Abstract

We propose and experimentally demonstrate a hybrid WDM/OCDMA ring with a dynamic add/drop function based on Fourier code for local area networks. Dynamic function is implemented by mechanically tuning the Fourier encoder/decoder for optical code division multiple access (OCDMA) encoding/decoding. Wavelength division multiplexing (WDM) is utilized for node assignment and 4-chip Fourier code recovers the matched signal from the codes. For an optical source well adapted to WDM channels and its short optical pulse generation, reflective semiconductor optical amplifiers (RSOAs) are used with a fiber Bragg grating (FBG) and gain-switched. To demonstrate we experimentally investigated a two-node hybrid WDM/OCDMA ring with a 4-chip Fourier encoder/decoder fabricated by cascading four FBGs with the bit error rate (BER) of <10−9 for the node span of 10.64 km at 1.25 Gb/s.

© 2011 OSA

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References

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  1. P. R. Prucnal, M. A. Santoro, and T. R. Fan, “Spread spectrum fiber-optic local area network using optical processing,” J. Lightwave Technol. 4(5), 547–554 (1986).
    [CrossRef]
  2. P. J. Urban, B. Huiszoon, R. Roy, M. M. de Laat, F. M. Huijskens, E. J. Klein, G. D. Khoe, A. M. J. Koonen, and H. de Waardt, “High-Bit-Rate Dynamically Reconfigurable WDM–TDM Access Network,” IEEE J. Opt. Commun. Netw. 1(2), A143–A159 (2009).
    [CrossRef]
  3. J.-F. Huang, Y.-T. Changa, and C.-C. Hsua, “Hybrid WDM and optical CDMA implemented over waveguide-grating-based fiber-to-the-home networks,” Opt. Fiber Technol. 13(3), 215–225 (2007).
    [CrossRef]
  4. X. Wang, N. Wada, T. Miyazaki, G. Cincotti, and K. Kitayama, “Hybrid WDM/OCDMA for next generation access network,” Proc. SPIE 6783, 678328, 678328-14 (2007).
    [CrossRef]
  5. X. Chen, G. Xia, D. Huang, and X. Yuan, “Experimental demonstration of 40 Gbit/s hybrid optical code-division multiplexing/wavelength-division multiplexing system,” Opt. Eng. 46(11), 115006 (2007).
    [CrossRef]
  6. C. Zhang and K. Qiu, “Design and analysis of coherent OCDM en/decoder based on photonic crystal,” Opt. Lasers Eng. 46(8), 582–589 (2008).
    [CrossRef]
  7. P. C. Teh, M. Ibsen, J. H. Lee, P. Petropoulos, and D. J. Richardson, “Demonstration of a four-channel WDM/OCDMA system using 255-chip 320-Gchip/s quarternary phase coding gratings,” IEEE Photon. Technol. Lett. 14(2), 227–229 (2002).
    [CrossRef]
  8. S. Boztas, R. Hammons, and P. V. Kumar, “4-phase sequences with near-optimum correlation properties,” IEEE Trans. Inf. Theory 38(3), 1101–1113 (1992).
    [CrossRef]
  9. M. Hanawa, “Fourier code: A novel orthogonal code for OCDM systems,” in Opto-Electronics and Communications Conference and Australian Conference on Optical Fibre Technology (OECC/ACOFT’ 2008), Sydney, 1–2 (2008).
  10. M. Hanawa, “Multiple access interference reduction by limiting receiver bandwidth on Fourier code based-OCDM system,” in Opto-Electronics and Communications Conference (OECC’ 2009), Hong Kong, 1–2 (2009).
  11. J. Wu and C.-L. Lin, “Fiber-Optic Code Division Add-Drop Multiplexers,” J. Lightwave Technol. 18(6), 819–824 (2000).
    [CrossRef]
  12. C. -S. Bre's, I. Glesk, R. J. Runser, and P. R. Prucnal, “All-Optical OCDMA Code-Drop Unit for Transparent Ring Networks,” IEEE Photon. Technol. Lett. 17, 1088–1090 (2005).
    [CrossRef]
  13. Advanced Optics Solutions Gmb, ( http://www.aos-fiber.com/eng/FBG/Athermalen.html ).
  14. K. Hosoya, M. Hanawa, and K. Nakamura, “Programmable FBG-based variable optical correlator for optical code division multiplexing,” in Asia-Pacific Conference Communications (APCC’2009), Shanghai, 560–563 (2009).
  15. N. Wada, “Optical Code Processing System, Device, and its Application,” JNW 5(2), 242–250 (2010).
    [CrossRef]

