Abstract

We experimentally investigate digital intra-channel nonlinear impairment compensation and inter-channel crosstalk suppression for 4 × 160.8-Gb/s wavelength division multiplexing (WDM) polarization division multiplexing quadrature phase shift keying (PDM-QPSK) transmission over 1300-km single-mode fiber-28 (SMF-28) on a 50-GHz grid with the spectral efficiency of 3.21b/s/Hz, adopting simplified heterodyne coherent detection. By using nonlinear compensation based on DBP with crosstalk suppression based on post filter and maximum likelihood sequence estimation (PF&MLSE), the BER has been improved from 1.0 × 10−3 to 3.5 × 10−4 for 4 × 160.8Gb/s WDM PDM-QPSK with heterodyne detection after 1300km SMF-28 transmission.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express16(2), 753–791 (2008).
    [CrossRef] [PubMed]
  2. S. J. Savory, “Digital Coherent Optical Receivers: Algorithms and Subsystems,” J. of Sel. Top. Quantum Electron.16(5), 1164–1179 (2010).
    [CrossRef]
  3. X. Zhou and J. Yu, “Multi-Level, Multi-Dimensional Coding for High-Speed and High-Spectral-Efficiency Optical Transmission,” J. Lightwave Technol.27(16), 3641–3653 (2009).
    [CrossRef]
  4. J. Yu, Z. Dong, H.-C. Chien, Y. Shao, and N. Chi, “7-Tb/s (7 × 1.284 Tb/s/ch) Signal Transmission Over 320 km Using PDM-64QAM Modulation,” IEEE Photon. Technol. Lett.24(4), 264–266 (2012).
    [CrossRef]
  5. J. Zhang, Z. Dong, J. Yu, N. Chi, L. Tao, X. Li, and Y. Shao, “Simplified coherent receiver with heterodyne detection of eight-channel 50 Gb/s PDM-QPSK WDM signal after 1040 km SMF-28 transmission,” Opt. Lett.37(19), 4050–4052 (2012).
    [CrossRef] [PubMed]
  6. X. Li, J. Yu, N. Chi, Z. Dong, J. Zhang, and J. Yu, “The reduction of the LO number for heterodyne coherent detection,” Opt. Express20(28), 29613–29619 (2012).
    [CrossRef] [PubMed]
  7. R. Zhu, K. Xu, Y. Zhang, Y. Li, J. Wu, X. Hong, and J. Lin, “QAM Coherent Subcarrier Multiplexing System Based on Heterodyne Detection using Intermediate Frequency Carrier Modulation,” in Proc. Of APMP, 165–168 (2008).
  8. M. Yoshida, H. Goto, K. Kasai, and M. Nakazawa, “64 and 128 coherent QAM optical transmission over 150 km using frequency-stabilized laser and heterodyne PLL detection,” Opt. Express16(2), 829–840 (2008).
    [CrossRef] [PubMed]
  9. Z. Dong, X. Li, J. Yu, and J. Yu, “Generation and transmission of 8 × 112-Gb/s WDM PDM-16QAM on a 25-GHz grid with simplified heterodyne detection,” Opt. Express21(2), 1773–1778 (2013).
    [CrossRef] [PubMed]
  10. P. C. Schindler, R. Schmogrow, D. Hillerkuss, M. Nazarathy, S. Ben-Ezra, C. Koos, W. Freude, and J. Leuthold, “Remote Heterodyne Reception of OFDM-QPSK as Downlink-Solution for Future Access Networks,” in Proc. Of OSA ANIC, AW4A.3 (2012).
  11. L. G. Kazovsky, “Optical Heterodyning Versus Optical Homodyning: A Comparison,” J. Opt. Commun.1, 18–24 (1985).
  12. E. Ip, “Nonlinear Compensation Using Backpropagation for Polarization-Multiplexed Transmission,” J. Lightwave Technol.28(6), 939–951 (2010).
    [CrossRef]
  13. E. Ip, Y. Huang, E. Mateo, Y. Aono, Y. Yano, T. Tajima, and T. Wang, “Interchannel Nonlinearity Compensation for 3λx114-Gb/s DP-8QAM using Three Synchronized Sampling Scopes,” in Proc. Of OFC’2012, OM3A.6 (2012).
  14. E. F. Mateo, X. Zhou, and G. Li, “Improved digital backward propagation for the compensation of inter-channel nonlinear effects in polarization-multiplexed WDM systems,” Opt. Express19(2), 570–583 (2011).
    [CrossRef] [PubMed]
  15. S. Zhang, M. Huang, F. Yaman, E. Mateo, D. Qian, Y. Zhang, L. Xu, Y. Shao, I. Djordjevic, T. Wang, Y. Inada, T. Inoue, T. Ogata, and Y. Aoki, “40×117.6 Gb/s PDM-16QAM OFDM Transmission over 10,181 km with Soft-Decision LDPC Coding and Nonlinearity Compensation,” in Proc. of OFC’2012, PDP5C.4 (2012).
  16. X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express16(2), 880–888 (2008).
    [CrossRef] [PubMed]
  17. L. Li, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Implementation Efficient Nonlinear Equalizer Based on Correlated Digital Backpropagation,” in Proc. of OFC’2011, OWW3 (2011).
  18. J. Li, Z. Tao, H. Zhang, W. Yan, T. Hoshida, and J. C. Rasmussen, “Spectrally Efficient Quadrature Duobinary Coherent Systems With Symbol-Rate Digital Signal Processing,” J. Lightwave Technol.29(8), 1098–1104 (2011).
    [CrossRef]
  19. Z. Dong, J. Yu, Z. Jia, H. C. Chien, X. Li, and G. K. Chang, “7x224 Gb/s/ch Nyquist-WDM transmission over 1600-km SMF-28 using PDM-CSRZ-QPSK modulation,” IEEE Photon. Technol. Lett.24(13), 1157–1159 (2012).
    [CrossRef]
  20. H. C. Chien, J. Yu, Z. Jia, Z. Dong, and X. Xiao, “Performance assessment of noise-suppressed Nyquist-WDM for Terabit superchannel transmission,” J. Lightwave Technol.30(24), 3965–3971 (2012).
    [CrossRef]
  21. T. Gui, C. Li, Q. Yang, X. Xiao, L. Meng, C. Li, X. Yi, C. Jin, and Z. Li, “Auto bias control technique for optical OFDM transmitter with bias dithering,” Opt. Express21(5), 5833–5841 (2013).
    [CrossRef] [PubMed]

