Abstract

An exact analytical expression of the signal-to-noise ratio (SNR) for an intersatellite microwave photonics link with an optical preamplifier is derived considering the signal fade caused by the pointing errors of the transceiver, and an optimized model for laser output power and direct current (DC) bias phase shift of the Mach–Zehnder modulator is established. It is shown that, given the desired SNR and the root mean square (rms) random pointing jitter, an optimal DC bias phase shift exists that minimizes laser output power. The effects of the optical preamplifier parameters on the minimum laser output power and optimal DC bias phase shift are also examined. Numerical results show that the preamplifier noise figure determines the minimum laser output power needed to achieve the desired SNR but affects the optimal DC bias phase shift little. For a SNR of 20 dB, doubling the preamplifier noise figure results in a 6.36 dB increase in minimum laser output power for rms pointing jitter of 0.4 μrad.

© 2012 Optical Society of America

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References

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  1. J. P. Yao, “Microwave photonics,” J. Lightwave Technol. 27, 314–335 (2009).
    [CrossRef]
  2. B. Benazet, M. Sotom, M. Maignan, and J. Perdigues, “Microwave photonics cross-connect repeater for telecommunication satellites,” Proc. SPIE 6194, 619403 (2006).
    [CrossRef]
  3. M. Sotom, B. Benazet, A. L. Kernec, and M. Maignan, “Microwave photonic technologies for flexible satellite telecom payloads,” in Proceedings of European Conference on Optical Communication (ECOC), paper 10.6.3 (2009).
  4. A. Bensoussan and M. Vanzi, “Optoelectronic devices product assurance guideline for space application,” in Proceedings of International Conference on Space Optics8–13 (2010).
  5. L. H. Cheng, S. Aditya, and A. Nirmalathas, “An exact analytical model for dispersive transmission in microwave fiber-optic links using Mach–Zehnder external modulator,” IEEE Photonics Technol. Lett. 17, 1525–1527 (2005).
    [CrossRef]
  6. A. Polishuk and S. Arnon, “Optimization of a laser satellite communication system with an optical preamplifier,” J. Opt. Soc. Am. A 21, 1307–1315 (2004).
    [CrossRef]
  7. S. Arnon, “Performance of a laser μsatellite network with an optical preamplifier,” J. Opt. Soc. Am. A 22, 708–715(2005).
    [CrossRef]
  8. J. L. Corral, J. Marti, and J. M. Fuster, “General expressions for IM/DD dispersive analog optical links With external modulation or optical up-conversion in a Mach–Zehnder electrooptical modulator,” IEEE Trans. Microw. Theory Tech. 49, 1968–1976(2001).
    [CrossRef]
  9. T. S. Cho, C. H. Yun, J. I. Song, and K. Kim, “Analysis of CNR penalty of radio-over-fiber systems including the effects of phase noise from laser and RF oscillator,” J. Lightwave Technol. 23, 4093–4100 (2005).
    [CrossRef]
  10. W. Lim, T. S. Cho, C. H. Yun, and K. Kim, “Average BER analysis of SCM-based free-space optical systems by considering the effect of IM3 with OSSB signals under turbulence channels,” Opt. Express. 17, 20721–20725 (2009).
    [CrossRef]
  11. W. Lim, C. H. Yun, and K. Kim, “BER performance analysis of radio over free-space optical systems considering laser phase noise under gamma-gamma turbulence channels,” Opt. Express. 17, 4479–4484 (2009).
    [CrossRef]
  12. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University, 1922).
  13. X. P. Zhang and A. Mitchell, “A simple black box model for erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 12, 28–30 (2000).
    [CrossRef]
  14. J. Devenport and A. Karim, “Optimization of an externally modulated RF photonic link,” Fiber Integr. Opt. 27, 7–14 (2007).
    [CrossRef]
  15. A. Karim and J. Devenport, “High dynamic range microwave photonic links for RF signal transport and RF-IF conversion,” J. Lightwave Technol. 26, 2718–2724 (2008).
    [CrossRef]
  16. A. Karim and J. Devenport, “Optimization of linearity figure of merit for microwave photonic links,” IEEE Photonics Technol. Lett. 21, 950–952 (2009).
    [CrossRef]

