Abstract

Recent advances in optical devices greatly enhance the feasibility of Optical Code Division Multiplexing/Wavelength Division Multiplexing (OCDM/WDM) Optical Packet Switch. In this paper, the performance of an OCDM/WDM switch is investigated when impairment due to both Multiple Access Interference and Beat noise are taken into account. Analytical models are proposed to dimension the switch resources as the number of optical codes carried on each wavelength and the number of needed optical converters. The Packet Loss Probability due to output packet contentions is evaluated as a function of the main switch and traffic parameters when Gold coherent optical codes are adopted. When the available bandwidth is fixed for the WDM/OCDM signal, due to a statistical multiplexing effect, we show that the use of more length codes and fewer wavelengths lead to lower packet loss probability, especially for low offered traffic.

© 2010 OSA

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  30. X. Wang, N. Wada, and K. Kitayama, “Inter-symbol interference and beat noise in flexible data-rate coherent OCDMA and the BER improvement by using optical thresholding,” Opt. Express 13, 10469–10474 (2005).
    [Crossref] [PubMed]
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    [Crossref]

2010 (1)

2008 (2)

2007 (6)

S. Goldberg and P. R. Prucnal, “On the Teletraffic Capacity of Optical CDMA,” IEEE Trans. Commun. 55, 1334–1343 (2007).
[Crossref]

G. Manzacca, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Comparative Study of Multiencoding Schemes for OCDM Using a Single Multiport Optical Encoder/Decoder,” IEEE Photon. Technol. Lett. 19, 559–561 (2007).
[Crossref]

G. Manzacca, A. M. Vegni, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Performance Analysis of a Multiport Encoder/Decoder in OCDMA Scenario,” IEEE J. Sel. Top. Quantum Electron. 13, 1415–1421 (2007).
[Crossref]

X. Wang, N. Wada, T. Miyazaki, G. Cincotti, and K. Kitayama, “Asynchronous Multiuser Coherent OCDMA System with Code-Shift-Keying and Balanced Detection,” IEEE J. Sel. Top. Quantum Electron. 13, 1463–1470 (2007).
[Crossref]

C. Tian, Z. Zhang, M. Ibsen, P. Petropoulos, and D. J. Richardson, “A 16-Channel Reconfigurable OCDMA/DWDM System Using Continuous Phase-Shift SSFBGs,” IEEE J. Sel. Top. Quantum Electron. 13, 1480–1486 (2007).
[Crossref]

T. Hamanaka, X. Wang, N. Wada, and K. Kitayama, “Compound Data Rate and Data-Rate-Flexible 622 Mb/s-10Gb/s OCDMA Experiments Using 511-Chip SSFBG and Cascaded SHG-DFG-Based PPLN Waveguide Optical Thresholder,” IEEE J. Sel. Top. Quantum Electron. 13, 1516–1521 (2007).
[Crossref]

2006 (3)

2005 (1)

2004 (2)

X. Wang and K. Kitayama, “Analysis of Beat Noise in Coherent and incoherent Time-Spreading OCDMA,” J. Lightwave Technol. 22, 2226–2234 (2004).
[Crossref]

H. Sotobayashi, W. Chujo, and K. Kitayama, “Highly Spectral-Efficient Optical Code-Division Multiplexing Transmission System,” IEEE J. Sel. Top. Quantum Electron. 10, 250–258 (2004).
[Crossref]

2002 (4)

H. Sotobayashi, W. Chujo, and K. Kitayama, “Transparent Virtual Code/Wavelength Path Network,” IEEE J. Sel. Top. Quantum Electron. 8, 699–704 (2002).
[Crossref]

Y. G. Wen, Y. Zhang, and L. K. Chen, “On Architecture and Limitation of Optical Multiprotocol Label Switching (MPLS) Networks using Optical-Orthogonal-Code (OCC)/Wavelength Label,” Opt. Fiber Technol. 8, 43–70 (2002).
[Crossref]

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

K. Kitayama, H. Sotobayashi, and N. Wada, “1,6 b/s/Hz 6,4 Tb/s QPSK-OCDM/WDM (4 OCDM×40WDM×40Gb/s) Transmission Experiment using Optical Hard Thresholding,” IEEE Photon. Technol. Lett. 14, 555–557 (2002).
[Crossref]

2001 (2)

K. Kitayama, H. Sotobayashi, and N. Wada, “1,52 Tbit/s OCDM/WDM (4 OCDM×19WDM×20 Gbit/s) Transmission Experiment,” Electron. Lett. 37, 700–701 (2001).
[Crossref]

P. C. Teh, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Phase Encoding and Decoding of Short Pulses at 10Gb/s using Superstructured Fiber Bragg Gratings,” IEEE Photon. Technol. Lett. 13, 154–156 (2001).
[Crossref]

2000 (2)

K. Kitayama, “Code Division Multiplexing Lightwave Networks Based upon Optical Code Conversion,” IEEE J. Sel. Areas Comm. 16, 1309–1319 (2000).
[Crossref]

V. Eramo and M. Listanti, “Packet Loss in a Bufferless WDM Switch Employing Shared Tuneable Wavelength Converters,” J. Lightwave Technol. 18, 1818–1833 (2000).
[Crossref]

1999 (1)

K. Kitayama, H. Sotobayashi, and N. Wada, “Optical Code Division Multiplexing (OCDM) and its Applications to Photonic Networks,” IEICE Trans. Fundamentals E82-A, 2616–2626 (1999).