2013

2012

2011

2010

E. Ip, “Nonlinear Compensation Using Backpropagation for Polarization-Multiplexed Transmission,” J. Lightwave Technol.28(6), 939–951 (2010).
[CrossRef]

S. J. Savory, “Digital Coherent Optical Receivers: Algorithms and Subsystems,” J. of Sel. Top. Quantum Electron.16(5), 1164–1179 (2010).
[CrossRef]

2009

2008

1985

L. G. Kazovsky, “Optical Heterodyning Versus Optical Homodyning: A Comparison,” J. Opt. Commun.1, 18–24 (1985).

Aono, Y.

E. Ip, Y. Huang, E. Mateo, Y. Aono, Y. Yano, T. Tajima, and T. Wang, “Interchannel Nonlinearity Compensation for 3λx114-Gb/s DP-8QAM using Three Synchronized Sampling Scopes,” in Proc. Of OFC’2012, OM3A.6 (2012).

Barros, D. J. F.

Ben-Ezra, S.

P. C. Schindler, R. Schmogrow, D. Hillerkuss, M. Nazarathy, S. Ben-Ezra, C. Koos, W. Freude, and J. Leuthold, “Remote Heterodyne Reception of OFDM-QPSK as Downlink-Solution for Future Access Networks,” in Proc. Of OSA ANIC, AW4A.3 (2012).

Chang, G. K.

Z. Dong, J. Yu, Z. Jia, H. C. Chien, X. Li, and G. K. Chang, “7x224 Gb/s/ch Nyquist-WDM transmission over 1600-km SMF-28 using PDM-CSRZ-QPSK modulation,” IEEE Photon. Technol. Lett.24(13), 1157–1159 (2012).
[CrossRef]

Chen, X.

