Abstract

For transmission within optical mesh networks, different signal routes acquire different impairments and are received with different signal-to-noise ratios (SNRs). The SNR can be utilized through adaptive bit- and code-rate modulation, which leads to data rates that are not multiples of the preferred 100 GbE client rate. This paper considers the use of slower 25 GbE lanes both with inverse multiplexed 100 GbE client rates and with native 25 GbE client rates and compares network blocking performance. The use of inverse multiplexed 100 GbE client data on four 25 GbE lanes accesses the lion’s share of stranded capacity within the network.

© 2016 Optical Society of America

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References

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    [Crossref]
  2. M. Arabaci, I. B. Djordjevic, L. Xu, and T. Wang, “Nonbinary LDPC-coded modulation for rate-adaptive optical fiber communication without bandwidth expansion,” IEEE Photonics Technol. Lett., vol. 24, no. 16, pp. 1402–1404, Aug. 2012.
    [Crossref]
  3. L. Potì, G. Meloni, G. Berrettini, F. Fresi, M. Secondini, T. Foggi, and G. Colavolpe, “Casting 1  Tb/s DP-QPSK communication into 200 GHz bandwidth,” in European Conf. on Optical Communication, Brussels, Belgium, 2012, paper P4.19.
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    [Crossref]
  5. A. Alvarado, D. J. Ives, S. J. Savory, and P. Bayvel, “On optimal modulation and FEC overhead for future optical networks,” in Optical Fiber Communication Conf., Los Angeles, CA, 2015, paper Th3E.1.
  6. D. J. Ives, P. Bayvel, and S. J. Savory, “Assessment of options for utilizing SNR margin to increase network data throughput,” in Optical Fiber Communication Conf., Los Angeles, CA, Mar. 2015, paper M2I.3.
  7. D. J. Ives, P. Bayvel, and S. J. Savory, “Physical layer transmitter and routing optimization to maximize the traffic throughput of a nonlinear optical mesh network,” in Optical Network Design and Modeling, Stockholm, Sweden, May 2014, pp. 168–173.
  8. M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, Nov. 2009.
    [Crossref]
  9. O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag., vol. 50, no. 2, pp. s12–s20, Feb. 2012.
    [Crossref]
  10. F. Fresi, “Self-adaptation technique for bandwidth-variable transponders,” in Photonics in Switching, 2015, pp. 157–159.
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    [Crossref]
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  13. X. Zhao, V. Vusirikala, B. Koley, V. Kamalov, and T. Hofmeister, “The prospect of inter-data-center optical networks,” IEEE Commun. Mag., vol. 51, no. 9, pp. 32–38, Sept. 2013.
    [Crossref]
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    [Crossref]
  17. P. Poggiolini, “The GN-model of fiber non-linear propagation and its applications,” J. Lightwave Technol., vol. 32, no. 4, pp. 694–721, Feb. 2014.
    [Crossref]
  18. S. J. Savory, “Congestion aware routing in nonlinear elastic optical networks,” IEEE Photonics Technol. Lett., vol. 26, no. 10, pp. 1057–1060, May 2014.
    [Crossref]
  19. A. Alvarado, D. J. Ives, S. J. Savory, and P. Bayvel, “On the impact of optimal modulation and FEC overhead on future optical networks,” J. Lightwave Technol., vol. 34, no. 9, pp. 2339–2352, May 2016.
    [Crossref]

2016 (2)

2014 (3)

2013 (1)

X. Zhao, V. Vusirikala, B. Koley, V. Kamalov, and T. Hofmeister, “The prospect of inter-data-center optical networks,” IEEE Commun. Mag., vol. 51, no. 9, pp. 32–38, Sept. 2013.
[Crossref]

2012 (4)

P. Poggiolini, “The GN model of non-linear propagation in uncompensated coherent optical systems,” J. Lightwave Technol., vol. 30, no. 24, pp. 3857–3879, Dec. 2012.
[Crossref]

G.-H. Gho and J. M. Kahn, “Rate-adaptive modulation and coding for optical fiber transmission systems,” J. Lightwave Technol., vol. 30, no. 12, pp. 1818–1828, June 2012.
[Crossref]

M. Arabaci, I. B. Djordjevic, L. Xu, and T. Wang, “Nonbinary LDPC-coded modulation for rate-adaptive optical fiber communication without bandwidth expansion,” IEEE Photonics Technol. Lett., vol. 24, no. 16, pp. 1402–1404, Aug. 2012.
[Crossref]

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag., vol. 50, no. 2, pp. s12–s20, Feb. 2012.
[Crossref]

2009 (1)

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, Nov. 2009.
[Crossref]

Alvarado, A.