1998 (1)

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

1989 (1)

J. A. Salehi, “Code Division Multiple Access Techniques in Optical Fiber Networks I: Fundamental Principles,” IEEE Trans. Commun. 37, 824–833 (1989).
[Crossref]

1985 (1)

S. Tamura, S. Nakano, and K. Okazaki, “Optical Code-Multiplex Transmission by Gold Sequences,” J. Lightwave Technol. LT-3, 121–127 (1985).
[Crossref]

1980 (1)

D. L. Sarwate and M. B. Pursley, “Crosscorrelation Properties of Pseudorandom and Related Sequences,” Proc. IEEE 68, 593–619 (1980).
[Crossref]

Amaya, W.

Andonovic, I.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Baba, K.

Bostica, B.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Callegati, F.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Capmany, J.

Chen, L. K.

Y. G. Wen, Y. Zhang, and L. K. Chen, “On Architecture and Limitation of Optical Multiprotocol Label Switching (MPLS) Networks using Optical-Orthogonal-Code (OCC)/Wavelength Label,” Opt. Fiber Technol. 8, 43–70 (2002).
[Crossref]

Y. Zhang and L. K. Chen, “Performance Improvement by Code Conversion in a Reconfigurable Optical Code/Wavelength Routing Network,” in Proceedings of Optical Network Design and Management, (2001).

Chiaroni, D.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Chujo, W.

H. Sotobayashi, W. Chujo, and K. Kitayama, “Highly Spectral-Efficient Optical Code-Division Multiplexing Transmission System,” IEEE J. Sel. Top. Quantum Electron. 10, 250–258 (2004).
[Crossref]

H. Sotobayashi, W. Chujo, and K. Kitayama, “Transparent Virtual Code/Wavelength Path Network,” IEEE J. Sel. Top. Quantum Electron. 8, 699–704 (2002).
[Crossref]

Cincotti, G.

G. Manzacca, A. M. Vegni, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Performance Analysis of a Multiport Encoder/Decoder in OCDMA Scenario,” IEEE J. Sel. Top. Quantum Electron. 13, 1415–1421 (2007).
[Crossref]

X. Wang, N. Wada, T. Miyazaki, G. Cincotti, and K. Kitayama, “Asynchronous Multiuser Coherent OCDMA System with Code-Shift-Keying and Balanced Detection,” IEEE J. Sel. Top. Quantum Electron. 13, 1463–1470 (2007).
[Crossref]

G. Manzacca, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Comparative Study of Multiencoding Schemes for OCDM Using a Single Multiport Optical Encoder/Decoder,” IEEE Photon. Technol. Lett. 19, 559–561 (2007).
[Crossref]

Corazza, G.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Danielsen, S. L.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Eramo, V.

Gambini, P.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Goldberg, S.

S. Goldberg and P. R. Prucnal, “On the Teletraffic Capacity of Optical CDMA,” IEEE Trans. Commun. 55, 1334–1343 (2007).
[Crossref]

Guillemot, C.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Guo, Y.

Hamanaka, T.

T. Hamanaka, X. Wang, N. Wada, and K. Kitayama, “Compound Data Rate and Data-Rate-Flexible 622 Mb/s-10Gb/s OCDMA Experiments Using 511-Chip SSFBG and Cascaded SHG-DFG-Based PPLN Waveguide Optical Thresholder,” IEEE J. Sel. Top. Quantum Electron. 13, 1516–1521 (2007).
[Crossref]

Hansen, P. B.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Henry, M.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Huang, S.

Ibsen, M.

C. Tian, Z. Zhang, M. Ibsen, P. Petropoulos, and D. J. Richardson, “A 16-Channel Reconfigurable OCDMA/DWDM System Using Continuous Phase-Shift SSFBGs,” IEEE J. Sel. Top. Quantum Electron. 13, 1480–1486 (2007).
[Crossref]

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

P. C. Teh, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Phase Encoding and Decoding of Short Pulses at 10Gb/s using Superstructured Fiber Bragg Gratings,” IEEE Photon. Technol. Lett. 13, 154–156 (2001).
[Crossref]

Imai, T.

Janz, C.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Kaneko, S.

Kataoka, N.

Kitayama, K.