Chi, N.

Chien, H. C.

H. C. Chien, J. Yu, Z. Jia, Z. Dong, and X. Xiao, “Performance assessment of noise-suppressed Nyquist-WDM for Terabit superchannel transmission,” J. Lightwave Technol.30(24), 3965–3971 (2012).
[CrossRef]

Z. Dong, J. Yu, Z. Jia, H. C. Chien, X. Li, and G. K. Chang, “7x224 Gb/s/ch Nyquist-WDM transmission over 1600-km SMF-28 using PDM-CSRZ-QPSK modulation,” IEEE Photon. Technol. Lett.24(13), 1157–1159 (2012).
[CrossRef]

Chien, H.-C.

J. Yu, Z. Dong, H.-C. Chien, Y. Shao, and N. Chi, “7-Tb/s (7 × 1.284 Tb/s/ch) Signal Transmission Over 320 km Using PDM-64QAM Modulation,” IEEE Photon. Technol. Lett.24(4), 264–266 (2012).
[CrossRef]

Dong, Z.

Freude, W.

P. C. Schindler, R. Schmogrow, D. Hillerkuss, M. Nazarathy, S. Ben-Ezra, C. Koos, W. Freude, and J. Leuthold, “Remote Heterodyne Reception of OFDM-QPSK as Downlink-Solution for Future Access Networks,” in Proc. Of OSA ANIC, AW4A.3 (2012).

Goldfarb, G.

Goto, H.

Gui, T.

Hillerkuss, D.

P. C. Schindler, R. Schmogrow, D. Hillerkuss, M. Nazarathy, S. Ben-Ezra, C. Koos, W. Freude, and J. Leuthold, “Remote Heterodyne Reception of OFDM-QPSK as Downlink-Solution for Future Access Networks,” in Proc. Of OSA ANIC, AW4A.3 (2012).

Hoshida, T.

Huang, Y.

E. Ip, Y. Huang, E. Mateo, Y. Aono, Y. Yano, T. Tajima, and T. Wang, “Interchannel Nonlinearity Compensation for 3λx114-Gb/s DP-8QAM using Three Synchronized Sampling Scopes,” in Proc. Of OFC’2012, OM3A.6 (2012).

Ip, E.

E. Ip, “Nonlinear Compensation Using Backpropagation for Polarization-Multiplexed Transmission,” J. Lightwave Technol.28(6), 939–951 (2010).
[CrossRef]

E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express16(2), 753–791 (2008).
[CrossRef] [PubMed]

E. Ip, Y. Huang, E. Mateo, Y. Aono, Y. Yano, T. Tajima, and T. Wang, “Interchannel Nonlinearity Compensation for 3λx114-Gb/s DP-8QAM using Three Synchronized Sampling Scopes,” in Proc. Of OFC’2012, OM3A.6 (2012).

Jia, Z.

H. C. Chien, J. Yu, Z. Jia, Z. Dong, and X. Xiao, “Performance assessment of noise-suppressed Nyquist-WDM for Terabit superchannel transmission,” J. Lightwave Technol.30(24), 3965–3971 (2012).
[CrossRef]

Z. Dong, J. Yu, Z. Jia, H. C. Chien, X. Li, and G. K. Chang, “7x224 Gb/s/ch Nyquist-WDM transmission over 1600-km SMF-28 using PDM-CSRZ-QPSK modulation,” IEEE Photon. Technol. Lett.24(13), 1157–1159 (2012).
[CrossRef]

Jin, C.

Kahn, J. M.

Kasai, K.

Kazovsky, L. G.

L. G. Kazovsky, “Optical Heterodyning Versus Optical Homodyning: A Comparison,” J. Opt. Commun.1, 18–24 (1985).

Kim, I.

Koos, C.

P. C. Schindler, R. Schmogrow, D. Hillerkuss, M. Nazarathy, S. Ben-Ezra, C. Koos, W. Freude, and J. Leuthold, “Remote Heterodyne Reception of OFDM-QPSK as Downlink-Solution for Future Access Networks,” in Proc. Of OSA ANIC, AW4A.3 (2012).