A. Alvarado, D. J. Ives, S. J. Savory, and P. Bayvel, “On the impact of optimal modulation and FEC overhead on future optical networks,” J. Lightwave Technol., vol. 34, no. 9, pp. 2339–2352, May 2016.
[Crossref]

A. Alvarado, D. J. Ives, S. J. Savory, and P. Bayvel, “On optimal modulation and FEC overhead for future optical networks,” in Optical Fiber Communication Conf., Los Angeles, CA, 2015, paper Th3E.1.

Arabaci, M.

M. Arabaci, I. B. Djordjevic, L. Xu, and T. Wang, “Nonbinary LDPC-coded modulation for rate-adaptive optical fiber communication without bandwidth expansion,” IEEE Photonics Technol. Lett., vol. 24, no. 16, pp. 1402–1404, Aug. 2012.
[Crossref]

Barreto, A. N.

Bayvel, P.

A. Alvarado, D. J. Ives, S. J. Savory, and P. Bayvel, “On the impact of optimal modulation and FEC overhead on future optical networks,” J. Lightwave Technol., vol. 34, no. 9, pp. 2339–2352, May 2016.
[Crossref]

A. Alvarado, D. J. Ives, S. J. Savory, and P. Bayvel, “On optimal modulation and FEC overhead for future optical networks,” in Optical Fiber Communication Conf., Los Angeles, CA, 2015, paper Th3E.1.

D. J. Ives, P. Bayvel, and S. J. Savory, “Assessment of options for utilizing SNR margin to increase network data throughput,” in Optical Fiber Communication Conf., Los Angeles, CA, Mar. 2015, paper M2I.3.

D. J. Ives, P. Bayvel, and S. J. Savory, “Physical layer transmitter and routing optimization to maximize the traffic throughput of a nonlinear optical mesh network,” in Optical Network Design and Modeling, Stockholm, Sweden, May 2014, pp. 168–173.

Berrettini, G.

L. Potì, G. Meloni, G. Berrettini, F. Fresi, M. Secondini, T. Foggi, and G. Colavolpe, “Casting 1  Tb/s DP-QPSK communication into 200 GHz bandwidth,” in European Conf. on Optical Communication, Brussels, Belgium, 2012, paper P4.19.

Beygi, L.

Castoldi, P.

Colavolpe, G.

L. Potì, G. Meloni, G. Berrettini, F. Fresi, M. Secondini, T. Foggi, and G. Colavolpe, “Casting 1  Tb/s DP-QPSK communication into 200 GHz bandwidth,” in European Conf. on Optical Communication, Brussels, Belgium, 2012, paper P4.19.

Cugini, F.

D’Errico, A.

de Lima, T. C.

Djordjevic, I. B.

M. Arabaci, I. B. Djordjevic, L. Xu, and T. Wang, “Nonbinary LDPC-coded modulation for rate-adaptive optical fiber communication without bandwidth expansion,” IEEE Photonics Technol. Lett., vol. 24, no. 16, pp. 1402–1404, Aug. 2012.
[Crossref]

Foggi, T.

L. Potì, G. Meloni, G. Berrettini, F. Fresi, M. Secondini, T. Foggi, and G. Colavolpe, “Casting 1  Tb/s DP-QPSK communication into 200 GHz bandwidth,” in European Conf. on Optical Communication, Brussels, Belgium, 2012, paper P4.19.

Fresi, F.

F. Cugini, F. Paolucci, F. Fresi, G. Meloni, N. Sambo, L. Potì, A. D’Errico, and P. Castoldi, “Toward plug-and-play software-defined elastic optical networks,” J. Lightwave Technol., vol. 34, no. 6, pp. 1494–1500, Mar. 2016.
[Crossref]

L. Potì, G. Meloni, G. Berrettini, F. Fresi, M. Secondini, T. Foggi, and G. Colavolpe, “Casting 1  Tb/s DP-QPSK communication into 200 GHz bandwidth,” in European Conf. on Optical Communication, Brussels, Belgium, 2012, paper P4.19.

F. Fresi, “Self-adaptation technique for bandwidth-variable transponders,” in Photonics in Switching, 2015, pp. 157–159.

Gerstel, O.

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag., vol. 50, no. 2, pp. s12–s20, Feb. 2012.
[Crossref]

Gho, G.-H.