2009 (4)

J. P. Yao, “Microwave photonics,” J. Lightwave Technol. 27, 314–335 (2009).
[CrossRef]

W. Lim, T. S. Cho, C. H. Yun, and K. Kim, “Average BER analysis of SCM-based free-space optical systems by considering the effect of IM3 with OSSB signals under turbulence channels,” Opt. Express. 17, 20721–20725 (2009).
[CrossRef]

W. Lim, C. H. Yun, and K. Kim, “BER performance analysis of radio over free-space optical systems considering laser phase noise under gamma-gamma turbulence channels,” Opt. Express. 17, 4479–4484 (2009).
[CrossRef]

A. Karim and J. Devenport, “Optimization of linearity figure of merit for microwave photonic links,” IEEE Photonics Technol. Lett. 21, 950–952 (2009).
[CrossRef]

2008 (1)

2007 (1)

J. Devenport and A. Karim, “Optimization of an externally modulated RF photonic link,” Fiber Integr. Opt. 27, 7–14 (2007).
[CrossRef]

2006 (1)

B. Benazet, M. Sotom, M. Maignan, and J. Perdigues, “Microwave photonics cross-connect repeater for telecommunication satellites,” Proc. SPIE 6194, 619403 (2006).
[CrossRef]

2005 (3)

2004 (1)

2001 (1)

J. L. Corral, J. Marti, and J. M. Fuster, “General expressions for IM/DD dispersive analog optical links With external modulation or optical up-conversion in a Mach–Zehnder electrooptical modulator,” IEEE Trans. Microw. Theory Tech. 49, 1968–1976(2001).
[CrossRef]

2000 (1)

X. P. Zhang and A. Mitchell, “A simple black box model for erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 12, 28–30 (2000).
[CrossRef]

Aditya, S.

L. H. Cheng, S. Aditya, and A. Nirmalathas, “An exact analytical model for dispersive transmission in microwave fiber-optic links using Mach–Zehnder external modulator,” IEEE Photonics Technol. Lett. 17, 1525–1527 (2005).
[CrossRef]

Arnon, S.

Benazet, B.

B. Benazet, M. Sotom, M. Maignan, and J. Perdigues, “Microwave photonics cross-connect repeater for telecommunication satellites,” Proc. SPIE 6194, 619403 (2006).
[CrossRef]

M. Sotom, B. Benazet, A. L. Kernec, and M. Maignan, “Microwave photonic technologies for flexible satellite telecom payloads,” in Proceedings of European Conference on Optical Communication (ECOC), paper 10.6.3 (2009).

Bensoussan, A.

A. Bensoussan and M. Vanzi, “Optoelectronic devices product assurance guideline for space application,” in Proceedings of International Conference on Space Optics8–13 (2010).

Cheng, L. H.

L. H. Cheng, S. Aditya, and A. Nirmalathas, “An exact analytical model for dispersive transmission in microwave fiber-optic links using Mach–Zehnder external modulator,” IEEE Photonics Technol. Lett. 17, 1525–1527 (2005).
[CrossRef]

Cho, T. S.

W. Lim, T. S. Cho, C. H. Yun, and K. Kim, “Average BER analysis of SCM-based free-space optical systems by considering the effect of IM3 with OSSB signals under turbulence channels,” Opt. Express. 17, 20721–20725 (2009).
[CrossRef]

T. S. Cho, C. H. Yun, J. I. Song, and K. Kim, “Analysis of CNR penalty of radio-over-fiber systems including the effects of phase noise from laser and RF oscillator,” J. Lightwave Technol. 23, 4093–4100 (2005).
[CrossRef]

Corral, J. L.

J. L. Corral, J. Marti, and J. M. Fuster, “General expressions for IM/DD dispersive analog optical links With external modulation or optical up-conversion in a Mach–Zehnder electrooptical modulator,” IEEE Trans. Microw. Theory Tech. 49, 1968–1976(2001).
[CrossRef]

Devenport, J.

