM4 WDM transmission over 80km SSMF with Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.2.

Zhuge, Q.

S. Fan, Q. Zhuge, M. Y. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, Y. Li, J. Wu, and D. V. Plant, “Single wavelength twin-SSB direct detection system based on Kramers-Kronig receiver and time-interleaved OFDM frame,” Opt. Commun. 425, 133–140 (2018).
[Crossref]

T. M. Hoang, M. Y. S. Sowailem, Q. Zhuge, Z. Xing, M. Morsy-Osman, E. El-Fiky, S. Fan, M. Xiang, and D. V. Plant, “Single wavelength 480  Gb/s direct detection over 80  km SSMF enabled by stokes vector Kramers-Kronig transceiver,” Opt. Express 25, 33534–33542 (2017).
[Crossref]

T. Hoang, Q. Zhuge, Z. Xing, M. Sowailem, M. Morsy-Osman, M. Xiang, E. El-Fiky, S. Fan, and D. V. Plant, “Direct detection optical transmission systems employing Stokes vector Kramers-Kronig transceivers,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.2.

S. Fan, Q. Zhuge, Z. Xing, K. Zhang, T. M. Hoang, M. Morsy-Osman, M. Y. S. Sowailem, Y. Li, J. Wu, and D. V. Plant, “264  Gb/s twin-SSB-KK direct detection transmission enabled by MIMO processing,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.5.

S. Fan, Q. Zhuge, M. Y. S. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, M. Qiu, Y. Li, J. Wu, and D. V. Plant, “Twin-SSB direct detection transmission over 80km SSMF using Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

Zou, K.

Y. Zhu, K. Zou, X. Ruan, and F. Zhang, “Single carrier 400G transmission with single-ended heterodyne detection,” IEEE Photon. Technol. Lett. 29, 1788–1791 (2017).
[Crossref]

K. Zou, Y. Zhu, F. Zhang, and Z. Chen, “Spectrally efficient terabit optical transmission with Nyquist 64-QAM half-cycle subcarrier modulation and direct detection,” Opt. Lett. 41, 2767–2770 (2016).
[Crossref]

Zuo, T.

T. Zuo, S. Zhang, L. Liu, W. Cheng, and X. Xu, “Single-lane 100  Gb/s 4-PAM transmission over 80  km SSMF based on K-K scheme and integrated 10G TOSA,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.6.

Adv. Opt. Photon. (1)

Am. Math. Monthly (1)

P. Duren, W. Hengartner, and R. S. Laugesen, “The argument principle for harmonic functions,” Am. Math. Monthly 103(5), 411–415 (1996).
[Crossref]

IEEE Photon. J. (1)

L. Shu, J. Li, Z. Wan, F. Gao, S. Fu, X. Li, Q. Yang, and K. Xu, “Single-lane 112-Gbit/s SSB-PAM4 transmission with dual-drive MZM and Kramers-Kronig detection over 80-km SSMF,” IEEE Photon. J. 9, 1–9 (2017).
[Crossref]

IEEE Photon. Technol. Lett. (3)

Z. Li, M. S. Erkilinç, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photon. Technol. Lett. 28, 2838–2841 (2016).
[Crossref]

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008).
[Crossref]

Y. Zhu, K. Zou, X. Ruan, and F. Zhang, “Single carrier 400G transmission with single-ended heterodyne detection,” IEEE Photon. Technol. Lett. 29, 1788–1791 (2017).
[Crossref]

J. Lightwave Technol. (7)

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Digital linearization of direct-detection transceivers for spectrally efficient 100  Gb/s/λ WDM metro networking,” J. Lightwave Technol. 36, 27–36 (2018).
[Crossref]

C. Antonelli, A. Mecozzi, M. Shtaif, X. Chen, S. Chandrasekhar, and P. J. Winzer, “Polarization multiplexing with the Kramers-Kronig receiver,” J. Lightwave Technol. 35, 5418–5424 (2017).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Spectrally efficient 168  Gb/s/λ WDM 64-QAM single-sideband Nyquist-subcarrier modulation with Kramers-Kronig direct-detection receivers,” J. Lightwave Technol. 36, 1340–1346 (2018).
[Crossref]

