Abstract

This paper proposes a novel optical adaptive power transmission using automatic power control (APC)-erbium-doped fiber amplifier (EDFA) for turbulence-tolerant free-space optical (FSO) communications. Based on the quasi-stationary characteristics of turbulence channel and average power dependent optical gain features of EDFA, the channel state information (CSI) of the received upstream on-off keying (OOK) signal is optically conveyed to the orthogonally polarized transmitted downstream OOK signal with channel inversion via EDFA in APC mode. The performance is analyzed under various dynamic gain frequencies of APC-EDFA and different power ratios between downstream and upstream signals. Simulation results revealed that the power of downstream signal was adaptively transmitted according to the received upstream signal under effective turbulence suppression, transmitted power efficiency, and required SNR reduction without the estimation of CSI.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Recently, free-space optical (FSO) communication has been intensively researched for the backhaul and fronthaul technologies in the fifth-generation (5G) mobile networks due to the advantages of unregulated spectrum, wide bandwidth, electromagnetic interference immunity, low cost, and much more [1]. Despite these undisputable advantages, like other technologies, it suffers a dramatic deterioration from various power losses, beam wander, beam spreading, beam scintillation, background noises, and cloud blockage in the atmospheric turbulence channel [2]. Out of these issues, the beam scintillation effect can cause a severe received intensity fluctuation, which is the major degrading factor for the vertical and long-distance horizontal FSO communications [3,4].

Various mitigation techniques, adaptive optics, adaptive threshold decision, diversity, gain saturated pre-amplifier, aperture averaging, have been researched to suppress the scintillation effect [2,5,6]. As to the turbulence channel, the temporal spectrum consists of low-frequency components (cutoff frequency < few kHz) [7]. Therefore, the variation of the signal intensity is relatively slow. Owing to this quasi-static channel characteristics, adaptive power transmission technique has been studied to mitigate the scintillation effect with transmitted power efficiency [810]. The transmitted power is altered by the knowledge of the inverted channel state information (CSI). However, the acquisition of CSI brings a complexity to the FSO communication system. As to the horizontal and short-distance vertical FSO links, there is a high reciprocity between upstream and downstream turbulence channels [1113]. Besides, erbium-doped fiber amplifier (EDFA) maintains a constant output power in automatic power control (APC) mode with dynamic gain frequency up to 10 MHz [14,15]. Therefore, APC-EDFA is researched to have an optical adaptive power transmission in this study.

In this paper, we propose a novel optical adaptive power transmission using APC-EDFA for turbulence-tolerant FSO communications. Counter-propagating upstream and downstream on-off keying (OOK) signals with orthogonal polarizations are optically combined and injected into EDFA in APC mode. The combined signal has intensity fluctuation due to the received upstream signal. APC-EDFA assigns different optical gains to the combine signal in order to keep a constant output power. Based on the quasi-stationary characteristics of turbulence channel and average power dependent optical gain features of APC-EDFA, the scintillation effect on the received upstream signal is mitigated and the transmitted power of the downstream signal is optically altered with the turbulence channel inversion by APC-EDFA. The scintillation effect on the transmitted downstream signal is mitigated by this channel inverted adaptive power transmission with transmitted power efficiency. The performance is analyzed under various dynamic gain frequencies of APC-EDFA and different power ratios between downstream and upstream signals. Simulation results showed that the power of downstream signal was adaptively transmitted by the proposed technique with effective turbulence suppression, transmitted power efficiency, and required SNR reduction without the acquisition of CSI.