2010

N. Wada, “Optical Code Processing System, Device, and its Application,” JNW 5(2), 242–250 (2010).
[CrossRef]

2009

P. J. Urban, B. Huiszoon, R. Roy, M. M. de Laat, F. M. Huijskens, E. J. Klein, G. D. Khoe, A. M. J. Koonen, and H. de Waardt, “High-Bit-Rate Dynamically Reconfigurable WDM–TDM Access Network,” IEEE J. Opt. Commun. Netw. 1(2), A143–A159 (2009).
[CrossRef]

2008

C. Zhang and K. Qiu, “Design and analysis of coherent OCDM en/decoder based on photonic crystal,” Opt. Lasers Eng. 46(8), 582–589 (2008).
[CrossRef]

2007

J.-F. Huang, Y.-T. Changa, and C.-C. Hsua, “Hybrid WDM and optical CDMA implemented over waveguide-grating-based fiber-to-the-home networks,” Opt. Fiber Technol. 13(3), 215–225 (2007).
[CrossRef]

X. Wang, N. Wada, T. Miyazaki, G. Cincotti, and K. Kitayama, “Hybrid WDM/OCDMA for next generation access network,” Proc. SPIE 6783, 678328, 678328-14 (2007).
[CrossRef]

X. Chen, G. Xia, D. Huang, and X. Yuan, “Experimental demonstration of 40 Gbit/s hybrid optical code-division multiplexing/wavelength-division multiplexing system,” Opt. Eng. 46(11), 115006 (2007).
[CrossRef]

2005

C. -S. Bre's, I. Glesk, R. J. Runser, and P. R. Prucnal, “All-Optical OCDMA Code-Drop Unit for Transparent Ring Networks,” IEEE Photon. Technol. Lett. 17, 1088–1090 (2005).
[CrossRef]

2002

P. C. Teh, M. Ibsen, J. H. Lee, P. Petropoulos, and D. J. Richardson, “Demonstration of a four-channel WDM/OCDMA system using 255-chip 320-Gchip/s quarternary phase coding gratings,” IEEE Photon. Technol. Lett. 14(2), 227–229 (2002).
[CrossRef]

2000

1992

S. Boztas, R. Hammons, and P. V. Kumar, “4-phase sequences with near-optimum correlation properties,” IEEE Trans. Inf. Theory 38(3), 1101–1113 (1992).
[CrossRef]

1986

P. R. Prucnal, M. A. Santoro, and T. R. Fan, “Spread spectrum fiber-optic local area network using optical processing,” J. Lightwave Technol. 4(5), 547–554 (1986).
[CrossRef]

Boztas, S.

S. Boztas, R. Hammons, and P. V. Kumar, “4-phase sequences with near-optimum correlation properties,” IEEE Trans. Inf. Theory 38(3), 1101–1113 (1992).
[CrossRef]

Bre's, C. -S.

C. -S. Bre's, I. Glesk, R. J. Runser, and P. R. Prucnal, “All-Optical OCDMA Code-Drop Unit for Transparent Ring Networks,” IEEE Photon. Technol. Lett. 17, 1088–1090 (2005).
[CrossRef]

Changa, Y.-T.

J.-F. Huang, Y.-T. Changa, and C.-C. Hsua, “Hybrid WDM and optical CDMA implemented over waveguide-grating-based fiber-to-the-home networks,” Opt. Fiber Technol. 13(3), 215–225 (2007).
[CrossRef]

Chen, X.

X. Chen, G. Xia, D. Huang, and X. Yuan, “Experimental demonstration of 40 Gbit/s hybrid optical code-division multiplexing/wavelength-division multiplexing system,” Opt. Eng. 46(11), 115006 (2007).
[CrossRef]

Cincotti, G.

X. Wang, N. Wada, T. Miyazaki, G. Cincotti, and K. Kitayama, “Hybrid WDM/OCDMA for next generation access network,” Proc. SPIE 6783, 678328, 678328-14 (2007).
[CrossRef]

de Laat, M. M.