Hofmeister, T.

X. Zhao, V. Vusirikala, B. Koley, V. Kamalov, and T. Hofmeister, “The prospect of inter-data-center optical networks,” IEEE Commun. Mag., vol. 51, no. 9, pp. 32–38, Sept. 2013.
[Crossref]

Ives, D. J.

A. Alvarado, D. J. Ives, S. J. Savory, and P. Bayvel, “On the impact of optimal modulation and FEC overhead on future optical networks,” J. Lightwave Technol., vol. 34, no. 9, pp. 2339–2352, May 2016.
[Crossref]

D. J. Ives, A. Lord, P. Wright, and S. J. Savory, “Quantifying the impact of non-linear impairments on blocking load in elastic optical networks,” in Optical Fiber Communication Conf., San Francisco, CA, Mar. 2014, paper W2A.55.

D. J. Ives, P. Bayvel, and S. J. Savory, “Physical layer transmitter and routing optimization to maximize the traffic throughput of a nonlinear optical mesh network,” in Optical Network Design and Modeling, Stockholm, Sweden, May 2014, pp. 168–173.

D. J. Ives, P. Bayvel, and S. J. Savory, “Assessment of options for utilizing SNR margin to increase network data throughput,” in Optical Fiber Communication Conf., Los Angeles, CA, Mar. 2015, paper M2I.3.

A. Alvarado, D. J. Ives, S. J. Savory, and P. Bayvel, “On optimal modulation and FEC overhead for future optical networks,” in Optical Fiber Communication Conf., Los Angeles, CA, 2015, paper Th3E.1.

Jinno, M.

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag., vol. 50, no. 2, pp. s12–s20, Feb. 2012.
[Crossref]

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, Nov. 2009.
[Crossref]

Kahn, J. M.

Kamalov, V.

X. Zhao, V. Vusirikala, B. Koley, V. Kamalov, and T. Hofmeister, “The prospect of inter-data-center optical networks,” IEEE Commun. Mag., vol. 51, no. 9, pp. 32–38, Sept. 2013.
[Crossref]

Koley, B.

X. Zhao, V. Vusirikala, B. Koley, V. Kamalov, and T. Hofmeister, “The prospect of inter-data-center optical networks,” IEEE Commun. Mag., vol. 51, no. 9, pp. 32–38, Sept. 2013.
[Crossref]

Kozicki, B.

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, Nov. 2009.
[Crossref]

Lord, A.

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag., vol. 50, no. 2, pp. s12–s20, Feb. 2012.
[Crossref]

D. J. Ives, A. Lord, P. Wright, and S. J. Savory, “Quantifying the impact of non-linear impairments on blocking load in elastic optical networks,” in Optical Fiber Communication Conf., San Francisco, CA, Mar. 2014, paper W2A.55.

Matsuoka, S.

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, Nov. 2009.
[Crossref]

Mello, D. A. A.

Meloni, G.

F. Cugini, F. Paolucci, F. Fresi, G. Meloni, N. Sambo, L. Potì, A. D’Errico, and P. Castoldi, “Toward plug-and-play software-defined elastic optical networks,” J. Lightwave Technol., vol. 34, no. 6, pp. 1494–1500, Mar. 2016.
[Crossref]

L. Potì, G. Meloni, G. Berrettini, F. Fresi, M. Secondini, T. Foggi, and G. Colavolpe, “Casting 1  Tb/s DP-QPSK communication into 200 GHz bandwidth,” in European Conf. on Optical Communication, Brussels, Belgium, 2012, paper P4.19.

Paolucci, F.

Poggiolini, P.

Portela, T. F.

Potì, L.

F. Cugini, F. Paolucci, F. Fresi, G. Meloni, N. Sambo, L. Potì, A. D’Errico, and P. Castoldi, “Toward plug-and-play software-defined elastic optical networks,” J. Lightwave Technol., vol. 34, no. 6, pp. 1494–1500, Mar. 2016.
[Crossref]

L. Potì, G. Meloni, G. Berrettini, F. Fresi, M. Secondini, T. Foggi, and G. Colavolpe, “Casting 1  Tb/s DP-QPSK communication into 200 GHz bandwidth,” in European Conf. on Optical Communication, Brussels, Belgium, 2012, paper P4.19.

Sambo, N.

Savory, S. J.

