Performance of subcarrier-wave quantum key distribution in the presence of spontaneous Raman scattering noise generated by classical DWDM channels

F. Kiselev; R. Goncharov; N. Veselkova; E. Samsonov; E. Samsonov; A. D. Kiselev; V. Egorov; V. Egorov

doi:10.1364/JOSAB.412289

Journal of the Optical Society of America B
Vol. 38,
Issue 2,
pp. 595-601
(2021)
•https://doi.org/10.1364/JOSAB.412289

Performance of subcarrier-wave quantum key distribution in the presence of spontaneous Raman scattering noise generated by classical DWDM channels

F. Kiselev, R. Goncharov, N. Veselkova, E. Samsonov, A. D. Kiselev, and V. Egorov

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F. Kiselev, R. Goncharov, N. Veselkova, E. Samsonov, A. D. Kiselev, and V. Egorov, "Performance of subcarrier-wave quantum key distribution in the presence of spontaneous Raman scattering noise generated by classical DWDM channels," J. Opt. Soc. Am. B 38, 595-601 (2021)

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Abstract

In this paper, we study the performance of the subcarrier-wave quantum key distribution system (SCW QKD) in the presence of spontaneous Raman scattering (SpRS) noise generated by classical channels of the dense wavelength division multiplexing (DWDM) network within a single-mode optical fiber. We present the mathematical model for evaluation of the quantum bit error rate and secure key generation rate with the SpRS noise taken into account. We consider two regimes of the SCW QKD system: the continuous wave regime, which uses a continuous wave laser, and the pulsed regime. For these regimes, performance of the system is analyzed depending on receiver sensitivity of classical DWDM. It is found that the pulsed regime outperforms the continuous wave regime in both the secure key generation rate and maximum achievable distance.

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Year
Author
Publication

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L.-J. Wang, L.-K. Chen, L. Ju, M.-L. Xu, Y. Zhao, K. Chen, Z.-B. Chen, T.-Y. Chen, and J.-W. Pan, “Experimental multiplexing of quantum key distribution with classical optical communication,” Appl. Phys. Lett. 106, 081108 (2015).
[Crossref]
B. Fröhlich, M. Lucamarini, J. F. Dynes, L. C. Comandar, W. W.-S. Tam, A. Plews, A. W. Sharpe, Z. Yuan, and A. J. Shields, “Long-distance quantum key distribution secure against coherent attacks,” Optica 4, 163–167 (2017).
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P. Townsend, “Simultaneous quantum cryptographic key distribution and conventional data transmission over installed fibre using wavelength-division multiplexing,” Electron. Lett. 33, 188–190 (1997).
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T. E. Chapuran, P. Toliver, N. A. Peters, J. Jackel, M. S. Goodman, R. J. Runser, S. R. McNown, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, C. G. Peterson, K. T. Tyagi, L. Mercer, and H. Dardy, “Optical networking for quantum key distribution and quantum communications,” New J. Phys. 11, 105001 (2009).
[Crossref]
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[Crossref]
L.-J. Wang, K.-H. Zou, W. Sun, Y. Mao, Y.-X. Zhu, H.-L. Yin, Q. Chen, Y. Zhao, F. Zhang, T.-Y. Chen, and J.-W. Pan, “Long-distance copropagation of quantum key distribution and terabit classical optical data channels,” Phys. Rev. A 95, 012301 (2017).
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J. Mora, W. Amaya, A. Ruiz-Alba, A. Martinez, D. Calvo, V. G. Muñoz, and J. Capmany, “Simultaneous transmission of 20x2 WDM/SCM-QKD and 4 bidirectional classical channels over a PON,” Opt. Express 20, 16358–16365 (2012).
[Crossref]
R. Kumar, H. Qin, and R. Alléaume, “Coexistence of continuous variable QKD with intense DWDM classical channels,” New J. Phys. 17, 043027 (2015).
[Crossref]
S. Bahrani, M. Razavi, and J. A. Salehi, “Wavelength assignment in hybrid quantum-classical networks,” Sci. Rep. 8, 3456 (2018).
[Crossref]
T. Ferreira da Silva, G. B. Xavier, G. P. Temporao, and J. P. von der Weid, “Impact of Raman scattered noise from multiple telecom channels on fiber-optic quantum key distribution systems,” J. Lightwave Technol. 32, 2332–2339 (2014).
[Crossref]
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[Crossref]
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[Crossref]
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[Crossref]
F. Kiselev, E. Samsonov, R. Goncharov, V. Chistyakov, A. Halturinsky, V. Egorov, A. Kozubov, A. Gaidash, and A. Gleĭm, “Analysis of the chromatic dispersion effect on the subcarrier wave QKD system,” Opt. Express 28, 28696–28712 (2020).
[Crossref]
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[Crossref]
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[Crossref]
A. V. Gleim, V. I. Egorov, Y. V. Nazarov, S. V. Smirnov, V. V. Chistyakov, O. I. Bannik, A. A. Anisimov, S. M. Kynev, A. E. Ivanova, R. J. Collins, S. A. Kozlov, and G. S. Buller, “Secure polarization-independent subcarrier quantum key distribution in optical fiber channel using BB84 protocol with a strong reference,” Opt. Express 24, 2619–2633 (2016).
[Crossref]
G. P. Miroshnichenko, A. V. Kozubov, A. A. Gaidash, A. V. Gleim, and D. B. Horoshko, “Security of subcarrier wave quantum key distribution against the collective beam-splitting attack,” Opt. Express 26, 11292–11308 (2018).
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[Crossref]