P. J. Urban, B. Huiszoon, R. Roy, M. M. de Laat, F. M. Huijskens, E. J. Klein, G. D. Khoe, A. M. J. Koonen, and H. de Waardt, “High-Bit-Rate Dynamically Reconfigurable WDM–TDM Access Network,” IEEE J. Opt. Commun. Netw. 1(2), A143–A159 (2009).
[CrossRef]

de Waardt, H.

P. J. Urban, B. Huiszoon, R. Roy, M. M. de Laat, F. M. Huijskens, E. J. Klein, G. D. Khoe, A. M. J. Koonen, and H. de Waardt, “High-Bit-Rate Dynamically Reconfigurable WDM–TDM Access Network,” IEEE J. Opt. Commun. Netw. 1(2), A143–A159 (2009).
[CrossRef]

Fan, T. R.

P. R. Prucnal, M. A. Santoro, and T. R. Fan, “Spread spectrum fiber-optic local area network using optical processing,” J. Lightwave Technol. 4(5), 547–554 (1986).
[CrossRef]

Glesk, I.

C. -S. Bre's, I. Glesk, R. J. Runser, and P. R. Prucnal, “All-Optical OCDMA Code-Drop Unit for Transparent Ring Networks,” IEEE Photon. Technol. Lett. 17, 1088–1090 (2005).
[CrossRef]

Hammons, R.

S. Boztas, R. Hammons, and P. V. Kumar, “4-phase sequences with near-optimum correlation properties,” IEEE Trans. Inf. Theory 38(3), 1101–1113 (1992).
[CrossRef]

Hsua, C.-C.

J.-F. Huang, Y.-T. Changa, and C.-C. Hsua, “Hybrid WDM and optical CDMA implemented over waveguide-grating-based fiber-to-the-home networks,” Opt. Fiber Technol. 13(3), 215–225 (2007).
[CrossRef]

Huang, D.

X. Chen, G. Xia, D. Huang, and X. Yuan, “Experimental demonstration of 40 Gbit/s hybrid optical code-division multiplexing/wavelength-division multiplexing system,” Opt. Eng. 46(11), 115006 (2007).
[CrossRef]

Huang, J.-F.

J.-F. Huang, Y.-T. Changa, and C.-C. Hsua, “Hybrid WDM and optical CDMA implemented over waveguide-grating-based fiber-to-the-home networks,” Opt. Fiber Technol. 13(3), 215–225 (2007).
[CrossRef]

Huijskens, F. M.

P. J. Urban, B. Huiszoon, R. Roy, M. M. de Laat, F. M. Huijskens, E. J. Klein, G. D. Khoe, A. M. J. Koonen, and H. de Waardt, “High-Bit-Rate Dynamically Reconfigurable WDM–TDM Access Network,” IEEE J. Opt. Commun. Netw. 1(2), A143–A159 (2009).
[CrossRef]

Huiszoon, B.

P. J. Urban, B. Huiszoon, R. Roy, M. M. de Laat, F. M. Huijskens, E. J. Klein, G. D. Khoe, A. M. J. Koonen, and H. de Waardt, “High-Bit-Rate Dynamically Reconfigurable WDM–TDM Access Network,” IEEE J. Opt. Commun. Netw. 1(2), A143–A159 (2009).
[CrossRef]

Ibsen, M.

P. C. Teh, M. Ibsen, J. H. Lee, P. Petropoulos, and D. J. Richardson, “Demonstration of a four-channel WDM/OCDMA system using 255-chip 320-Gchip/s quarternary phase coding gratings,” IEEE Photon. Technol. Lett. 14(2), 227–229 (2002).
[CrossRef]

Khoe, G. D.

P. J. Urban, B. Huiszoon, R. Roy, M. M. de Laat, F. M. Huijskens, E. J. Klein, G. D. Khoe, A. M. J. Koonen, and H. de Waardt, “High-Bit-Rate Dynamically Reconfigurable WDM–TDM Access Network,” IEEE J. Opt. Commun. Netw. 1(2), A143–A159 (2009).
[CrossRef]

Kitayama, K.

X. Wang, N. Wada, T. Miyazaki, G. Cincotti, and K. Kitayama, “Hybrid WDM/OCDMA for next generation access network,” Proc. SPIE 6783, 678328, 678328-14 (2007).
[CrossRef]

Klein, E. J.