A. Karim and J. Devenport, “Optimization of linearity figure of merit for microwave photonic links,” IEEE Photonics Technol. Lett. 21, 950–952 (2009).
[CrossRef]

A. Karim and J. Devenport, “High dynamic range microwave photonic links for RF signal transport and RF-IF conversion,” J. Lightwave Technol. 26, 2718–2724 (2008).
[CrossRef]

J. Devenport and A. Karim, “Optimization of an externally modulated RF photonic link,” Fiber Integr. Opt. 27, 7–14 (2007).
[CrossRef]

Fuster, J. M.

J. L. Corral, J. Marti, and J. M. Fuster, “General expressions for IM/DD dispersive analog optical links With external modulation or optical up-conversion in a Mach–Zehnder electrooptical modulator,” IEEE Trans. Microw. Theory Tech. 49, 1968–1976(2001).
[CrossRef]

Karim, A.

A. Karim and J. Devenport, “Optimization of linearity figure of merit for microwave photonic links,” IEEE Photonics Technol. Lett. 21, 950–952 (2009).
[CrossRef]

A. Karim and J. Devenport, “High dynamic range microwave photonic links for RF signal transport and RF-IF conversion,” J. Lightwave Technol. 26, 2718–2724 (2008).
[CrossRef]

J. Devenport and A. Karim, “Optimization of an externally modulated RF photonic link,” Fiber Integr. Opt. 27, 7–14 (2007).
[CrossRef]

Kernec, A. L.

M. Sotom, B. Benazet, A. L. Kernec, and M. Maignan, “Microwave photonic technologies for flexible satellite telecom payloads,” in Proceedings of European Conference on Optical Communication (ECOC), paper 10.6.3 (2009).

Kim, K.

W. Lim, C. H. Yun, and K. Kim, “BER performance analysis of radio over free-space optical systems considering laser phase noise under gamma-gamma turbulence channels,” Opt. Express. 17, 4479–4484 (2009).
[CrossRef]

W. Lim, T. S. Cho, C. H. Yun, and K. Kim, “Average BER analysis of SCM-based free-space optical systems by considering the effect of IM3 with OSSB signals under turbulence channels,” Opt. Express. 17, 20721–20725 (2009).
[CrossRef]

T. S. Cho, C. H. Yun, J. I. Song, and K. Kim, “Analysis of CNR penalty of radio-over-fiber systems including the effects of phase noise from laser and RF oscillator,” J. Lightwave Technol. 23, 4093–4100 (2005).
[CrossRef]

Lim, W.

W. Lim, T. S. Cho, C. H. Yun, and K. Kim, “Average BER analysis of SCM-based free-space optical systems by considering the effect of IM3 with OSSB signals under turbulence channels,” Opt. Express. 17, 20721–20725 (2009).
[CrossRef]

W. Lim, C. H. Yun, and K. Kim, “BER performance analysis of radio over free-space optical systems considering laser phase noise under gamma-gamma turbulence channels,” Opt. Express. 17, 4479–4484 (2009).
[CrossRef]

Maignan, M.

B. Benazet, M. Sotom, M. Maignan, and J. Perdigues, “Microwave photonics cross-connect repeater for telecommunication satellites,” Proc. SPIE 6194, 619403 (2006).
[CrossRef]

M. Sotom, B. Benazet, A. L. Kernec, and M. Maignan, “Microwave photonic technologies for flexible satellite telecom payloads,” in Proceedings of European Conference on Optical Communication (ECOC), paper 10.6.3 (2009).

Marti, J.

J. L. Corral, J. Marti, and J. M. Fuster, “General expressions for IM/DD dispersive analog optical links With external modulation or optical up-conversion in a Mach–Zehnder electrooptical modulator,” IEEE Trans. Microw. Theory Tech. 49, 1968–1976(2001).
[CrossRef]

Mitchell, A.

X. P. Zhang and A. Mitchell, “A simple black box model for erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 12, 28–30 (2000).
[CrossRef]

Nirmalathas, A.

L. H. Cheng, S. Aditya, and A. Nirmalathas, “An exact analytical model for dispersive transmission in microwave fiber-optic links using Mach–Zehnder external modulator,” IEEE Photonics Technol. Lett. 17, 1525–1527 (2005).
[CrossRef]

Perdigues, J.

B. Benazet, M. Sotom, M. Maignan, and J. Perdigues, “Microwave photonics cross-connect repeater for telecommunication satellites,” Proc. SPIE 6194, 619403 (2006).
[CrossRef]

Polishuk, A.