G. Manzacca, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Comparative Study of Multiencoding Schemes for OCDM Using a Single Multiport Optical Encoder/Decoder,” IEEE Photon. Technol. Lett. 19, 559–561 (2007).
[Crossref]

T. Hamanaka, X. Wang, N. Wada, and K. Kitayama, “Compound Data Rate and Data-Rate-Flexible 622 Mb/s-10Gb/s OCDMA Experiments Using 511-Chip SSFBG and Cascaded SHG-DFG-Based PPLN Waveguide Optical Thresholder,” IEEE J. Sel. Top. Quantum Electron. 13, 1516–1521 (2007).
[Crossref]

X. Wang, N. Wada, T. Miyazaki, G. Cincotti, and K. Kitayama, “Asynchronous Multiuser Coherent OCDMA System with Code-Shift-Keying and Balanced Detection,” IEEE J. Sel. Top. Quantum Electron. 13, 1463–1470 (2007).
[Crossref]

G. Manzacca, A. M. Vegni, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Performance Analysis of a Multiport Encoder/Decoder in OCDMA Scenario,” IEEE J. Sel. Top. Quantum Electron. 13, 1415–1421 (2007).
[Crossref]

S. Huang, K. Baba, M. Murata, and K. Kitayama, “Architecture Design and Performance Evaluation of Multi-granularity Optical Networks Based on Optical Code Division Multiplexing,” J. Opt. Netw. 5, 1028–1042 (2006).
[Crossref]

X. Wang, N. Wada, and K. Kitayama, “Inter-symbol interference and beat noise in flexible data-rate coherent OCDMA and the BER improvement by using optical thresholding,” Opt. Express 13, 10469–10474 (2005).
[Crossref] [PubMed]

X. Wang and K. Kitayama, “Analysis of Beat Noise in Coherent and incoherent Time-Spreading OCDMA,” J. Lightwave Technol. 22, 2226–2234 (2004).
[Crossref]

H. Sotobayashi, W. Chujo, and K. Kitayama, “Highly Spectral-Efficient Optical Code-Division Multiplexing Transmission System,” IEEE J. Sel. Top. Quantum Electron. 10, 250–258 (2004).
[Crossref]

H. Sotobayashi, W. Chujo, and K. Kitayama, “Transparent Virtual Code/Wavelength Path Network,” IEEE J. Sel. Top. Quantum Electron. 8, 699–704 (2002).
[Crossref]

K. Kitayama, H. Sotobayashi, and N. Wada, “1,6 b/s/Hz 6,4 Tb/s QPSK-OCDM/WDM (4 OCDM×40WDM×40Gb/s) Transmission Experiment using Optical Hard Thresholding,” IEEE Photon. Technol. Lett. 14, 555–557 (2002).
[Crossref]

K. Kitayama, H. Sotobayashi, and N. Wada, “1,52 Tbit/s OCDM/WDM (4 OCDM×19WDM×20 Gbit/s) Transmission Experiment,” Electron. Lett. 37, 700–701 (2001).
[Crossref]

K. Kitayama, “Code Division Multiplexing Lightwave Networks Based upon Optical Code Conversion,” IEEE J. Sel. Areas Comm. 16, 1309–1319 (2000).
[Crossref]

K. Kitayama, H. Sotobayashi, and N. Wada, “Optical Code Division Multiplexing (OCDM) and its Applications to Photonic Networks,” IEICE Trans. Fundamentals E82-A, 2616–2626 (1999).

Kitayama, K.-I.

Kloch, A.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Krhenbhl, R.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Kumozaki, K.

Li, Y.

Listanti, M.

Manzacca, G.

G. Manzacca, A. M. Vegni, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Performance Analysis of a Multiport Encoder/Decoder in OCDMA Scenario,” IEEE J. Sel. Top. Quantum Electron. 13, 1415–1421 (2007).
[Crossref]

G. Manzacca, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Comparative Study of Multiencoding Schemes for OCDM Using a Single Multiport Optical Encoder/Decoder,” IEEE Photon. Technol. Lett. 19, 559–561 (2007).
[Crossref]

Miki, N.

Miyazaki, T.

X. Wang, N. Wada, T. Miyazaki, G. Cincotti, and K. Kitayama, “Asynchronous Multiuser Coherent OCDMA System with Code-Shift-Keying and Balanced Detection,” IEEE J. Sel. Top. Quantum Electron. 13, 1463–1470 (2007).
[Crossref]

Mukherjee, B.

B. Mukherjee, Optical Communication Networks (Mc Graw-Hill, New York, 1997).

Murata, M.

Nakagawa, J.

Nakagawa, N.

Nakano, S.

S. Tamura, S. Nakano, and K. Okazaki, “Optical Code-Multiplex Transmission by Gold Sequences,” J. Lightwave Technol. LT-3, 121–127 (1985).
[Crossref]

Noda, M.

Nogami, M.