P. J. Urban, B. Huiszoon, R. Roy, M. M. de Laat, F. M. Huijskens, E. J. Klein, G. D. Khoe, A. M. J. Koonen, and H. de Waardt, “High-Bit-Rate Dynamically Reconfigurable WDM–TDM Access Network,” IEEE J. Opt. Commun. Netw. 1(2), A143–A159 (2009).
[CrossRef]

Koonen, A. M. J.

P. J. Urban, B. Huiszoon, R. Roy, M. M. de Laat, F. M. Huijskens, E. J. Klein, G. D. Khoe, A. M. J. Koonen, and H. de Waardt, “High-Bit-Rate Dynamically Reconfigurable WDM–TDM Access Network,” IEEE J. Opt. Commun. Netw. 1(2), A143–A159 (2009).
[CrossRef]

Kumar, P. V.

S. Boztas, R. Hammons, and P. V. Kumar, “4-phase sequences with near-optimum correlation properties,” IEEE Trans. Inf. Theory 38(3), 1101–1113 (1992).
[CrossRef]

Lee, J. H.

P. C. Teh, M. Ibsen, J. H. Lee, P. Petropoulos, and D. J. Richardson, “Demonstration of a four-channel WDM/OCDMA system using 255-chip 320-Gchip/s quarternary phase coding gratings,” IEEE Photon. Technol. Lett. 14(2), 227–229 (2002).
[CrossRef]

Lin, C.-L.

Miyazaki, T.

X. Wang, N. Wada, T. Miyazaki, G. Cincotti, and K. Kitayama, “Hybrid WDM/OCDMA for next generation access network,” Proc. SPIE 6783, 678328, 678328-14 (2007).
[CrossRef]

Petropoulos, P.

P. C. Teh, M. Ibsen, J. H. Lee, P. Petropoulos, and D. J. Richardson, “Demonstration of a four-channel WDM/OCDMA system using 255-chip 320-Gchip/s quarternary phase coding gratings,” IEEE Photon. Technol. Lett. 14(2), 227–229 (2002).
[CrossRef]

Prucnal, P. R.

C. -S. Bre's, I. Glesk, R. J. Runser, and P. R. Prucnal, “All-Optical OCDMA Code-Drop Unit for Transparent Ring Networks,” IEEE Photon. Technol. Lett. 17, 1088–1090 (2005).
[CrossRef]

P. R. Prucnal, M. A. Santoro, and T. R. Fan, “Spread spectrum fiber-optic local area network using optical processing,” J. Lightwave Technol. 4(5), 547–554 (1986).
[CrossRef]

Qiu, K.

C. Zhang and K. Qiu, “Design and analysis of coherent OCDM en/decoder based on photonic crystal,” Opt. Lasers Eng. 46(8), 582–589 (2008).
[CrossRef]

Richardson, D. J.

P. C. Teh, M. Ibsen, J. H. Lee, P. Petropoulos, and D. J. Richardson, “Demonstration of a four-channel WDM/OCDMA system using 255-chip 320-Gchip/s quarternary phase coding gratings,” IEEE Photon. Technol. Lett. 14(2), 227–229 (2002).
[CrossRef]

Roy, R.

P. J. Urban, B. Huiszoon, R. Roy, M. M. de Laat, F. M. Huijskens, E. J. Klein, G. D. Khoe, A. M. J. Koonen, and H. de Waardt, “High-Bit-Rate Dynamically Reconfigurable WDM–TDM Access Network,” IEEE J. Opt. Commun. Netw. 1(2), A143–A159 (2009).
[CrossRef]

Runser, R. J.

C. -S. Bre's, I. Glesk, R. J. Runser, and P. R. Prucnal, “All-Optical OCDMA Code-Drop Unit for Transparent Ring Networks,” IEEE Photon. Technol. Lett. 17, 1088–1090 (2005).
[CrossRef]

Santoro, M. A.

P. R. Prucnal, M. A. Santoro, and T. R. Fan, “Spread spectrum fiber-optic local area network using optical processing,” J. Lightwave Technol. 4(5), 547–554 (1986).
[CrossRef]

Teh, P. C.

P. C. Teh, M. Ibsen, J. H. Lee, P. Petropoulos, and D. J. Richardson, “Demonstration of a four-channel WDM/OCDMA system using 255-chip 320-Gchip/s quarternary phase coding gratings,” IEEE Photon. Technol. Lett. 14(2), 227–229 (2002).
[CrossRef]

Urban, P. J.