Song, J. I.

Sotom, M.

B. Benazet, M. Sotom, M. Maignan, and J. Perdigues, “Microwave photonics cross-connect repeater for telecommunication satellites,” Proc. SPIE 6194, 619403 (2006).
[CrossRef]

M. Sotom, B. Benazet, A. L. Kernec, and M. Maignan, “Microwave photonic technologies for flexible satellite telecom payloads,” in Proceedings of European Conference on Optical Communication (ECOC), paper 10.6.3 (2009).

Vanzi, M.

A. Bensoussan and M. Vanzi, “Optoelectronic devices product assurance guideline for space application,” in Proceedings of International Conference on Space Optics8–13 (2010).

Watson, G. N.

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University, 1922).

Yao, J. P.

Yun, C. H.

W. Lim, C. H. Yun, and K. Kim, “BER performance analysis of radio over free-space optical systems considering laser phase noise under gamma-gamma turbulence channels,” Opt. Express. 17, 4479–4484 (2009).
[CrossRef]

W. Lim, T. S. Cho, C. H. Yun, and K. Kim, “Average BER analysis of SCM-based free-space optical systems by considering the effect of IM3 with OSSB signals under turbulence channels,” Opt. Express. 17, 20721–20725 (2009).
[CrossRef]

T. S. Cho, C. H. Yun, J. I. Song, and K. Kim, “Analysis of CNR penalty of radio-over-fiber systems including the effects of phase noise from laser and RF oscillator,” J. Lightwave Technol. 23, 4093–4100 (2005).
[CrossRef]

Zhang, X. P.

X. P. Zhang and A. Mitchell, “A simple black box model for erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 12, 28–30 (2000).
[CrossRef]

Fiber Integr. Opt. (1)

J. Devenport and A. Karim, “Optimization of an externally modulated RF photonic link,” Fiber Integr. Opt. 27, 7–14 (2007).
[CrossRef]

IEEE Photonics Technol. Lett. (3)

L. H. Cheng, S. Aditya, and A. Nirmalathas, “An exact analytical model for dispersive transmission in microwave fiber-optic links using Mach–Zehnder external modulator,” IEEE Photonics Technol. Lett. 17, 1525–1527 (2005).
[CrossRef]

X. P. Zhang and A. Mitchell, “A simple black box model for erbium-doped fiber amplifiers,” IEEE Photonics Technol. Lett. 12, 28–30 (2000).
[CrossRef]

A. Karim and J. Devenport, “Optimization of linearity figure of merit for microwave photonic links,” IEEE Photonics Technol. Lett. 21, 950–952 (2009).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

J. L. Corral, J. Marti, and J. M. Fuster, “General expressions for IM/DD dispersive analog optical links With external modulation or optical up-conversion in a Mach–Zehnder electrooptical modulator,” IEEE Trans. Microw. Theory Tech. 49, 1968–1976(2001).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. A (2)

Opt. Express. (2)

W. Lim, T. S. Cho, C. H. Yun, and K. Kim, “Average BER analysis of SCM-based free-space optical systems by considering the effect of IM3 with OSSB signals under turbulence channels,” Opt. Express. 17, 20721–20725 (2009).
[CrossRef]

W. Lim, C. H. Yun, and K. Kim, “BER performance analysis of radio over free-space optical systems considering laser phase noise under gamma-gamma turbulence channels,” Opt. Express. 17, 4479–4484 (2009).
[CrossRef]

Proc. SPIE (1)

B. Benazet, M. Sotom, M. Maignan, and J. Perdigues, “Microwave photonics cross-connect repeater for telecommunication satellites,” Proc. SPIE 6194, 619403 (2006).
[CrossRef]

Other (3)

M. Sotom, B. Benazet, A. L. Kernec, and M. Maignan, “Microwave photonic technologies for flexible satellite telecom payloads,” in Proceedings of European Conference on Optical Communication (ECOC), paper 10.6.3 (2009).

A. Bensoussan and M. Vanzi, “Optoelectronic devices product assurance guideline for space application,” in Proceedings of International Conference on Space Optics8–13 (2010).

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University, 1922).