A. Yekani, S. Amiralizadeh, and L. A. Rusch, “Analytical study of optical SSB-DMT with IMDD,” J. Lightwave Technol. 36, 666–674 (2018).
[Crossref]

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “SSBI mitigation and the Kramers-Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35, 1887–1893 (2017).
[Crossref]

C. Antonelli, A. Mecozzi, and M. Shtaif, “Kramers-Kronig PAM transceiver and two-sided polarization-multiplexed Kramers-Kronig transceiver,” J. Lightwave Technol. 36, 468–475 (2018).
[Crossref]

F. Derr, “Coherent optical QPSK intradyne system: concept and digital receiver realization,” J. Lightwave Technol. 10, 1290–1296 (1992).
[Crossref]

Opt. Commun. (2)

Y. Zhu, M. Jiang, X. Ruan, Z. Chen, C. Li, and F. Zhang, “6.4  Tb/s (32 × 200  Gb/s) WDM direct-detection transmission with twin-SSB modulation and Kramers-Kronig receiver,” Opt. Commun. 415, 64–69 (2018).
[Crossref]

S. Fan, Q. Zhuge, M. Y. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, Y. Li, J. Wu, and D. V. Plant, “Single wavelength twin-SSB direct detection system based on Kramers-Kronig receiver and time-interleaved OFDM frame,” Opt. Commun. 425, 133–140 (2018).
[Crossref]

Opt. Express (12)

M. Zhu, J. Zhang, X. Yi, H. Ying, X. Li, M. Luo, Y. Song, X. Huang, and K. Qiu, “Optical single side-band Nyquist PAM-4 transmission using dual-drive MZM modulation and direct detection,” Opt. Express 26, 6629–6638 (2018).
[Crossref]

P. Dong, X. Chen, K. Kim, S. Chandrasekhar, Y.-K. Chen, and J. H. Sinsky, “128-Gb/s 100-km transmission with direct detection using silicon photonic Stokes vector receiver and I/Q modulator,” Opt. Express 24, 14208–14214 (2016).
[Crossref]

T. M. Hoang, M. Y. S. Sowailem, Q. Zhuge, Z. Xing, M. Morsy-Osman, E. El-Fiky, S. Fan, M. Xiang, and D. V. Plant, “Single wavelength 480  Gb/s direct detection over 80  km SSMF enabled by stokes vector Kramers-Kronig transceiver,” Opt. Express 25, 33534–33542 (2017).
[Crossref]

Y. Zhu, M. Jiang, and F. Zhang, “Direct detection of polarization multiplexed single sideband signals with orthogonal offset carriers,” Opt. Express 26, 15887–15898 (2018).
[Crossref]

W. Shieh and K.-P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16, 15718–15727 (2008).
[Crossref]

A. J. Lowery and J. Armstrong, “Orthogonal-frequency-division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express 14, 2079–2084 (2006).
[Crossref]

A. Mecozzi and M. Shtaif, “Coherent detection with an incoherent local oscillator,” Opt. Express 26, 33970–33981 (2018).
[Crossref]

W.-R. Peng, X. Wu, K.-M. Feng, V. R. Arbab, B. Shamee, J.-Y. Yang, L. C. Christen, A. E. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission employing an iterative estimation and cancellation technique,” Opt. Express 17, 9099–9111 (2009).
[Crossref]

Z. Li, M. S. Erkilinç, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Comparison of digital signal-signal beat interference compensation techniques in direct-detection subcarrier modulation systems,” Opt. Express 24, 29176–29189 (2016).
[Crossref]

T. Bo and H. Kim, “Kramers-Kronig receiver operable without digital upsampling,” Opt. Express 26, 13810–13818 (2018).
[Crossref]