Okazaki, K.

S. Tamura, S. Nakano, and K. Okazaki, “Optical Code-Multiplex Transmission by Gold Sequences,” J. Lightwave Technol. LT-3, 121–127 (1985).
[Crossref]

Pastor, D.

Petropoulos, P.

C. Tian, Z. Zhang, M. Ibsen, P. Petropoulos, and D. J. Richardson, “A 16-Channel Reconfigurable OCDMA/DWDM System Using Continuous Phase-Shift SSFBGs,” IEEE J. Sel. Top. Quantum Electron. 13, 1480–1486 (2007).
[Crossref]

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

P. C. Teh, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Phase Encoding and Decoding of Short Pulses at 10Gb/s using Superstructured Fiber Bragg Gratings,” IEEE Photon. Technol. Lett. 13, 154–156 (2001).
[Crossref]

Prucnal, P. R.

S. Goldberg and P. R. Prucnal, “On the Teletraffic Capacity of Optical CDMA,” IEEE Trans. Commun. 55, 1334–1343 (2007).
[Crossref]

Pu, T.

Pursley, M. B.

D. L. Sarwate and M. B. Pursley, “Crosscorrelation Properties of Pseudorandom and Related Sequences,” Proc. IEEE 68, 593–619 (1980).
[Crossref]

Raffaelli, C.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Ramaswami, R.

R. Ramaswami and K. N. Sivarjan, Optical Networks (Morgan Kaufmann, New York, 1998).

Renaud, M.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Richardson, D. J.

C. Tian, Z. Zhang, M. Ibsen, P. Petropoulos, and D. J. Richardson, “A 16-Channel Reconfigurable OCDMA/DWDM System Using Continuous Phase-Shift SSFBGs,” IEEE J. Sel. Top. Quantum Electron. 13, 1480–1486 (2007).
[Crossref]

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

P. C. Teh, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Phase Encoding and Decoding of Short Pulses at 10Gb/s using Superstructured Fiber Bragg Gratings,” IEEE Photon. Technol. Lett. 13, 154–156 (2001).
[Crossref]

Salehi, J. A.

J. A. Salehi, “Code Division Multiple Access Techniques in Optical Fiber Networks I: Fundamental Principles,” IEEE Trans. Commun. 37, 824–833 (1989).
[Crossref]

Sarwate, D. L.

D. L. Sarwate and M. B. Pursley, “Crosscorrelation Properties of Pseudorandom and Related Sequences,” Proc. IEEE 68, 593–619 (1980).
[Crossref]

Schilling, M.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Sivarjan, K. N.

R. Ramaswami and K. N. Sivarjan, Optical Networks (Morgan Kaufmann, New York, 1998).

Sotobayashi, H.

H. Sotobayashi, W. Chujo, and K. Kitayama, “Highly Spectral-Efficient Optical Code-Division Multiplexing Transmission System,” IEEE J. Sel. Top. Quantum Electron. 10, 250–258 (2004).
[Crossref]

K. Kitayama, H. Sotobayashi, and N. Wada, “1,6 b/s/Hz 6,4 Tb/s QPSK-OCDM/WDM (4 OCDM×40WDM×40Gb/s) Transmission Experiment using Optical Hard Thresholding,” IEEE Photon. Technol. Lett. 14, 555–557 (2002).
[Crossref]

H. Sotobayashi, W. Chujo, and K. Kitayama, “Transparent Virtual Code/Wavelength Path Network,” IEEE J. Sel. Top. Quantum Electron. 8, 699–704 (2002).
[Crossref]

K. Kitayama, H. Sotobayashi, and N. Wada, “1,52 Tbit/s OCDM/WDM (4 OCDM×19WDM×20 Gbit/s) Transmission Experiment,” Electron. Lett. 37, 700–701 (2001).
[Crossref]

K. Kitayama, H. Sotobayashi, and N. Wada, “Optical Code Division Multiplexing (OCDM) and its Applications to Photonic Networks,” IEICE Trans. Fundamentals E82-A, 2616–2626 (1999).

Suzuki, N.

Talneau, A.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Tamura, S.

S. Tamura, S. Nakano, and K. Okazaki, “Optical Code-Multiplex Transmission by Gold Sequences,” J. Lightwave Technol. LT-3, 121–127 (1985).
[Crossref]

Taniguchi, T.

Teh, P. C.

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

P. C. Teh, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Phase Encoding and Decoding of Short Pulses at 10Gb/s using Superstructured Fiber Bragg Gratings,” IEEE Photon. Technol. Lett. 13, 154–156 (2001).
[Crossref]

Tian, C.

C. Tian, Z. Zhang, M. Ibsen, P. Petropoulos, and D. J. Richardson, “A 16-Channel Reconfigurable OCDMA/DWDM System Using Continuous Phase-Shift SSFBGs,” IEEE J. Sel. Top. Quantum Electron. 13, 1480–1486 (2007).
[Crossref]

Tsubokawa, M.