Lau, A. P. T.

Leuthold, J.

P. C. Schindler, R. Schmogrow, D. Hillerkuss, M. Nazarathy, S. Ben-Ezra, C. Koos, W. Freude, and J. Leuthold, “Remote Heterodyne Reception of OFDM-QPSK as Downlink-Solution for Future Access Networks,” in Proc. Of OSA ANIC, AW4A.3 (2012).

Li, C.

Li, G.

Li, J.

Li, X.

Li, Z.

Mateo, E.

X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express16(2), 880–888 (2008).
[CrossRef] [PubMed]

E. Ip, Y. Huang, E. Mateo, Y. Aono, Y. Yano, T. Tajima, and T. Wang, “Interchannel Nonlinearity Compensation for 3λx114-Gb/s DP-8QAM using Three Synchronized Sampling Scopes,” in Proc. Of OFC’2012, OM3A.6 (2012).

Mateo, E. F.

Meng, L.

Nakazawa, M.

Nazarathy, M.

P. C. Schindler, R. Schmogrow, D. Hillerkuss, M. Nazarathy, S. Ben-Ezra, C. Koos, W. Freude, and J. Leuthold, “Remote Heterodyne Reception of OFDM-QPSK as Downlink-Solution for Future Access Networks,” in Proc. Of OSA ANIC, AW4A.3 (2012).

Rasmussen, J. C.

Savory, S. J.

S. J. Savory, “Digital Coherent Optical Receivers: Algorithms and Subsystems,” J. of Sel. Top. Quantum Electron.16(5), 1164–1179 (2010).
[CrossRef]

Schindler, P. C.

P. C. Schindler, R. Schmogrow, D. Hillerkuss, M. Nazarathy, S. Ben-Ezra, C. Koos, W. Freude, and J. Leuthold, “Remote Heterodyne Reception of OFDM-QPSK as Downlink-Solution for Future Access Networks,” in Proc. Of OSA ANIC, AW4A.3 (2012).

Schmogrow, R.

P. C. Schindler, R. Schmogrow, D. Hillerkuss, M. Nazarathy, S. Ben-Ezra, C. Koos, W. Freude, and J. Leuthold, “Remote Heterodyne Reception of OFDM-QPSK as Downlink-Solution for Future Access Networks,” in Proc. Of OSA ANIC, AW4A.3 (2012).

Shao, Y.

J. Zhang, Z. Dong, J. Yu, N. Chi, L. Tao, X. Li, and Y. Shao, “Simplified coherent receiver with heterodyne detection of eight-channel 50 Gb/s PDM-QPSK WDM signal after 1040 km SMF-28 transmission,” Opt. Lett.37(19), 4050–4052 (2012).
[CrossRef] [PubMed]

J. Yu, Z. Dong, H.-C. Chien, Y. Shao, and N. Chi, “7-Tb/s (7 × 1.284 Tb/s/ch) Signal Transmission Over 320 km Using PDM-64QAM Modulation,” IEEE Photon. Technol. Lett.24(4), 264–266 (2012).
[CrossRef]

Tajima, T.

E. Ip, Y. Huang, E. Mateo, Y. Aono, Y. Yano, T. Tajima, and T. Wang, “Interchannel Nonlinearity Compensation for 3λx114-Gb/s DP-8QAM using Three Synchronized Sampling Scopes,” in Proc. Of OFC’2012, OM3A.6 (2012).

Tao, L.

Tao, Z.

Wang, T.

E. Ip, Y. Huang, E. Mateo, Y. Aono, Y. Yano, T. Tajima, and T. Wang, “Interchannel Nonlinearity Compensation for 3λx114-Gb/s DP-8QAM using Three Synchronized Sampling Scopes,” in Proc. Of OFC’2012, OM3A.6 (2012).

Xiao, X.

Yaman, F.

Yan, W.

Yang, Q.

Yano, Y.

E. Ip, Y. Huang, E. Mateo, Y. Aono, Y. Yano, T. Tajima, and T. Wang, “Interchannel Nonlinearity Compensation for 3λx114-Gb/s DP-8QAM using Three Synchronized Sampling Scopes,” in Proc. Of OFC’2012, OM3A.6 (2012).