P. J. Urban, B. Huiszoon, R. Roy, M. M. de Laat, F. M. Huijskens, E. J. Klein, G. D. Khoe, A. M. J. Koonen, and H. de Waardt, “High-Bit-Rate Dynamically Reconfigurable WDM–TDM Access Network,” IEEE J. Opt. Commun. Netw. 1(2), A143–A159 (2009).
[CrossRef]

Wada, N.

N. Wada, “Optical Code Processing System, Device, and its Application,” JNW 5(2), 242–250 (2010).
[CrossRef]

X. Wang, N. Wada, T. Miyazaki, G. Cincotti, and K. Kitayama, “Hybrid WDM/OCDMA for next generation access network,” Proc. SPIE 6783, 678328, 678328-14 (2007).
[CrossRef]

Wang, X.

X. Wang, N. Wada, T. Miyazaki, G. Cincotti, and K. Kitayama, “Hybrid WDM/OCDMA for next generation access network,” Proc. SPIE 6783, 678328, 678328-14 (2007).
[CrossRef]

Wu, J.

Xia, G.

X. Chen, G. Xia, D. Huang, and X. Yuan, “Experimental demonstration of 40 Gbit/s hybrid optical code-division multiplexing/wavelength-division multiplexing system,” Opt. Eng. 46(11), 115006 (2007).
[CrossRef]

Yuan, X.

X. Chen, G. Xia, D. Huang, and X. Yuan, “Experimental demonstration of 40 Gbit/s hybrid optical code-division multiplexing/wavelength-division multiplexing system,” Opt. Eng. 46(11), 115006 (2007).
[CrossRef]

Zhang, C.

C. Zhang and K. Qiu, “Design and analysis of coherent OCDM en/decoder based on photonic crystal,” Opt. Lasers Eng. 46(8), 582–589 (2008).
[CrossRef]

IEEE J. Opt. Commun. Netw.

P. J. Urban, B. Huiszoon, R. Roy, M. M. de Laat, F. M. Huijskens, E. J. Klein, G. D. Khoe, A. M. J. Koonen, and H. de Waardt, “High-Bit-Rate Dynamically Reconfigurable WDM–TDM Access Network,” IEEE J. Opt. Commun. Netw. 1(2), A143–A159 (2009).
[CrossRef]

IEEE Photon. Technol. Lett.

P. C. Teh, M. Ibsen, J. H. Lee, P. Petropoulos, and D. J. Richardson, “Demonstration of a four-channel WDM/OCDMA system using 255-chip 320-Gchip/s quarternary phase coding gratings,” IEEE Photon. Technol. Lett. 14(2), 227–229 (2002).
[CrossRef]

C. -S. Bre's, I. Glesk, R. J. Runser, and P. R. Prucnal, “All-Optical OCDMA Code-Drop Unit for Transparent Ring Networks,” IEEE Photon. Technol. Lett. 17, 1088–1090 (2005).
[CrossRef]

IEEE Trans. Inf. Theory

S. Boztas, R. Hammons, and P. V. Kumar, “4-phase sequences with near-optimum correlation properties,” IEEE Trans. Inf. Theory 38(3), 1101–1113 (1992).
[CrossRef]

J. Lightwave Technol.

P. R. Prucnal, M. A. Santoro, and T. R. Fan, “Spread spectrum fiber-optic local area network using optical processing,” J. Lightwave Technol. 4(5), 547–554 (1986).
[CrossRef]

J. Wu and C.-L. Lin, “Fiber-Optic Code Division Add-Drop Multiplexers,” J. Lightwave Technol. 18(6), 819–824 (2000).
[CrossRef]

JNW

N. Wada, “Optical Code Processing System, Device, and its Application,” JNW 5(2), 242–250 (2010).
[CrossRef]

Opt. Eng.

X. Chen, G. Xia, D. Huang, and X. Yuan, “Experimental demonstration of 40 Gbit/s hybrid optical code-division multiplexing/wavelength-division multiplexing system,” Opt. Eng. 46(11), 115006 (2007).
[CrossRef]

Opt. Fiber Technol.

J.-F. Huang, Y.-T. Changa, and C.-C. Hsua, “Hybrid WDM and optical CDMA implemented over waveguide-grating-based fiber-to-the-home networks,” Opt. Fiber Technol. 13(3), 215–225 (2007).
[CrossRef]

Opt. Lasers Eng.