S. Bahrani, M. Razavi, and J. A. Salehi, “Wavelength assignment in hybrid quantum-classical networks,” Sci. Rep. 8, 3456 (2018).
[Crossref]

Z.-Q. Yin, S. Wang, W. Chen, Y.-G. Han, R. Wang, G.-C. Guo, and Z.-F. Han, “Improved security bound for the round-robin-differential-phase-shift quantum key distribution,” Nat. Commun. 9, 457 (2018).
[Crossref]

Q. Li, C. Zhu, S. Ma, K. Wei, and C. Pei, “Reference-frame-independent and measurement-device-independent quantum key distribution using one single source,” Int. J. Theor. Phys. 57, 2192–2202 (2018).
[Crossref]

J.-N. Niu, Y.-M. Sun, C. Cai, and Y.-F. Ji, “Optimized channel allocation scheme for jointly reducing four-wave mixing and Raman scattering in the DWDM-QKD system,” Appl. Opt. 57, 7987–7996 (2018).
[Crossref]

2017 (6)

B. Fröhlich, M. Lucamarini, J. F. Dynes, L. C. Comandar, W. W.-S. Tam, A. Plews, A. W. Sharpe, Z. Yuan, and A. J. Shields, “Long-distance quantum key distribution secure against coherent attacks,” Optica 4, 163–167 (2017).
[Crossref]

H.-L. Yin, W.-L. Wang, Y.-L. Tang, Q. Zhao, H. Liu, X.-X. Sun, W.-J. Zhang, H. Li, I. V. Puthoor, L.-X. You, E. Andersson, Z. Wang, Y. Liu, X. Jiang, X. Ma, Q. Zhang, M. Curty, T.-Y. Chen, and J.-W. Pan, “Experimental measurement-device-independent quantum digital signatures over a metropolitan network,” Phys. Rev. A 95, 042338 (2017).
[Crossref]

D.-Y. He, S. Wang, W. Chen, Z.-Q. Yin, Y.-J. Qian, Z. Zhou, G.-C. Guo, and Z.-F. Han, “Sine-wave gating InGaAs/InP single photon detector with ultralow afterpulse,” Appl. Phys. Lett. 110, 111104 (2017).
[Crossref]

L.-J. Wang, K.-H. Zou, W. Sun, Y. Mao, Y.-X. Zhu, H.-L. Yin, Q. Chen, Y. Zhao, F. Zhang, T.-Y. Chen, and J.-W. Pan, “Long-distance copropagation of quantum key distribution and terabit classical optical data channels,” Phys. Rev. A 95, 012301 (2017).
[Crossref]

G. P. Miroshnichenko, A. D. Kiselev, A. I. Trifanov, and A. V. Gleim, “Algebraic approach to electro-optic modulation of light: exactly solvable multimode quantum model,” J. Opt. Soc. Am. B 34, 1177–1190 (2017).
[Crossref]

A. V. Gleĭm, V. V. Chistyakov, O. I. Bannik, V. I. Egorov, N. V. Buldakov, A. B. Vasilev, A. A. Gaĭdash, A. V. Kozubov, S. V. Smirnov, S. M. Kynev, S. E. Khoruzhnikov, S. A. Kozlov, and V. N. Vasil’ev, “Sideband quantum communication at 1 Mbit/s on a metropolitan area network,” J. Opt. Technol. 84, 362–367 (2017).
[Crossref]

2016 (5)

Y. Sun, Y. Lu, J. Niu, and Y. Ji, “Reduction of FWM noise in WDM-based QKD systems using interleaved and unequally spaced channels,” Chin. Opt. Lett. 14, 060602 (2016).
[Crossref]