Y. Zhang, M. O’Sullivan, and R. Hui, “Theoretical and experimental investigation of compatible SSB modulation for single channel long-distance optical OFDM transmission,” Opt. Express 18, 16751–16764 (2010).
[Crossref]

D. Li, Q. Yu, L. Deng, L. Huo, S. Fu, M. Tang, M. Cheng, M. Zhang, and D. Liu, “Bidirectional long-reach PON using Kramers-Kronig-based receiver for Rayleigh backscattering noise and SSBI interference elimination,” Opt. Express 26, 19020–19036 (2018).
[Crossref]

Opt. Lett. (4)

Optica (1)

Proc. IRE (1)

L. R. Kahn, “Compatible single sideband,” Proc. IRE 49, 1503–1527 (1961).
[Crossref]

Other (51)

Note that this equation implies Faa(−M)=0.

We use the definition of the DFT where the factor 1/(2M) is placed in the definition of the DFT instead of the inverse DFT. This choice slightly simplifies the derivation and the final result. It is also interesting to note that, with Iaa(t) periodic with period T, Eq. (37) is the numerical approximation by the trapezoidal rule, with M+1 points and integration step T/(2M), of the integral at right-hand side of Eq. (34).

T. Bo and H. Kim, “Kramers-Kronig receiver without digital upsampling,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.2.

The difference with respect to Eq. (44) is that here the inverse DFT of the coefficients La,DFT(k,1) returns the waveform a(t) sampled at rate 2B, whereas the inverse DFT of those given by Eq. (44) returns a(t) sampled at rate B.

The positivity of I(t) is required for every t∈[0,T), and it is not sufficient that only the 2M samples are positive. In practice, the validity of the condition I(t)>0 should be checked after sufficient oversampling.

This is because (a) the reality of I(t) implies the condition ZI(Z)=[ZI(1/Z*)]* and hence, if Zk is a zero of ZI(Z), also 1/Zk* must be a zero, and (b) the condition that I(t) is always positive implies that there is no zero Zk¯ for which Zk¯=1/Zk¯* (they would be on the unit circle and correspond to real zeros of I(t)), and hence each of the 2(M−1) zeros of ZI(Z) must have its distinct inverse conjugate counterpart.

If I(t) changes sign, Eq. (57) cannot be derived from the condition ZI(Z)=[ZI(1/Z*)]*. Assume I(t)=2 cos(Ωt). We have ZI(Z)=−i(Z+i)(1/Z+i), which does not have the form of Eq. (57) because both zeros (which correspond to the two real zeros of the cosine) are on the unit circle. In this case, each one of the two zeros coincides with its complex conjugate, so that ZI(Z)=[ZI(1/Z*)]* automatically holds.

X. Chen, S. Chandrasekhar, S. Olsson, A. Adamiecki, and P. Winzer, “Impact of O/E front-end frequency response on Kramers-Kronig receivers and its compensation,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.5.

M. Schuster, B. Spinnler, C. A. Bunge, and K. Petermann, “Spectrally efficient OFDM-transmission with compatible single-sideband modulation for direct detection,” in 33rd European Conference and Exhibition of Optical Communication (2007).

In this section we will proceed with the convention that the spectrum vanishes below the cutoff frequency.

Of course, if the trajectory of a(t) encircles the origin, the component in phase with the carrier drops below zero, but there are instances where the signal does not encircle the origin although the component in-phase with the carrier drops below zero, but these are unlikely.

L. G. Guerrero, H. Shams, I. Fatadin, M. J. Fice, M. Naftaly, A. J. Seeds, and C. C. Renaud, “Spectrally efficient SSB signals for W-band links enabled by Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Th2A.61.

S. T. Le and K. Schuh, “Experimental verification of equalization enhanced phase noise in Kramers-Kronig transmissions,” in Optical Fiber Communication Conference (OFC) (Optical Society of America, 2019), paper Tu2B.2.