Vegni, A. M.

G. Manzacca, A. M. Vegni, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Performance Analysis of a Multiport Encoder/Decoder in OCDMA Scenario,” IEEE J. Sel. Top. Quantum Electron. 13, 1415–1421 (2007).
[Crossref]

Wada, N.

G. Manzacca, A. M. Vegni, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Performance Analysis of a Multiport Encoder/Decoder in OCDMA Scenario,” IEEE J. Sel. Top. Quantum Electron. 13, 1415–1421 (2007).
[Crossref]

X. Wang, N. Wada, T. Miyazaki, G. Cincotti, and K. Kitayama, “Asynchronous Multiuser Coherent OCDMA System with Code-Shift-Keying and Balanced Detection,” IEEE J. Sel. Top. Quantum Electron. 13, 1463–1470 (2007).
[Crossref]

G. Manzacca, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Comparative Study of Multiencoding Schemes for OCDM Using a Single Multiport Optical Encoder/Decoder,” IEEE Photon. Technol. Lett. 19, 559–561 (2007).
[Crossref]

T. Hamanaka, X. Wang, N. Wada, and K. Kitayama, “Compound Data Rate and Data-Rate-Flexible 622 Mb/s-10Gb/s OCDMA Experiments Using 511-Chip SSFBG and Cascaded SHG-DFG-Based PPLN Waveguide Optical Thresholder,” IEEE J. Sel. Top. Quantum Electron. 13, 1516–1521 (2007).
[Crossref]

X. Wang, N. Wada, and K. Kitayama, “Inter-symbol interference and beat noise in flexible data-rate coherent OCDMA and the BER improvement by using optical thresholding,” Opt. Express 13, 10469–10474 (2005).
[Crossref] [PubMed]

K. Kitayama, H. Sotobayashi, and N. Wada, “1,6 b/s/Hz 6,4 Tb/s QPSK-OCDM/WDM (4 OCDM×40WDM×40Gb/s) Transmission Experiment using Optical Hard Thresholding,” IEEE Photon. Technol. Lett. 14, 555–557 (2002).
[Crossref]

K. Kitayama, H. Sotobayashi, and N. Wada, “1,52 Tbit/s OCDM/WDM (4 OCDM×19WDM×20 Gbit/s) Transmission Experiment,” Electron. Lett. 37, 700–701 (2001).
[Crossref]

K. Kitayama, H. Sotobayashi, and N. Wada, “Optical Code Division Multiplexing (OCDM) and its Applications to Photonic Networks,” IEICE Trans. Fundamentals E82-A, 2616–2626 (1999).

Wang, X.

T. Hamanaka, X. Wang, N. Wada, and K. Kitayama, “Compound Data Rate and Data-Rate-Flexible 622 Mb/s-10Gb/s OCDMA Experiments Using 511-Chip SSFBG and Cascaded SHG-DFG-Based PPLN Waveguide Optical Thresholder,” IEEE J. Sel. Top. Quantum Electron. 13, 1516–1521 (2007).
[Crossref]

G. Manzacca, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Comparative Study of Multiencoding Schemes for OCDM Using a Single Multiport Optical Encoder/Decoder,” IEEE Photon. Technol. Lett. 19, 559–561 (2007).
[Crossref]

X. Wang, N. Wada, T. Miyazaki, G. Cincotti, and K. Kitayama, “Asynchronous Multiuser Coherent OCDMA System with Code-Shift-Keying and Balanced Detection,” IEEE J. Sel. Top. Quantum Electron. 13, 1463–1470 (2007).
[Crossref]

G. Manzacca, A. M. Vegni, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Performance Analysis of a Multiport Encoder/Decoder in OCDMA Scenario,” IEEE J. Sel. Top. Quantum Electron. 13, 1415–1421 (2007).
[Crossref]

X. Wang, N. Wada, and K. Kitayama, “Inter-symbol interference and beat noise in flexible data-rate coherent OCDMA and the BER improvement by using optical thresholding,” Opt. Express 13, 10469–10474 (2005).
[Crossref] [PubMed]

X. Wang and K. Kitayama, “Analysis of Beat Noise in Coherent and incoherent Time-Spreading OCDMA,” J. Lightwave Technol. 22, 2226–2234 (2004).
[Crossref]

Wen, Y. G.

Y. G. Wen, Y. Zhang, and L. K. Chen, “On Architecture and Limitation of Optical Multiprotocol Label Switching (MPLS) Networks using Optical-Orthogonal-Code (OCC)/Wavelength Label,” Opt. Fiber Technol. 8, 43–70 (2002).
[Crossref]

Yoshima, S.

Yoshimoto, N.

Yoshino, M.

Zhang, H.

Zhang, Y.