A. V. Gleim, V. I. Egorov, Y. V. Nazarov, S. V. Smirnov, V. V. Chistyakov, O. I. Bannik, A. A. Anisimov, S. M. Kynev, A. E. Ivanova, R. J. Collins, S. A. Kozlov, and G. S. Buller, “Secure polarization-independent subcarrier quantum key distribution in optical fiber channel using BB84 protocol with a strong reference,” Opt. Express 24, 2619–2633 (2016).
[Crossref]

J. Ma, B. Bai, L.-J. Wang, C.-Z. Tong, G. Jin, J. Zhang, and J.-W. Pan, “Design considerations of high-performance InGaAs/InP single-photon avalanche diodes for quantum key distribution,” Appl. Opt. 55, 7497–7502 (2016).
[Crossref]

J. F. Dynes, W. W.-S. Tam, A. Plews, B. Fröhlich, A. W. Sharpe, M. Lucamarini, Z. Yuan, C. Radig, A. Straw, T. Edwards, and A. J. Shields, “Ultra-high bandwidth quantum secured data transmission,” Sci. Rep. 6, 35149 (2016).
[Crossref]

H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M. J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over a 404 km optical fiber,” Phys. Rev. Lett. 117, 190501 (2016).
[Crossref]

2015 (2)

L.-J. Wang, L.-K. Chen, L. Ju, M.-L. Xu, Y. Zhao, K. Chen, Z.-B. Chen, T.-Y. Chen, and J.-W. Pan, “Experimental multiplexing of quantum key distribution with classical optical communication,” Appl. Phys. Lett. 106, 081108 (2015).
[Crossref]

R. Kumar, H. Qin, and R. Alléaume, “Coexistence of continuous variable QKD with intense DWDM classical channels,” New J. Phys. 17, 043027 (2015).
[Crossref]

2014 (3)

T. Ferreira da Silva, G. B. Xavier, G. P. Temporao, and J. P. von der Weid, “Impact of Raman scattered noise from multiple telecom channels on fiber-optic quantum key distribution systems,” J. Lightwave Technol. 32, 2332–2339 (2014).
[Crossref]

K. A. Patel, J. F. Dynes, M. Lucamarini, I. Choi, A. W. Sharpe, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Quantum key distribution for 10 Gb/s dense wavelength division multiplexing networks,” Appl. Phys. Lett. 104, 051123 (2014).
[Crossref]

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” Theor. Comput. Sci. 560, 7–11 (2014).
[Crossref]

2012 (1)

J. Mora, W. Amaya, A. Ruiz-Alba, A. Martinez, D. Calvo, V. G. Muñoz, and J. Capmany, “Simultaneous transmission of 20x2 WDM/SCM-QKD and 4 bidirectional classical channels over a PON,” Opt. Express 20, 16358–16365 (2012).
[Crossref]

2011 (2)

I. Choi, R. J. Young, and P. D. Townsend, “Quantum information to the home,” New J. Phys. 13, 063039 (2011).
[Crossref]

G. B. Xavier, G. V. de Faria, T. F. da Silva, G. P. Temporão, and J. P. von der Weid, “Active polarization control for quantum communication in long-distance optical fibers with shared telecom traffic,” Microw. Opt. Technol. Lett. 53, 2661–2665 (2011).
[Crossref]

2010 (1)

P. Eraerds, N. Walenta, M. Legré, N. Gisin, and H. Zbinden, “Quantum key distribution and 1 Gbps data encryption over a single fibre,” New J. Phys. 12, 063027 (2010).
[Crossref]

2009 (2)

N. A. Peters, P. Toliver, T. E. Chapuran, R. J. Runser, S. R. McNown, C. G. Peterson, D. Rosenberg, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, and K. T. Tyagi, “Dense wavelength multiplexing of 1550 nm QKD with strong classical channels in reconfigurable networking environments,” New J. Phys. 11, 045012 (2009).
[Crossref]

T. E. Chapuran, P. Toliver, N. A. Peters, J. Jackel, M. S. Goodman, R. J. Runser, S. R. McNown, N. Dallmann, R. J. Hughes, K. P. McCabe, J. E. Nordholt, C. G. Peterson, K. T. Tyagi, L. Mercer, and H. Dardy, “Optical networking for quantum key distribution and quantum communications,” New J. Phys. 11, 105001 (2009).
[Crossref]

2008 (1)

K. Kikuchi and S. Tsukamoto, “Evaluation of sensitivity of the digital coherent receiver,” J. Lightwave Technol. 26, 1817–1822 (2008).
[Crossref]

2007 (1)