A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers-Kronig receivers: supplementary material,” figshare (2019), https://doi.org/10.6084/m9.figshare.7982966 .

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing, 2nd ed. (Prentice Hall, 1999).

We used in Eq. (15) that ln(S)=ln|S|+i arg(S) and that ∮Za(C)d log|S|=0.

Zeros on the unit circle can always be considered the limit case of zeros outside the unit circle.

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Joint optimisation of resampling rate and carrier-to-signal power ratio in direct-detection Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (2017).

L. Blech, Y. Eldar, C. Antonelli, A. Mecozzi, and M. Shtaif, “The enhanced Kramers Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.7.

Various flavors of these iterative methods have been proposed, including that reported in Appendix B of [4]. The method reported here is the simplest but, in general, not the most efficient, and it is used only for the purpose of discussion.

S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s discrete-multitone transmission over 80-km SSMF using single-sideband modulation with novel interference-cancellation scheme,” in European Conference on Optical Communication (ECOC) (2015).

A simple example is when the first root Za,1 is replaced by 1/Za,1* and A is replaced by A/Za,1*. The effect of this transformation on Eqs. (6) and (7) is Za˜(Z)=A/Za,1*(−1/Za,1*)∏k=2M−1(−Za,k)(Z−1Za,1*)∏k=2M−1(Z−Za,k), and Za˜*(Z)=A*/Za,1ZM−1(Z−Za,1)∏k=2M−1(Z−1Za,k*). It is easy to check that ZIaa(Z)=Za˜(Z)Za˜*(Z), showing that the intensity remains unchanged.

T. Hoang, Q. Zhuge, Z. Xing, M. Sowailem, M. Morsy-Osman, M. Xiang, E. El-Fiky, S. Fan, and D. V. Plant, “Direct detection optical transmission systems employing Stokes vector Kramers-Kronig transceivers,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.2.

M. Zhu, J. Zhang, H. Ying, X. Li, M. Luo, X. Huang, Y. Song, F. Li, X. Yi, and K. Qiu, “56-Gb/s optical SSB PAM-4 transmission over 800-km SSMF using DDMZM transmitter and simplified direct detection Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper M2C.5.

S. Fan, Q. Zhuge, M. Y. S. Sowailem, M. Morsy-Osman, T. M. Hoang, F. Zhang, M. Qiu, Y. Li, J. Wu, and D. V. Plant, “Twin-SSB direct detection transmission over 80km SSMF using Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

S. Fan, Q. Zhuge, Z. Xing, K. Zhang, T. M. Hoang, M. Morsy-Osman, M. Y. S. Sowailem, Y. Li, J. Wu, and D. V. Plant, “264  Gb/s twin-SSB-KK direct detection transmission enabled by MIMO processing,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.5.

M. Presi, G. Cossu, G. Contestabile, E. Ciaramella, C. Antonelli, A. Mecozzi, and M. Shtaif, “Transmission in 125-km SMF with 3.9  bit/s/Hz spectral efficiency using a single-drive MZM and a direct-detection Kramers-Kronig receiver without optical CD compensation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.3.

Y. Zhu, M. Jiang, X. Ruan, C. Li, and F. Zhang, “16×112  Gb/s single-sideband PAM4 WDM transmission over 80km SSMF with Kramers-Kronig receiver,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.2.

Z. Wu, H. Jiang, X. Feng, and S. Gao, “Demonstration of cost-effective single-photodetector coherent receiver for free-space optical communications,” in Asia Communications and Photonics Conference (Optical Society of America, 2017), paper M3G.4.

T. Zuo, S. Zhang, L. Liu, W. Cheng, and X. Xu, “Single-lane 100  Gb/s 4-PAM transmission over 80  km SSMF based on K-K scheme and integrated 10G TOSA,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.6.