Y. G. Wen, Y. Zhang, and L. K. Chen, “On Architecture and Limitation of Optical Multiprotocol Label Switching (MPLS) Networks using Optical-Orthogonal-Code (OCC)/Wavelength Label,” Opt. Fiber Technol. 8, 43–70 (2002).
[Crossref]

Y. Zhang and L. K. Chen, “Performance Improvement by Code Conversion in a Reconfigurable Optical Code/Wavelength Routing Network,” in Proceedings of Optical Network Design and Management, (2001).

Zhang, Z.

C. Tian, Z. Zhang, M. Ibsen, P. Petropoulos, and D. J. Richardson, “A 16-Channel Reconfigurable OCDMA/DWDM System Using Continuous Phase-Shift SSFBGs,” IEEE J. Sel. Top. Quantum Electron. 13, 1480–1486 (2007).
[Crossref]

Zucchelli, L.

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

Electron. Lett. (1)

K. Kitayama, H. Sotobayashi, and N. Wada, “1,52 Tbit/s OCDM/WDM (4 OCDM×19WDM×20 Gbit/s) Transmission Experiment,” Electron. Lett. 37, 700–701 (2001).
[Crossref]

IEEE J. Sel. Areas Comm. (2)

K. Kitayama, “Code Division Multiplexing Lightwave Networks Based upon Optical Code Conversion,” IEEE J. Sel. Areas Comm. 16, 1309–1319 (2000).
[Crossref]

P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krhenbhl, C. Raffaelli, M. Schilling, A. Talneau, and L. Zucchelli, “Transparent Optical Packet Switching: Network Architecture and Demonstrators in the KEOPS project,” IEEE J. Sel. Areas Comm. 16, 1245–1259 (1998).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (6)

H. Sotobayashi, W. Chujo, and K. Kitayama, “Highly Spectral-Efficient Optical Code-Division Multiplexing Transmission System,” IEEE J. Sel. Top. Quantum Electron. 10, 250–258 (2004).
[Crossref]

H. Sotobayashi, W. Chujo, and K. Kitayama, “Transparent Virtual Code/Wavelength Path Network,” IEEE J. Sel. Top. Quantum Electron. 8, 699–704 (2002).
[Crossref]

G. Manzacca, A. M. Vegni, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Performance Analysis of a Multiport Encoder/Decoder in OCDMA Scenario,” IEEE J. Sel. Top. Quantum Electron. 13, 1415–1421 (2007).
[Crossref]

X. Wang, N. Wada, T. Miyazaki, G. Cincotti, and K. Kitayama, “Asynchronous Multiuser Coherent OCDMA System with Code-Shift-Keying and Balanced Detection,” IEEE J. Sel. Top. Quantum Electron. 13, 1463–1470 (2007).
[Crossref]

C. Tian, Z. Zhang, M. Ibsen, P. Petropoulos, and D. J. Richardson, “A 16-Channel Reconfigurable OCDMA/DWDM System Using Continuous Phase-Shift SSFBGs,” IEEE J. Sel. Top. Quantum Electron. 13, 1480–1486 (2007).
[Crossref]

T. Hamanaka, X. Wang, N. Wada, and K. Kitayama, “Compound Data Rate and Data-Rate-Flexible 622 Mb/s-10Gb/s OCDMA Experiments Using 511-Chip SSFBG and Cascaded SHG-DFG-Based PPLN Waveguide Optical Thresholder,” IEEE J. Sel. Top. Quantum Electron. 13, 1516–1521 (2007).
[Crossref]

IEEE Photon. Technol. Lett. (4)

K. Kitayama, H. Sotobayashi, and N. Wada, “1,6 b/s/Hz 6,4 Tb/s QPSK-OCDM/WDM (4 OCDM×40WDM×40Gb/s) Transmission Experiment using Optical Hard Thresholding,” IEEE Photon. Technol. Lett. 14, 555–557 (2002).
[Crossref]

G. Manzacca, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Comparative Study of Multiencoding Schemes for OCDM Using a Single Multiport Optical Encoder/Decoder,” IEEE Photon. Technol. Lett. 19, 559–561 (2007).
[Crossref]

P. C. Teh, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Phase Encoding and Decoding of Short Pulses at 10Gb/s using Superstructured Fiber Bragg Gratings,” IEEE Photon. Technol. Lett. 13, 154–156 (2001).
[Crossref]

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

IEEE Trans. Commun. (2)

S. Goldberg and P. R. Prucnal, “On the Teletraffic Capacity of Optical CDMA,” IEEE Trans. Commun. 55, 1334–1343 (2007).
[Crossref]

J. A. Salehi, “Code Division Multiple Access Techniques in Optical Fiber Networks I: Fundamental Principles,” IEEE Trans. Commun. 37, 824–833 (1989).
[Crossref]

IEICE Trans. Fundamentals (1)

K. Kitayama, H. Sotobayashi, and N. Wada, “Optical Code Division Multiplexing (OCDM) and its Applications to Photonic Networks,” IEICE Trans. Fundamentals E82-A, 2616–2626 (1999).