C. Zhang and K. Qiu, “Design and analysis of coherent OCDM en/decoder based on photonic crystal,” Opt. Lasers Eng. 46(8), 582–589 (2008).
[CrossRef]

Proc. SPIE

X. Wang, N. Wada, T. Miyazaki, G. Cincotti, and K. Kitayama, “Hybrid WDM/OCDMA for next generation access network,” Proc. SPIE 6783, 678328, 678328-14 (2007).
[CrossRef]

Other

M. Hanawa, “Fourier code: A novel orthogonal code for OCDM systems,” in Opto-Electronics and Communications Conference and Australian Conference on Optical Fibre Technology (OECC/ACOFT’ 2008), Sydney, 1–2 (2008).

M. Hanawa, “Multiple access interference reduction by limiting receiver bandwidth on Fourier code based-OCDM system,” in Opto-Electronics and Communications Conference (OECC’ 2009), Hong Kong, 1–2 (2009).

Advanced Optics Solutions Gmb, ( http://www.aos-fiber.com/eng/FBG/Athermalen.html ).

K. Hosoya, M. Hanawa, and K. Nakamura, “Programmable FBG-based variable optical correlator for optical code division multiplexing,” in Asia-Pacific Conference Communications (APCC’2009), Shanghai, 560–563 (2009).

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Figures (10)

Fig. 1
Fig. 1

Proposed hybrid WDM/OCDMA ring for LANs

Fig. 2
Fig. 2

Schematic of the short pulse generator based on the RSOA and the external FBG

Fig. 3
Fig. 3

Fabricated coder for 4-chip Fourier code, (a) Encoder, (b) Decoder

Fig. 4
Fig. 4

Experimental setup. RSOA: reflective semiconductor optical amplifier, AMP: electrical amplifier, EDFA: erbium-doped fiber amplifier, SMF: single mode fiber, ISO: isolator, PPG: pulse pattern generator, PD: photo detector, BERT: bit error rate tester, DCA: digital communication analyzer

Fig. 5
Fig. 5

Optical short pulse trains and their optical spectra: the signals at (a) pulse width: 32 ps, λ1: 1552.07 nm, (b) pulse width: 32 ps, λ2: 1552.82 nm

Fig. 6
Fig. 6

(a) the pulse train modulated by the data pattern ‘1011’, (b) the modulation signal encoded by C 1, and (c) the modulation signal encoded by C 2

Fig. 7
Fig. 7

The optical spectra of the modulated signals on λ1: (a) by C 1, (b) by C 2

Fig. 8
Fig. 8

Measured (left) and theoretical (right) correlation waveforms after being decoded, (a) auto-correlation waveform for (C 1, λ1) × (C 1, λ1), (b) cross-correlation waveform for (C 2, λ1) × (C 1, λ1)

Fig. 9
Fig. 9

Measured (left) and theoretical (right) correlation waveforms after code switching to Decoder#1, (a) auto-correlation waveform for (C 1+C 2, λ1)×(C 1, λ1), (b) auto-correlation waveform for (C 1+C 2, λ1)×(C 2, λ1), (c) cross-correlation waveform for (C 1+C 2, λ1)×(C 3, λ1), (d) cross-correlation waveform for (C 1+C 2, λ1)×(C 4, λ1)

Fig. 10
Fig. 10

Measured BER curves, : BER for (C 1, λ1) × (C 1, λ1), : BER for (C 1, λ1) × (C 1, λ1) on wavelength shift of 0.018nm, : BER for (C 1, λ1 + λ2) × (C 1, λ1), : BER for (C 1 + C 2, λ1) × (C 1, λ1), : BER for (C 1 + C 2, λ1) × (C 2, λ1)

Equations (3)

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

F 4 = [ + 1 + 1 + 1 + 1 + 1 + j 1 j + 1 1 + 1 1 + 1 j 1 + j ] = [ C 1 C 2 C 3 C 4 ]
               Δ φ 12        Δ φ 23       Δ φ 34 Δ F 4 = [ 0 0 0 π / 2 π / 2 π / 2 π π π 3 π / 2 3 π / 2 3 π / 2 ]
Δ ϕ = 2 π λ B { ( 2 L n ) mod λ B }

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