Yi, X.

Yoshida, M.

Yu, J.

Z. Dong, X. Li, J. Yu, and J. Yu, “Generation and transmission of 8 × 112-Gb/s WDM PDM-16QAM on a 25-GHz grid with simplified heterodyne detection,” Opt. Express21(2), 1773–1778 (2013).
[CrossRef] [PubMed]

Z. Dong, X. Li, J. Yu, and J. Yu, “Generation and transmission of 8 × 112-Gb/s WDM PDM-16QAM on a 25-GHz grid with simplified heterodyne detection,” Opt. Express21(2), 1773–1778 (2013).
[CrossRef] [PubMed]

X. Li, J. Yu, N. Chi, Z. Dong, J. Zhang, and J. Yu, “The reduction of the LO number for heterodyne coherent detection,” Opt. Express20(28), 29613–29619 (2012).
[CrossRef] [PubMed]

X. Li, J. Yu, N. Chi, Z. Dong, J. Zhang, and J. Yu, “The reduction of the LO number for heterodyne coherent detection,” Opt. Express20(28), 29613–29619 (2012).
[CrossRef] [PubMed]

J. Zhang, Z. Dong, J. Yu, N. Chi, L. Tao, X. Li, and Y. Shao, “Simplified coherent receiver with heterodyne detection of eight-channel 50 Gb/s PDM-QPSK WDM signal after 1040 km SMF-28 transmission,” Opt. Lett.37(19), 4050–4052 (2012).
[CrossRef] [PubMed]

J. Yu, Z. Dong, H.-C. Chien, Y. Shao, and N. Chi, “7-Tb/s (7 × 1.284 Tb/s/ch) Signal Transmission Over 320 km Using PDM-64QAM Modulation,” IEEE Photon. Technol. Lett.24(4), 264–266 (2012).
[CrossRef]

Z. Dong, J. Yu, Z. Jia, H. C. Chien, X. Li, and G. K. Chang, “7x224 Gb/s/ch Nyquist-WDM transmission over 1600-km SMF-28 using PDM-CSRZ-QPSK modulation,” IEEE Photon. Technol. Lett.24(13), 1157–1159 (2012).
[CrossRef]

H. C. Chien, J. Yu, Z. Jia, Z. Dong, and X. Xiao, “Performance assessment of noise-suppressed Nyquist-WDM for Terabit superchannel transmission,” J. Lightwave Technol.30(24), 3965–3971 (2012).
[CrossRef]

X. Zhou and J. Yu, “Multi-Level, Multi-Dimensional Coding for High-Speed and High-Spectral-Efficiency Optical Transmission,” J. Lightwave Technol.27(16), 3641–3653 (2009).
[CrossRef]

Zhang, H.

Zhang, J.

Zhou, X.

IEEE Photon. Technol. Lett.

J. Yu, Z. Dong, H.-C. Chien, Y. Shao, and N. Chi, “7-Tb/s (7 × 1.284 Tb/s/ch) Signal Transmission Over 320 km Using PDM-64QAM Modulation,” IEEE Photon. Technol. Lett.24(4), 264–266 (2012).
[CrossRef]

Z. Dong, J. Yu, Z. Jia, H. C. Chien, X. Li, and G. K. Chang, “7x224 Gb/s/ch Nyquist-WDM transmission over 1600-km SMF-28 using PDM-CSRZ-QPSK modulation,” IEEE Photon. Technol. Lett.24(13), 1157–1159 (2012).
[CrossRef]

J. Lightwave Technol.

J. of Sel. Top. Quantum Electron.

S. J. Savory, “Digital Coherent Optical Receivers: Algorithms and Subsystems,” J. of Sel. Top. Quantum Electron.16(5), 1164–1179 (2010).
[CrossRef]

J. Opt. Commun.

L. G. Kazovsky, “Optical Heterodyning Versus Optical Homodyning: A Comparison,” J. Opt. Commun.1, 18–24 (1985).

Opt. Express

Opt. Lett.