J. Lightwave Technol. (8)

W. Amaya, D. Pastor, and J. Capmany, “Modeling of a Time-Spreading OCDMA System Including Nonperfect Time Gating, Optical Thresholding and Fully Asynchronous Signal/Interference Overlapping,” J. Lightwave Technol. 26, 768–776 (2008).
[Crossref]

M. Yoshino, S. Kaneko, T. Taniguchi, N. Miki, K. Kumozaki, T. Imai, N. Yoshimoto, and M. Tsubokawa, “Beat Noise Mitigation of Spectral Amplitude Coding OCDMA Using Heterodyne Detection,” J. Lightwave Technol. 26, 962–970 (2008).
[Crossref]

S. Yoshima, N. Nakagawa, N. Kataoka, N. Suzuki, M. Noda, M. Nogami, J. Nakagawa, and K.-I. Kitayama, “10Gb/s-Based PON Over OCDMA Uplink Burst Transmission Using SSFBG Encoder/Multi-Port Decoder and Burst Mode Receiver,” J. Lightwave Technol. 28, 365–371 (2010).
[Crossref]

S. Tamura, S. Nakano, and K. Okazaki, “Optical Code-Multiplex Transmission by Gold Sequences,” J. Lightwave Technol. LT-3, 121–127 (1985).
[Crossref]

T. Pu, H. Zhang, Y. Guo, and Y. Li, “Evaluation of Beat Noise in OCDMA System with Non-Gaussian Approximated Method,” J. Lightwave Technol. 24, 3574–3582 (2006).
[Crossref]

V. Eramo, “An Analytical Model for TOWC Dimensioning in a Multifiber Optical-Packet Switch,” J. Lightwave Technol. 24, 4799–4810 (2006).
[Crossref]

V. Eramo and M. Listanti, “Packet Loss in a Bufferless WDM Switch Employing Shared Tuneable Wavelength Converters,” J. Lightwave Technol. 18, 1818–1833 (2000).
[Crossref]

X. Wang and K. Kitayama, “Analysis of Beat Noise in Coherent and incoherent Time-Spreading OCDMA,” J. Lightwave Technol. 22, 2226–2234 (2004).
[Crossref]

J. Opt. Netw. (1)

Opt. Express (1)

Opt. Fiber Technol. (1)

Y. G. Wen, Y. Zhang, and L. K. Chen, “On Architecture and Limitation of Optical Multiprotocol Label Switching (MPLS) Networks using Optical-Orthogonal-Code (OCC)/Wavelength Label,” Opt. Fiber Technol. 8, 43–70 (2002).
[Crossref]

Proc. IEEE (1)

D. L. Sarwate and M. B. Pursley, “Crosscorrelation Properties of Pseudorandom and Related Sequences,” Proc. IEEE 68, 593–619 (1980).
[Crossref]

Other (3)

R. Ramaswami and K. N. Sivarjan, Optical Networks (Morgan Kaufmann, New York, 1998).

B. Mukherjee, Optical Communication Networks (Mc Graw-Hill, New York, 1997).

Y. Zhang and L. K. Chen, “Performance Improvement by Code Conversion in a Reconfigurable Optical Code/Wavelength Routing Network,” in Proceedings of Optical Network Design and Management, (2001).

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Figures (9)

Fig. 1.
Fig. 1.

WDM/OCDM Optical Packet Switch.

Fig. 2.
Fig. 2.

Scheduling Algorithm in WDM/OCDM Optical Packet Switch; Initialization and Conversion Code phases are described.

Fig. 3.
Fig. 3.

Scheduling Algorithm in WDM/OCDM Optical Packet Switch; Wavelength Conversion phase is described.

Fig. 4.
Fig. 4.

Packet Loss Probability due to MAI and beat noise as a function of the number F of Optical Codes. The code length is L=511. The traffic parameters are H=500 bytes and p varying from 0.2 to 1.

Fig. 5.
Fig. 5.

Packet Loss Probability due to MAI and beat noise as a function of the number F of Optical Codes. The code length is L=1023. The traffic parameters are H=500 bytes and p varying from 0.2 to 1.

Fig. 6.
Fig. 6.

Packet Loss Probability due to MAI and beat noise as a function of the number F of Optical Codes. The code length is L=2047. The traffic parameters are H=500 bytes and p varying from 0.2 to 1.

Fig. 7.
Fig. 7.

Dimensioning of the number F of optical codes versus p for H=500 bytes, Pnoise,th loss = 10 −9 and L=1023, 2047. The ratio of the number of optical codes for L=1023 to the number of optical codes for L=2047 is also reported.

Fig. 8.
Fig. 8.