S. van der Heide, J. van Weerdenburg, M. Bigot-Astruc, A. Amezcua-Correa, J. Antonio-Lopez, J. C. Alvarado-Zacarias, H. de Waardt, T. Koonen, P. Sillard, R. Amezcua-Correa, and C. Okonkwo, “Single carrier 1  Tbit/s mode-multiplexed transmission over graded-index 50  μm core multi-mode fiber employing Kramers-Kronig receivers,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Tu1G.3.

S. Ohlendorf, R. Joy, S. Pachnicke, and W. Rosenkranz, “Flexible PAM in DWDM transmission with Kramers-Kronig DSP,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.6.

C. Li, M. Luo, Q. You, and X. Li, “114-Gb/s PDM-DMT transmission over 100-km SSMF with high phase noise tolerance using Kramers-Kronig detection and digital carrier regeneration,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.4.

R. S. Luìs, G. Rademacher, B. J. Puttnam, S. Shinada, H. Furukawa, R. Maruyama, K. Aikawa, and N. Wada, “A coherent Kramers-Kronig receiver for 3-mode few-mode fiber transmission,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper Mo3F.3.

D. Kong, E. P. da Silva, Y. Sasaki, K. Aikawa, F. D. Ros, M. Galili, T. Morioka, L. K. Oxenløwe, and H. Hu, “Kramers-Kronig detection with adaptive rates for 909.5  Tbit/s dense SDM and WDM data channels,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.5.

Q. Zhang and C. Shu, “Carrier regeneration assisted Kramers-Kronig detection of an independent sideband signal,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2018), paper STu3C.2.

Q. Zhang and C. Shu, “Kramers-Kronig detection of polarization multiplexing signals by a single-ended photodiode,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W2A.55.

After the two orthogonal polarization components are detected independently, they are jointly processed digitally so as to deal with a possible polarization rotation as well as other polarization distortions caused by the fiber-optic channel.

In order to see that, note that there is no way to avoid the possibility that one of the polarization eigenstates of the beam splitter is orthogonal to the polarization of the overall CW tone.

Z. Li, M. Erkilinç, K. Shi, E. Sillekens, L. Galdino, T. Xu, B. Thomsen, P. Bayvel, and R. Killey, “DSP for single-sideband direct-detection systems,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpM2G.5.

Z. Li, L. Galdino, T. Xu, M. Erkilinç, K. Shi, E. Sillekens, B. Thomsen, P. Bayvel, and R. Killey, “Performance of digital back-propagation in Kramers-Kronig direct-detection receivers,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper Tu2D.4.

Z. Li, M. S. Erkilinç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “168  Gb/s direct-detection 64-QAM SSB Nyquist-SCM transmission over 80  km uncompensated SSMF at 4.54  b/s/Hz net ISD using a Kramers-Kronig receiver,” in European Conference on Optical Communication (ECOC) (2017).

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, J. Sinsky, A. Mecozzi, M. Shtaif, and P. Winzer, “218-Gb/s single-wavelength, single-polarization, single-photodiode transmission over 125-km of standard singlemode fiber using Kramers-Kronig detection,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2017), paper Th5B.6.

X. Chen, S. Chandrasekhar, and P. Winzer, “Frequency-resolved measurements of signal, noise, and signal-signal beat interference in self-coherent direct-detection receivers,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.6.

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, A. Mecozzi, M. Shtaif, and P. Winzer, “4 × 240  Gb/s dense WDM and PDM Kramers-Kronig detection with 125-km SSMF transmission,” in European Conference on Optical Communication (ECOC) (2017).

X. Chen, J. Cho, S. Chandrasekhar, P. Winzer, C. Antonelli, A. Mecozzi, and M. Shtaif, “Single-wavelength, single-polarization, single-photodiode Kramers-Kronig detection of 440-gb/s entropy-loaded discrete multitone modulation transmitted over 100-km SSMF,” in IEEE Photonics Conference (IPC) Part II (2017).