Other

P. C. Schindler, R. Schmogrow, D. Hillerkuss, M. Nazarathy, S. Ben-Ezra, C. Koos, W. Freude, and J. Leuthold, “Remote Heterodyne Reception of OFDM-QPSK as Downlink-Solution for Future Access Networks,” in Proc. Of OSA ANIC, AW4A.3 (2012).

R. Zhu, K. Xu, Y. Zhang, Y. Li, J. Wu, X. Hong, and J. Lin, “QAM Coherent Subcarrier Multiplexing System Based on Heterodyne Detection using Intermediate Frequency Carrier Modulation,” in Proc. Of APMP, 165–168 (2008).

L. Li, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Implementation Efficient Nonlinear Equalizer Based on Correlated Digital Backpropagation,” in Proc. of OFC’2011, OWW3 (2011).

S. Zhang, M. Huang, F. Yaman, E. Mateo, D. Qian, Y. Zhang, L. Xu, Y. Shao, I. Djordjevic, T. Wang, Y. Inada, T. Inoue, T. Ogata, and Y. Aoki, “40×117.6 Gb/s PDM-16QAM OFDM Transmission over 10,181 km with Soft-Decision LDPC Coding and Nonlinearity Compensation,” in Proc. of OFC’2012, PDP5C.4 (2012).

E. Ip, Y. Huang, E. Mateo, Y. Aono, Y. Yano, T. Tajima, and T. Wang, “Interchannel Nonlinearity Compensation for 3λx114-Gb/s DP-8QAM using Three Synchronized Sampling Scopes,” in Proc. Of OFC’2012, OM3A.6 (2012).

Cited By

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

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

(a)The main block of nonlinear compensation; (b) the process block of linear compensation for CD; (c) the process block of nonlinear compensation. (LC: linear compensation; NLC: nonlinear compensation; F and F−1: FFT and IFFT processing)

Fig. 2
Fig. 2

An illustration of filtering effect caused by AWG and ADC bandwidth limitation and the principle of 9-QAM signal generation by digital post filter

Fig. 3
Fig. 3

The experimental setup for 4 × 160.8-Gb/s WDM PDM-QPSK signal with heterodyne detection over 1300-km SMF-28 transmission on a 50-GHz grid. (I/Q Mod.: I/Q modulator; Att.: Attenuation; EDFA: Erbium-doped fiber amplifier; LO: Local oscillator; PD: balanced photo detector; EA: electrical amplifier; WSS: wavelength selective switch)

Fig. 4
Fig. 4

Optical spectrum of 4X160.8-Gb/s PDM-QPSK channels (a) after AWG; (b) after 1300-km transmission. (The optical spectrum of even and odd channels is a little different due to the different gain of the driver of the I (Q) electrical signals in the two sets of the transmitters, but we find that the receiver sensitivity of the two sets has no much difference); (c) Optical spectrum of PDM-QPSK signal with LO measured before balanced detectors after transmission; (d) Electrical spectrum of the received IF signals after balanced detector and 45GHz ADC.

Fig. 5
Fig. 5

(a) The Back to back BER performance of single-channel and WDM channels varying with OSNR with and without post filter and MLSE. Inset (i) and (ii) show the X-polarization constellations of different cases; (b) Single-channel BER performance varying with input power for different processing schemes over 850-km transmission; (c) Single-channel BER performance for NLC varying with calculation step length for different input power.

Fig. 6
Fig. 6

(a) WDM channels BER performance of channel 2 in 4 × 160.8-Gb/s varying with input power for different processing schemes over 850-km transmission; (b) BER performance of channel 2 in 4 × 160.8-Gb/s WDM channels varying with transmission distance from 400 to 1300km for different processing schemes. Inset (i) and (ii) show the X-polarization constellations after 1300-km transmission for different schemes.

Equations (2)

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

E x,y z =- α 2 E x,y -j β 2 2 2 E x,y t 2 +j 8 9 γ(| E x,y | 2 +| E y,x | 2 ) E x,y =( D ^ + N ^ ) E x,y
D ^ =- α 2 -j β 2 2 2 t 2 , N ^ =j 8 9 γ(| E x,y | 2 +| E y,x | 2 )

Metrics