R. J. Runser, T. Chapuran, P. Toliver, N. A. Peters, M. S. Goodman, J. T. Kosloski, N. Nweke, S. R. McNown, R. J. Hughes, D. Rosenberg, C. G. Peterson, K. P. McCabe, J. E. Nordholt, K. Tyagi, P. A. Hiskett, and N. Dallmann, “Progress toward quantum communications networks: opportunities and challenges,” Proc. SPIE 6476, 64760I (2007).
[Crossref]

2005 (1)

I. Devetak and A. Winter, “Distillation of secret key and entanglement from quantum states,” Proc. R. Soc. London Ser. A Math. Phys. Eng. Sci. 461, 207–235 (2005).
[Crossref]

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

1997 (1)

P. Townsend, “Simultaneous quantum cryptographic key distribution and conventional data transmission over installed fibre using wavelength-division multiplexing,” Electron. Lett. 33, 188–190 (1997).
[Crossref]

Aleksic, S.

S. Aleksic, F. Hipp, D. Winkler, A. Poppe, B. Schrenk, and G. Franzl, “Impairment evaluation toward QKD integration in a conventional 20-channel metro network,” in Optical Fiber Communication Conference (OSA, 2015), paper W4F.2.

Alléaume, R.

R. Kumar, H. Qin, and R. Alléaume, “Coexistence of continuous variable QKD with intense DWDM classical channels,” New J. Phys. 17, 043027 (2015).
[Crossref]

Amaya, W.

Andersson, E.

Anisimov, A. A.

Bahrani, S.

S. Bahrani, M. Razavi, and J. A. Salehi, “Wavelength assignment in hybrid quantum-classical networks,” Sci. Rep. 8, 3456 (2018).
[Crossref]

Bai, B.

Bannik, O. I.

Bennett, C. H.

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” Theor. Comput. Sci. 560, 7–11 (2014).
[Crossref]

Brassard, G.

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” Theor. Comput. Sci. 560, 7–11 (2014).
[Crossref]

Buldakov, N. V.

Buller, G. S.

Cai, C.

Calvo, D.

Capmany, J.

Chapuran, T.

Chapuran, T. E.

Chen, H.

Chen, K.

Chen, L.-K.

Chen, Q.

Chen, S.-J.

Chen, T.-Y.

Chen, W.

Chen, Z.-B.

Chistyakov, V.

Chistyakov, V. V.

Choi, I.

I. Choi, R. J. Young, and P. D. Townsend, “Quantum information to the home,” New J. Phys. 13, 063039 (2011).
[Crossref]

Collins, R. J.

Comandar, L. C.

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing) (Wiley-Interscience, 2006).

Curty, M.

da Silva, T. F.

Dallmann, N.

Dardy, H.

de Faria, G. V.

Devetak, I.

I. Devetak and A. Winter, “Distillation of secret key and entanglement from quantum states,” Proc. R. Soc. London Ser. A Math. Phys. Eng. Sci. 461, 207–235 (2005).
[Crossref]

Dynes, J. F.

Edwards, T.

Egorov, V.

Egorov, V. I.

Eraerds, P.

P. Eraerds, N. Walenta, M. Legré, N. Gisin, and H. Zbinden, “Quantum key distribution and 1 Gbps data encryption over a single fibre,” New J. Phys. 12, 063027 (2010).
[Crossref]

Ferreira da Silva, T.

Franzl, G.

Fröhlich, B.

Gaidash, A.

A. Kozubov, A. Gaidash, and G. Miroshnichenko, “Finite-key security for quantum key distribution systems utilizing weak coherent states,” arXiv preprint arXiv:1903.04371 (2019).

Gaidash, A. A.

A. A. Gaidash, “Unambiguous discrimination of phase-modulated states in communication by optical channels,” Ph.D. thesis (ITMO University, 2019).

Gisin, N.

P. Eraerds, N. Walenta, M. Legré, N. Gisin, and H. Zbinden, “Quantum key distribution and 1 Gbps data encryption over a single fibre,” New J. Phys. 12, 063027 (2010).
[Crossref]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Gleim, A.

Gleim, A. V.

Goncharov, R.

Goodman, M. S.

Guo, G.-C.

Halturinsky, A.

Han, Y.-G.

Han, Z.-F.

He, D.-Y.

Hipp, F.

Hiskett, P. A.

Horoshko, D. B.

Huang, M.-Q.

Hughes, R. J.

Ivanova, A. E.

Jackel, J.

Ji, Y.