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Figures (8)

Fig. 1.
Fig. 1.

Architecture of an intersatellite microwave photonics link with an optical preamplifier.

Fig. 2.
Fig. 2.

SNR as a function of the rms pointing jitter.

Fig. 3.
Fig. 3.

Power penalty for the desired SNR as a function of the rms pointing jitter.

Fig. 4.
Fig. 4.

Minimum laser output power for 20 dB SNR as a function of DC bias phase shift for different rms pointing jitter values.

Fig. 5.
Fig. 5.

Minimum laser output power as a function of SNR for three values of preamplifier gain.

Fig. 6.
Fig. 6.

Optimum DC bias phase shift as a function of SNR for three values of preamplifier gain.

Fig. 7.
Fig. 7.

Minimum laser output power as a function of SNR for three values of preamplifier noise figure.

Fig. 8.
Fig. 8.

Optimum DC bias phase shift as a function of SNR for three values of preamplifier noise figure.

Tables (1)

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Table 1. Link Budget Parameters

Equations (33)

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E out ( t ) = α 2 E in [ e j m cos ( w rf t ) + e j θ e j m cos ( w rf t + π ) ] ,
E out ( t ) = α 2 E in [ p = + j p J p ( m ) e j p w rf t + e j θ q = + j q J q ( m ) e j q ( w rf t + π ) ] ,
P out ( t ) = 1 4 α 2 E in 2 [ p 1 = + j p 1 J p 1 ( m ) e j p 1 w rf t + e j θ q 1 = + j q 1 J q 1 ( m ) e j q 1 ( w rf t + π ) ] [ p 2 = + j p 2 J p 2 ( m ) e j p 2 w rf t + e j θ q 2 = + j q 2 J q 2 ( m ) e j q 2 ( w rf t + π ) ] = 1 4 α 2 P optin { M = + [ J M ( 0 ) e j M ( w rf t + 1 2 π ) + e j θ J M ( 2 m ) e j M ( w rf t + π ) + e j θ J M ( 2 m ) e j M w rf t + J M ( 0 ) e j M ( w rf t + 3 2 π ) ] } ,
P out mzm = 1 2 α 2 P optin [ 1 + cos θ J 0 ( 2 m ) ] .
G e d f a = G 0 1 + ( G 0 P out mzm P out max ) β = G 0 1 + ( G 0 α 2 P optin [ 1 + cos θ J 0 ( 2 m ) ] 2 P out max ) β ,
L t ( ε t ) = e G t ε t 2 ,
L r ( ε r ) = e G r ε r 2 ,
f ( ε t ) = ε t σ t 2 e ε t 2 2 σ t 2 ,
f ( ε r ) = ε r σ r 2 e ε r 2 2 σ r 2 ,
P rf out = 1 2 0 0 [ R α 2 P optin sin θ J 1 ( 2 m ) G edfa G t ( λ 4 π z ) 2 G r G pre L t ( ε t ) L r ( ε r ) ] 2 f ( ε t ) f ( ε r ) R l d ε t d ε r ,
G t = G r = G = η ( π D λ ) 2 ,
P rf out = 1 2 0 0 { R α 2 P optin sin θ J 1 ( 2 m ) G 0 1 + { G 0 α 2 P optin [ 1 + cos θ J 0 ( 2 m ) ] 2 P outmax } β ( λ 4 π z ) 2 [ η ( π D λ ) 2 ] 2 G pre e G ( ε t 2 + ε r 2 ) } 2 ε t σ t 2 e ε t 2 2 σ t 2 ε r σ r 2 e ε r 2 2 σ r 2 d ε t d ε r .