R. Rios-Muller, J. Estaran, J. Renaudier, and G. Charlet, “Dual polarization in-phase and quadrature high speed submarine transmission with only two photodiodes, ADCs, MZMs and DACs,” in IEEE Photonics Conference (IPC) Part II (2017).

I. Sackey, C. Schmidt-Langhorst, R. Emmerich, R. Elschner, T. Kato, T. Tanimura, S. Watanabe, T. Hoshida, and C. Schubert, “Distributed aggregation and reception of a 400-Gb/s net rate superchannel in a single-photodiode 110-GHz Kramers-Kronig receiver,” in Optical Fiber Communication Conference Postdeadline Papers (Optical Society of America, 2018), paper Th4C.7.

C. Füllner, S. Wolf, J. N. Kemal, J. Lutz, L. Altenhain, R. Schmid, W. Freude, C. Koos, and S. Randel, “Transmission of 80-GBd 16-QAM over 300  km and Kramers-Kronig reception using a low-complexity FIR Hilbert filter approximation,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper W4E.3.

T. Harter, C. Füllner, J. N. Kemal, S. Ummethala, M. Brosi, E. Bründermann, W. Freude, S. Randel, and C. Koos, “110-m THz wireless transmission at 100  Gbit/s using a Kramers-Kronig Schottky barrier diode receiver,” in European Conference on Optical Communication (ECOC) (IEEE, 2018), paper pdpTh3F.7.

L. Shu, J. Li, Z. Wan, Y. Fan, F. Yin, Y. Zhou, Y. Dai, and K. Xu, “56-Gb/s single-photodiode 16QAM transmission over 140-km SSMF using Kramers-Kronig detection,” in Asia Communications and Photonics Conference (Optical Society of America, 2017), paper M2B.2.

Supplementary Material (1)

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» Code 1       MatLab code used to generate Figs. 2-6 and 8-13 of this paper.

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Figures (13)