Packet Loss Probability Popc loss due to output packet contentions as a function of the number r of used WCs for p=0.6, 0.7, 0.8, N=8, H=500 bytes and (M,L)={(8,2047),(16,1023)}. The threshold Packet Loss Probability Pnoise,th loss due to MAI and beat noise is 10−9.

Fig. 9.
Fig. 9.

OCDM Receiver model and noise sources.

Tables (1)

Tables Icon

Table 1. Packet Loss Probability Popc loss due to output packets contentions versus the number M of wavelengths and the code length L for r=8, 78, N=8, H=500 bytes and Pnoise,th loss =10−9, p=0.6, 0.7, 0.8

Equations (22)

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

P loss noise = i = 0 F P loss noise , i ( F i ) p i ( 1 p ) F i .
P loss noise , i = { 0 i = 0 , 1 1 ( 1 P bit noise , i ) H i = 2 , , F
P bit noise , i = { 0 i = 0 , 1 ( 1 2 ) i 1 h = 0 i 1 ( i 1 h ) P bit , h noise , i , target i = 2 , , F
P bit , h noise , i , target = 1 4 erfc ( th i m Z 0 , h 2 σ Z 0 , h ) + 1 4 erfc ( m Z 1 , h th i 2 σ Z 1 , h ) .
m Z 0 , h = 1 2 h T c ( L + 1 1 L ) MAI noise .
m Z 1 , h = 1 2 T c L 2 Signal + 1 2 h T c ( L + 1 1 L ) MAI noise .
σ Z 0 , h = T c 1 4 h ( L 2 + 2 L 2 L 1 L 2 ) MAI noise + 1 4 h ( h 1 ) ( L + 1 1 L ) 2 Secondary Beat noise .
σ Z 1 , h = T c 1 4 h ( L 2 + 2 L 2 L 1 L 2 ) MAI noise + 1 2 h L 2 ( L + 1 1 L ) Primary Beat noise + 1 4 h ( h 1 ) ( L + 1 1 L ) 2 Secondary Beat noise .
th i = σ Z 0 , 1 2 ( i 1 ) m Z 1 , 1 2 ( i 1 ) + σ Z 1 , 1 2 ( i 1 ) m Z 0 , 1 2 ( i 1 ) σ Z 0 , 1 2 ( i 1 ) + σ Z 1 , 1 2 ( i 1 ) .
P loss opc = i = 0 r P loss opc , OF , i p Q ( i ) .
p Q ( i ) = { 1 N j = 1 N p W j 1 ( r i ) i 0 1 N j = 1 N h = r j ( M 1 ) p W j 1 ( h ) i = 0
pW j ( i ) = { δ ( i ) j = 0 pW ( i ) …… pW ( i ) ( j 1 ) times j 0
δ ( i ) = { 1 if i = 0 0 if i 0
Z a , h = 1 2 a T c S ac 2 signal + 1 2 T c j = 1 h S cc , j 2 MAI noise + a T c j = 1 h S ac S cc , j cos Δ φ d , j Primary Beat noise + T c j = 1 h 1 u = j + 1 h S cc , j S cc , u cos Δ φ j , u . Secondary Beat noise
S cc = { 1 + t with probability α L 1 with probability 1 t with probability γ L β L
m S cc 2 = L + 1 1 L σ S cc 2 2 = L 2 + 2 L 2 L 1 L 2 .
P bit , h noise , i , target = 1 4 erfc ( th i m Z 0 , h 2 σ Z 0 , h ) + 1 4 erfc ( m Z 1 , h th i 2 σ Z 1 , h ) .
m Z a , h = 1 2 a T c L 2 + 1 2 T c j = 1 h m S cc , j 2 + a T c L j = 1 h m S cc , j m cos φ d , j + T c j = 1 h 1 u = j + 1 h m S cc , j m S cc , u m cos φ j , u .
σ Z a , h 2 = 1 4 h 2 T c 2 σ S cc 2 2 + a 2 T c 2 L 2 j = 1 h m S cc , j 2 m cos φ d , j 2 + 2 T c 2 j = 1 h 1 u = j + 1 h m S cc , j 2 m S cc , u 2 m cos φ j , u 2 .
m Z a , h = 1 2 a T c L 2 + 1 2 h T c ( L + 1 1 L ) .
σ Z a , h 2 = 2 T c 2 ( 1 4 h ( L 2 + 2 L 2 L 1 L 2 ) + 1 2 ahL 2 ( L + 1 1 L ) + 1 4 h ( h 1 ) ( L + 1 1 L ) 2 ) .
th i = σ Z 0 , 1 2 ( i 1 ) m Z 1 , 1 2 ( i 1 ) + σ Z 1 , 1 2 ( i 1 ) m Z 0 , 1 2 ( i 1 ) σ Z 0 , 1 2 ( i 1 ) + σ Z 1 , 1 2 ( i 1 ) .

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