χ = ε t 2 + ε r 2 .
f ( χ ) = a χ e χ 2 σ χ 2 U ( χ ) ,
a = 1 ( σ χ 2 ) 4 Γ ( 2 ) .
Γ ( x ) = 0 t x 1 e t d t 1 x 2 .
Γ ( x + 1 ) = x Γ ( x ) .
P rf out = 1 2 0 { R α 2 P optin sin θ J 1 ( 2 m ) G 0 1 + { G 0 α 2 P optin [ 1 + cos θ J 0 ( 2 m ) ] 2 P outmax } β ( λ 4 π z ) 2 [ η ( π D λ ) 2 ] 2 G pre e G χ } 2 a χ e χ 2 σ χ 2 R l d χ = h 1 [ h 2 ( 4 G σ χ 2 + 1 ) ] 2 R l ,
h 1 = [ R α 2 P optin sin θ J 1 ( 2 m ) ] 2 2 ,
h 2 = G 0 1 + { G 0 α 2 P optin [ 1 + cos θ J 0 ( 2 m ) ] 2 P out max } β ( λ 4 π z ) 2 [ η ( π D λ ) 2 ] 2 G pre ,
σ th 2 = ( G rf + 1 ) k 0 T B el ,
P ase 1 = 0 2 q n sp 1 ( G edfa 1 ) G 2 L G pre B o R e G χ a χ e χ 2 σ χ 2 d χ = h 3 ( 2 G σ χ 2 + 1 ) 2 ,
h 3 = 2 q n sp 1 ( G edfa 1 ) G 2 L G pre B o R ,
n sp 1 F n 1 2 ,
P ase 2 = q F n 2 ( G pre 1 ) B o R ,
σ ase - ase 2 = { R [ h 3 ( 2 G σ χ 2 + 1 ) 2 + h 4 ] } 2 R l ,
σ s ase 2 = 2 R 2 R l [ h 3 ( 2 G σ χ 2 + 1 ) 2 + h 4 ] { 0 1 2 α 2 P optin [ 1 + cos θ J 0 ( 2 m ) ] G edfa G 2 L G pre e G χ a χ e χ 2 σ χ 2 d χ } = 2 R 2 R l [ h 3 ( 2 G σ χ 2 + 1 ) 2 + h 4 ] [ P out mzm h 2 ( 2 G σ χ 2 + 1 ) 2 ] .
σ shot 2 = 2 q R B el R l [ P out mzm h 2 + h 3 ( 2 G σ χ 2 + 1 ) 2 + h 4 ] .
σ rin 2 = 10 RIN / 10 [ R P out mzm h 2 ( 2 G σ χ 2 + 1 ) 2 ] 2 B el R l ,
SNR = h 1 [ h 2 ( 4 G σ χ 2 + 1 ) ] 2 ( G rf + 1 ) k 0 T B el R l + { R [ h 3 ( 2 G σ χ 2 + 1 ) 2 + h 4 ] } 2 + 2 R 2 [ h 3 ( 2 G σ χ 2 + 1 ) 2 + h 4 ] [ P out mzm h 2 ( 2 G σ χ 2 + 1 ) 2 ] + 2 q R B el [ P out mzm h 2 + h 3 ( 2 G σ χ 2 + 1 ) 2 + h 4 ] + 10 RIN / 10 [ R P out mzm h 2 ( 2 G σ χ 2 + 1 ) 2 ] 2 B el .
SNR θ = F 1 ( P optin , θ , σ χ ) θ F 2 ( P optin , θ , σ χ ) F 1 ( P optin , θ , σ χ ) F 2 ( P optin , θ , σ χ ) θ [ F 2 ( P optin , θ , σ χ ) ] 2 = 0 ,
F 1 ( P optin , θ , σ χ ) = h 1 ( P optin , θ ) [ h 2 ( P optin , θ ) ( 4 G σ χ 2 + 1 ) ] 2 ,
F 2 ( P optin , θ , σ χ ) = { G rf [ h 1 ( P optin , θ ) , h 2 ( P optin , θ ) , σ χ ] + 1 } k 0 T B el R l + { R [ h 3 ( P optin , θ ) ( 2 G σ χ 2 + 1 ) 2 + h 4 ] } 2 + 2 R 2 [ h 3 ( P optin , θ ) ( 2 G σ χ 2 + 1 ) 2 + h 4 ] [ P out mzm h 2 ( P optin , θ ) ( 2 G σ χ 2 + 1 ) 2 ] + 2 q R B el [ P out mzm h 2 ( P optin , θ ) + h 3 ( P optin , θ ) ( 2 G σ χ 2 + 1 ) 2 + h 4 ] + 10 RIN / 10 [ R P out mzm h 2 ( P optin , θ ) ( 2 G σ χ 2 + 1 ) 2 ] 2 B el .

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