Figure 1.
Figure 1. Schematic description of the heterodyne schemes: (a) single-ended photodiode, with intense LO; (b) single-ended photodiode, with spectral gap between signal and LO; (c) balanced heterodyne scheme.
Figure 2.
Figure 2. Spectra (amplitude of the Fourier transform) of the data-carrying signal 2ARe[as(t)] (blue) and of the SSBN |as(t)|2 (red). In the right panel. the data-carrying signal includes a gap between zero and B/2.
Figure 3.
Figure 3. Zeros of a minimum-phase sequence of M=64 independent and identically distributed Gaussian samples with ξ=100. The dashed curve is a circle of radius ρ=1.0647, obtained using Eq. (9).
Figure 4.
Figure 4. Zeros of the original sequence (red circles) and of the minimum-phase sequence (blue crosses) of M=64 independent and identically distributed Gaussian samples with ξ=5. The dashed circle of radius ρ, defined by Eq. (9), is the geometric mean of the amplitudes of all zeros.
Figure 5.
Figure 5. Representation in the complex plane of the waveform a(t) whose zeros are reported in Fig. 4. Solid blue line, actual waveform; dashed red line, waveform reconstructed from its intensity using Eq. (32). The circles represent the sample points.
Figure 6.
Figure 6. In the left (right) panel, representation of the real (imaginary) part of the complex waveform a(t). Dashed red line: real (imaginary) part of the waveform a(t) reconstructed from the intensity using Eq. (32).
Figure 7.
Figure 7. Schematic representation of the modulus of the DFT of logIaa(t) (top) and of loga(t) (bottom) with Iaa(t)=|a(t)|2 and with a(t) being periodic with period T and sampled at sample rate 2M/T (no up-sampling is assumed). The samples of the function a(t) at rate 2M/T are obtained by the inverse DFT of the sum of the curves whose modulus is represented by the thick red curves of the bottom figure, restricted to the frequency range shaded in yellow (M/T,M/T]. This is equivalent to (but more computationally efficient than) down-sampling the outcome of the inverse DFT of an up-sampled spectrum of loga(t). The samples of the function a(t) at rate M/T, as discussed in the text, are obtained similarly, by inverse DFT of the sum of replicas periodic in frequency by M/T instead of 2M/T.
Figure 8.
Figure 8. Representation in the complex plane of the waveform a(t) with ξ=5 and M=64 independent and identically distributed Gaussian samples. Circles: sample points. Solid blue line: waveform a(t) sampled with one sample per symbol. Dashed red line: waveform a(t) reconstructed using Eq. (32), in which the inverse DFT is performed with one sample per symbol (hence using a sequence of length M=64).
Figure 9.
Figure 9. Representation with two samples per symbol of the complex waveform a(t) with CSPR ξ=13, and M=64 independent and identically distributed Gaussian samples. Solid blue line: waveform a(t). Dashed red line: waveform a(t) reconstructed using the KK algorithm without oversampling, using a correction of the phase noise error and renormalized to the measured intensity. Circles: sample points.
Figure 10.
Figure 10. In the left (right) panel, a representation of the real (imaginary) part of the complex waveform for the curves of Fig. 9. Solid blue line: real (imaginary) part of the waveform a(t). Dashed red line: real (imaginary) part of the waveform a(t) reconstructed using the KK algorithm without oversampling, using a correction of the phase noise error and renormalized to the measured intensity. Circles: sample points.
Figure 11.
Figure 11. Representation with two samples per symbol of the complex waveform a(t) with CSPR ξ=13 and with M=64 independent and identically distributed Gaussian samples. Circles: sample points. Solid blue line: waveform a(t). Dashed red line: waveform a(t) reconstructed using the KK algorithm without oversampling and with no corrections.
Figure 12.
Figure 12. Representation with two samples per symbol of the complex waveform a(t) with CSPR ξ=13 and with M=64 independent and identically distributed Gaussian samples. Circles: sample points. Solid blue line: waveform a(t). Dashed red line: waveform a(t) reconstructed by a conventional decoding of a self-heterodyne signal and with no corrections for the SSBN term.
Figure 13.
Figure 13. In the left (right) panel, the solid blue line represents the real (imaginary) part of the signal as(t) with CSPR ξ=10. The dashed red line represents the real (imaginary) part of the reconstructed and rescaled waveform as(t) for an error ϵ=0.1. Circles are the sample points.

Equations (72)