Y. Sun, Y. Lu, J. Niu, and Y. Ji, “Reduction of FWM noise in WDM-based QKD systems using interleaved and unequally spaced channels,” Chin. Opt. Lett. 14, 060602 (2016).
[Crossref]

Ji, Y.-F.

Jiang, X.

Jin, G.

Ju, L.

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Proc. R. Soc. London Ser. A Math. Phys. Eng. Sci. (1)

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L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

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Fig. 1. Schematic of the subcarrier-wave quantum key distribution system. Insets (in circles) show the simplified intensity spectra. An optical isolator is required to prevent reflection of the beam light, and an attenuator is required to achieve the needed mean photon number in the quantum channel.

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Fig. 2. QBER and contributions to the probability of detection

${P_{\rm{det}}}$

[see Eq. (8)] versus optical fiber length for (a) continuous wave and (b) pulsed laser regimes. The sensitivity of the classical channel receiver is

${-}28\; {\rm{dBm}}$

Download Full Size | PPT Slide | PDF

Fig. 3. Secure key generation rate versus optical fiber length for (a) continuous and (b) pulsed laser regimes. The sensitivity of the classical channel receiver is

${-}28\; {\rm{dBm}}$

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Fig. 4. Secure key generation rate versus optical fiber length for (a) continuous and (b) pulsed laser regimes. The sensitivity of the classical channel receiver is

${-}48\; {\rm{dBm}}$

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Fig. 5. Maximum possible distance at which the SCW QKD system can operate versus classical channel receiver sensitivity.

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Tables (1)

Table 1. Parameters of DWDM System and Allocation of Quantum Channel

View Table

Equations (16)

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

P_{r a m, f} = P_{o u t} L \sum_{c = 1}^{N_{c h}} ρ (λ_{c}, λ_{q}) Δ λ .

P_{r a m, b} = P_{o u t} \frac{\sinh (ξ L)}{ξ} \sum_{c = 1}^{N_{c h}} ρ (λ_{c}, λ_{q}) Δ λ,

P_{o u t} [d B m] = R_{x} [d B m] + I L [d B] .

p_{r a m, f / b} = \frac{P_{r a m, f / b}}{h c / λ_{q}} Δ t η_{D} η_{B},

n_{p h} (φ_{A}, φ_{B}) = μ_{0} η (L) η_{B} (1 - (1 - ϑ) {| d_{00}^{S} (β^{'}) |}^{2}),

\begin{aligned} \cos β^{'} & \equiv 1 - \frac{1}{2} {(\frac{m^{'}}{S + 0.5})}^{2} \\ = \cos^{2} β - \sin^{2} β \cos (φ_{A} - φ_{B}), \\ \cos β = 1 - \frac{1}{2} {(\frac{m}{S + 0.5})}^{2}, \end{aligned}

d_{00}^{S} (β^{'}) \approx J_{0} (m^{'}) \approx 1 - (m^{'})^{2} / 4,

\begin{aligned} P_{d e t} (φ_{A}, φ_{B}) & = (η_{D} \frac{n_{p h} (φ_{A}, φ_{B})}{T} + γ_{d a r k}) Δ t + p_{r a m} \\ = p_{c l} (φ_{A}, φ_{B}) + p_{d a r k} + p_{r a m}, \end{aligned}

f o r w a r d : p_{r a m} = p_{r a m, f},

f o r w a r d + b a c k w a r d (f u l l) : p_{r a m} = p_{r a m, f} + p_{r a m, b} .

E = P_{d e t} (0, π + δ φ),

1 - G - E = P_{d e t} (0, δ φ),

Q = \frac{E}{1 - G} = \frac{P_{d e t} (0, π + δ φ)}{P_{d e t} (0, δ φ) + P_{d e t} (0, π + δ φ)},

Q = \frac{2 μ τ η (1 - ϑ) (1 - \cos (δ φ)) + τ ϑ μ_{0} η + p_{d a r k} + p_{r a m}}{4 μ τ η (1 - ϑ) + 2 τ ϑ μ_{0} η + 2 p_{d a r k} + 2 p_{r a m}},

K = v_{S} P_{B} [1 - l e a k_{EC} (Q) - max_{E} χ (A : E)],

K = \frac{(1 - G) v_{S}}{2} [1 - h (Q) - h (\frac{1 - e^{- μ_{0} m^{2}}}{2})],

Parameter	Value
$ξ$	0.18 dB/km
$Δ λ$	15 GHz
$N_{c h}$	40
$R_{x}$	from $- 23 d B m$ to $- 48 d B m$
IL	8 dB
$λ_{q}$	1535 nm
$λ_{c}$	from 1548.5 nm to 1564.3 nm

Abstract

References

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