A. Alvarado, D. J. Ives, S. J. Savory, and P. Bayvel, “On the impact of optimal modulation and FEC overhead on future optical networks,” J. Lightwave Technol., vol. 34, no. 9, pp. 2339–2352, May 2016.
[Crossref]

S. J. Savory, “Congestion aware routing in nonlinear elastic optical networks,” IEEE Photonics Technol. Lett., vol. 26, no. 10, pp. 1057–1060, May 2014.
[Crossref]

D. J. Ives, A. Lord, P. Wright, and S. J. Savory, “Quantifying the impact of non-linear impairments on blocking load in elastic optical networks,” in Optical Fiber Communication Conf., San Francisco, CA, Mar. 2014, paper W2A.55.

A. Alvarado, D. J. Ives, S. J. Savory, and P. Bayvel, “On optimal modulation and FEC overhead for future optical networks,” in Optical Fiber Communication Conf., Los Angeles, CA, 2015, paper Th3E.1.

D. J. Ives, P. Bayvel, and S. J. Savory, “Assessment of options for utilizing SNR margin to increase network data throughput,” in Optical Fiber Communication Conf., Los Angeles, CA, Mar. 2015, paper M2I.3.

D. J. Ives, P. Bayvel, and S. J. Savory, “Physical layer transmitter and routing optimization to maximize the traffic throughput of a nonlinear optical mesh network,” in Optical Network Design and Modeling, Stockholm, Sweden, May 2014, pp. 168–173.

Secondini, M.

L. Potì, G. Meloni, G. Berrettini, F. Fresi, M. Secondini, T. Foggi, and G. Colavolpe, “Casting 1  Tb/s DP-QPSK communication into 200 GHz bandwidth,” in European Conf. on Optical Communication, Brussels, Belgium, 2012, paper P4.19.

Sone, Y.

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, Nov. 2009.
[Crossref]

Takara, H.

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, Nov. 2009.
[Crossref]

Tsukishima, Y.

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, Nov. 2009.
[Crossref]

Vusirikala, V.

X. Zhao, V. Vusirikala, B. Koley, V. Kamalov, and T. Hofmeister, “The prospect of inter-data-center optical networks,” IEEE Commun. Mag., vol. 51, no. 9, pp. 32–38, Sept. 2013.
[Crossref]

Wang, T.

M. Arabaci, I. B. Djordjevic, L. Xu, and T. Wang, “Nonbinary LDPC-coded modulation for rate-adaptive optical fiber communication without bandwidth expansion,” IEEE Photonics Technol. Lett., vol. 24, no. 16, pp. 1402–1404, Aug. 2012.
[Crossref]

Wright, P.

D. J. Ives, A. Lord, P. Wright, and S. J. Savory, “Quantifying the impact of non-linear impairments on blocking load in elastic optical networks,” in Optical Fiber Communication Conf., San Francisco, CA, Mar. 2014, paper W2A.55.

Xu, L.

M. Arabaci, I. B. Djordjevic, L. Xu, and T. Wang, “Nonbinary LDPC-coded modulation for rate-adaptive optical fiber communication without bandwidth expansion,” IEEE Photonics Technol. Lett., vol. 24, no. 16, pp. 1402–1404, Aug. 2012.
[Crossref]

Yoo, S. J. B.

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag., vol. 50, no. 2, pp. s12–s20, Feb. 2012.
[Crossref]

Zhao, X.

X. Zhao, V. Vusirikala, B. Koley, V. Kamalov, and T. Hofmeister, “The prospect of inter-data-center optical networks,” IEEE Commun. Mag., vol. 51, no. 9, pp. 32–38, Sept. 2013.
[Crossref]

IEEE Commun. Mag. (3)

M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, and S. Matsuoka, “Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies,” IEEE Commun. Mag., vol. 47, no. 11, pp. 66–73, Nov. 2009.
[Crossref]

O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag., vol. 50, no. 2, pp. s12–s20, Feb. 2012.
[Crossref]

X. Zhao, V. Vusirikala, B. Koley, V. Kamalov, and T. Hofmeister, “The prospect of inter-data-center optical networks,” IEEE Commun. Mag., vol. 51, no. 9, pp. 32–38, Sept. 2013.
[Crossref]

IEEE Photonics Technol. Lett. (2)

S. J. Savory, “Congestion aware routing in nonlinear elastic optical networks,” IEEE Photonics Technol. Lett., vol. 26, no. 10, pp. 1057–1060, May 2014.
[Crossref]

M. Arabaci, I. B. Djordjevic, L. Xu, and T. Wang, “Nonbinary LDPC-coded modulation for rate-adaptive optical fiber communication without bandwidth expansion,” IEEE Photonics Technol. Lett., vol. 24, no. 16, pp. 1402–1404, Aug. 2012.
[Crossref]

J. Lightwave Technol. (6)

Other (8)

D. J. Ives, A. Lord, P. Wright, and S. J. Savory, “Quantifying the impact of non-linear impairments on blocking load in elastic optical networks,” in Optical Fiber Communication Conf., San Francisco, CA, Mar. 2014, paper W2A.55.