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E(t)=Real{a(t)eiω0t},
|a(t)|2=2AReal{as(t)}+|as(t)|2+A2.
a(t)=k=0M1Fa(k)eikΩt,
Fa(k)=1T0Ta(t)eikΩtdt,k=0,,M1.
Za(Z)=k=0M1Fa(k)Zk,
Za(Z)=Ak=1M1(Za,k)k=1M1(ZZa,k).
Za*(Z)=[k=0M1Fa(k)(1Z*)k]*=[Za(1/Z*)]*=A*ZM1k=1M1(Z1Za,k*).
Fa(M1)=Ak=1M1(Za,k),
ρ=(k=1M1|Za,k|)1/(M1)=|AFa(M1)|1/(M1).
ξ=|A|2Ps,
Ps=k=1M1|Fa(k)|2
Za(Z)=A+k=1M1Fa(k)Zk,
Za,keiϕ0|AFa(M1)|1/(M1)e2πik/(M1)=ρei(ϕ0+2πkM1),k=1,,M1,
W=12πiC1Za(Z)dZa(Z)dZdZ=NP,
W=12πiCdlog[Za(Z)]dZdZ=12πiZa(C)dlog(S)=12πZa(C)darg(S),
ϕ(t)=p.v.0Tlog(|a(t)|)π(tt)dt,
log(a(t))=k=La(k)eikΩt,
La(k)=1T0Tlog(a(t))eikΩtdt.
La(k)=i2πCuZk1log(Za(Z))dZ,
La(k)=0,k<0.
log(a(t))=12log(|a(t)|2)+iϕ(t),
La(k)=La(r)(k)+iLa(i)(k),
La(r)(k)=1T0T12log(|a(t)|2)eikΩtdt,
La(i)(k)=1T0Tϕ(t)eikΩtdt.
iLa(i)(k)=sign(k)La(r)(k),
ϕ(t)=p.v.1T0Tcot[π(tt)T]log(|a(t)|)dt.
ϕ(t)=iS(t)*log(|a(t)|),
S(t)=k=+sign(k)exp(ikΩt).
sign(k)sign(k1)=δk,0+δk,1.
[1exp(iΩt)]S(t)=1+exp(iΩt).
S(t)=icot(πtT).
a(t)=exp[k=eikΩtLa(k)]=exp[La(r)(0)+2k=1eikΩtLa(r)(k)],
2AReal{as(t)}=|a(t)|2A2|as(t)|2.
La(r)(k)=1T0T12log[Iaa(t)]eikΩtdt,
Iaa(t)=|a(t)|2=k=MM1Faa(k)eikΩt,
Faa(k)=h=kM1Fa(k+h)Fa*(h),k=M,,M1,
La,DFT(r)(k,1)=12Mh=02M112log[Iaa(hT2M)]ei2πkh2M,
La,DFT(r)(k,1)=12M0Th=δ(tT2Mh)12log[Iaa(t)]eikΩtdt.
n=ei2MnΩt=T2Mh=δ(tT2Mh),
La,DFT(r)(k,1)=n=1T0T12log[Iaa(t)]ei(k2Mn)Ωtdt.
La,DFT(r)(k,1)=n=La(r)(k2Mn),k=M,,M1,
La(r)(k,no)=1T0T12log[k=noMnoM1Faa(k)eikΩt]eikΩtdtk=noM,,noM1,
La,DFT(r)(k,no)=n=La(r)(k2noMn),k=noM,,noM1,
La,DFT(k,1/2)=n=La(kMn)=n=02noLa(k+Mn),k=0,,M1,
La,DFT(k,1)=n=0La(k+2Mn),k=M,,M1,
La,DFT(k,1)=n=0[1+sign(k+2Mn)]La(r)(k+2Mn),k=M,,M1.
a(th)=exp[k=MM1eikΩthLa,DFT(k,1)].
La,DFT(k,1)=[1+sign(k)]La,DFT(r)(k,1),
La,DFT(k,1)=[1+sign(k)]n=La(r)(k+2Mn).
a(th)=exp[k=MM1eikΩthLa,DFT(k,1)],
a(t)=a(t)Φ(t),
Φ(t)=exp[iΔφerr(t)]
Δφerr(t)=k=M+1M1eikΩtLΔφ(k),
LΔφ(k)=i[L(k)*L(k)]
L(k)=[1+sign(k)]n=1La(r)(k2Mn),
ADFT(k)=[ADFT(k)+ADFT*(k)]uH(k),
ZI(Z)=Kk=1M(ZZk)(1/ZZk*),
Za(Z)=Kak=1M(ZZa,k),
Faa(0)=|A|2+h=1M1|Fa(h)|2=Pc+Ps.
Pc=Faa(0)1+ξ1.
Faa(0)=(1+ϵ)Faa(0),
a(t)=A+as(t),
|A+as(t)|2=|A+as(t)|2Faa(0)+Faa(0).
Real{as(t)}=AAReal{as(t)}.
as(t)=AAas(t),
Ps=PcPcPsPcPc=ξξ.
PcPc=Faa(0)/(1+ξ1)Faa(0)/(1+ξ1)=(1+ϵ)(1+ξ1)1+ξ1,
ξ=Cϵ+Cϵ21,Cϵ=(1+ϵ)2(ξ+1)22ξ2ξ.
PsPs=PcPc=ξξ.
p(x)=1πPsexp(x2Ps),
Prob(x>A)=Ap(x)dx=Q(2ξ)exp(ξ),
a(t)=a(t)exp[iϕ(t)],

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