25 Gb/s Ethernet Task Force, IEEE P802.3, 2015 [Online]. Available: http://www.ieee802.org/3/by .

25 Gigabit Ethernet Consortium [Online]. Available: http://25gethernet.org .

A. Alvarado, D. J. Ives, S. J. Savory, and P. Bayvel, “On optimal modulation and FEC overhead for future optical networks,” in Optical Fiber Communication Conf., Los Angeles, CA, 2015, paper Th3E.1.

D. J. Ives, P. Bayvel, and S. J. Savory, “Assessment of options for utilizing SNR margin to increase network data throughput,” in Optical Fiber Communication Conf., Los Angeles, CA, Mar. 2015, paper M2I.3.

D. J. Ives, P. Bayvel, and S. J. Savory, “Physical layer transmitter and routing optimization to maximize the traffic throughput of a nonlinear optical mesh network,” in Optical Network Design and Modeling, Stockholm, Sweden, May 2014, pp. 168–173.

L. Potì, G. Meloni, G. Berrettini, F. Fresi, M. Secondini, T. Foggi, and G. Colavolpe, “Casting 1  Tb/s DP-QPSK communication into 200 GHz bandwidth,” in European Conf. on Optical Communication, Brussels, Belgium, 2012, paper P4.19.

F. Fresi, “Self-adaptation technique for bandwidth-variable transponders,” in Photonics in Switching, 2015, pp. 157–159.

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Figures (7)

Fig. 1.
Fig. 1. Transceiver hardware connection options considered: (a) is used with simulation options 1) and 2), (b) is used with simulation option 3), and (c) is used with simulation option 4).
Fig. 2.
Fig. 2. Nonlinear interference factor X ( L ) versus span length.
Fig. 3.
Fig. 3. Client data rate versus symbol SNR for various code rate and modulation formats.
Fig. 4.
Fig. 4. BT 20 + 2 node UK core topology showing link lengths in kilometers (km). The two yellow nodes did not supply or receive traffic and are for routing purposes only.
Fig. 5.
Fig. 5. Process of routing and accepting sequential demands.
Fig. 6.
Fig. 6. Blocking probability versus network load for the BT 20 + 2 node UK core network. For the four transceiver configurations considered, FF = fixed FEC-OH, and AF = adaptive FEC-OH.
Fig. 7.
Fig. 7. Number of active transceivers versus network load for the BT 20 + 2 node UK core network. For the four transceiver configurations considered, FF = fixed FEC-OH, and AF = adaptive FEC-OH. The triangle, circle, and square symbols correspond to blocking probabilities of 0.1%, 1%, and 10%, respectively. The dotted line indicates 380 transceivers, the minimum required to fully connect the network.

Tables (2)

Tables Icon

TABLE I Modulation Formats, Data Rates, and Required Symbol SNRs for the 32 Gbaud Signals Used

Tables Icon

TABLE II Network Load for a Number of Blocking Probabilities and the Number of Active Transceivers at a Network Load of 200    Tb · s 1 for the Four Transceiver Configurations Considered

Equations (9)

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

SNR = p i ASE i + p 3 j X ( L j ) ,
ASE i = 10 NF 10 h ν 10 A i 10 R ,
X ( L ) = 16 27 γ 2 g ( f 1 ) g ( f 2 ) g ( f 1 + f 2 f ) H ( f ) × 1 + e 2 α L 2 e α L cos [ 4 π 2 β 2 ( f 1 f ) ( f 2 f ) L ] α 2 + [ 4 π 2 β 2 ( f 1 f ) ( f 2 f ) ] 2 d f 1 d f 2 d f ,
g ( f ) = 1 R i = 50 49 rect ( f + i * Δ f R ) ,
H ( f ) = rect ( f R ) .
X ( L ) = X ( ) [ 1 e a 0 L ] a 1 ,
r c = 1 + P b log 2 [ P b ] + ( 1 P b ) log 2 [ 1 P b ] ,
CBP i = Block i i ,
BP i = ( i + 1 ) CBP i + 1 i CBP i .