2. Optical adaptive power transmission

Figure 1 shows the block diagram of the proposed optical adaptive power transmission. OOK signal ${s_1}(t)$ and ${s_2}(t)$ are transmitted with orthogonal linear x- and y- polarizations. Upstream signal ${s_1}(t)$ experiences the scintillation effect in the turbulence channel, which causes the intensity fluctuation of the received signal ${r_1}(t)$. The received upstream signal ${r_1}(t)$ and transmitted downstream signal ${s_2}(t)$ are optically combined into $c(t)$ using PBC. $c(t)$ has an intensity fluctuation according to received upstream signal ${r_1}(t)$ as well. It is given by

$$\begin{aligned} c(t) &= {I_c}(t){s_c}(t) + {n_{U - BG}}\\ &= {r_1}(t) + {s_2}(t) + {n_{U - BG}}\\ &= I{}_1(t){s_1}(t) + {s_2}(t) + {n_{U - BG}}, \end{aligned}$$
where ${I_1}(t)$ and ${I_c}(t)$ are the intensity fluctuation of ${r_1}(t)$ and $c(t)$ respectively, and ${n_{U - BG}}$ is the background noises of the upstream transmission. Then, $c(t)$ is imported into EDFA with the dynamic gain frequency ${f_{EDFA}}$ in APC mode. APC-EDFA estimates the average power of $c(t)$ during the dynamic gain period ${T_{EDFA}} = {1 / {{f_{EDFA}}}}$, and assigns different optical gains ${G_{EDFA}}(t)$ to $c(t)$ in order to keep a constant output power [14]. The combined signal after APC-EDFA $c^{\prime}(t)$ is represented by
$$\begin{aligned} c^{\prime}(t) &= {G_{EDFA}}(n{T_{EDFA}})c(t) + {n_{ASE}}\\ &= {G_{EDFA}}(n{T_{EDFA}}){I_c}(t){s_c}(t) + {n_{ASE}}\\ & \approx I_c^{ - 1}(t){I_c}(t){s_c}(t) + {n_{ASE}}, \end{aligned}$$
where n is the integer number, $I_c^{ - 1}$ is the optical inversion of ${I_c}$, and ${n_{ASE}}$ is the amplified spontaneous emission (ASE) noises. ${I_c}$ can be effectively inverted by APC-EDFA with dynamic optical gains. Because the customized EDFA has ${f_{EDFA}}$ up to 10 MHz, which is much larger than the frequencies of intensity variation caused by the turbulence channel (< few kHz) [15]. The correlation coefficient ${\rho _{I_c^{ - 1}I_1^{ - 1}}}$ between $I_c^{ - 1}$ and ${I_1}^{ - 1}$ is calculated by
$${\rho _{I_c^{ - 1}I_1^{ - 1}}} = \frac{{Cov(I_c^{ - 1},I_1^{ - 1})}}{{{\sigma _{I_c^{ - 1}}}{\sigma _{I_1^{ - 1}}}}},$$
where $I_1^{ - 1}$ is the optical inversion of ${I_1}$, $Cov(I_c^{ - 1},I_1^{ - 1})$ is the covariance between $I_c^{ - 1}$ and ${I_1}^{ - 1}$, ${\sigma _{I_c^{ - 1}}}$ is the standard deviation of $I_c^{ - 1}$, and ${\sigma _{I_1^{ - 1}}}$ is the standard deviation of ${I_1}^{ - 1}$. High value of ${\rho _{I_c^{ - 1}I_1^{ - 1}}}$ can be obtained by the optimization process of ${f_{EDFA}}$ and power ratio between ${r_1}(t)$ and ${s_2}(t)$. Besides, the optical power of the combined signal $c(t)$ is required in the dynamic range of APC-EDFA in order to have a normal operation. $c^{\prime}(t)$ is split into upstream signal ${r_1}^{\prime}(t)$ and downstream signal ${s_2}^{\prime}(t)$ using PBS. Figure 2 shows the principles of optical channel inversion using APC-EDFA. The scintillation effect on the received upstream signal is optically mitigated by APC-EDFA, and the channel information from the upstream signal is optically transformed into the transmitted downstream signal with channel inversion by APC-EDFA as well. As to the upstream signal after APC-EDFA ${r_1}^{\prime}(t)$, it is calculated by
$$\begin{aligned} {r_1}^{\prime}(t) &\approx I_c^{ - 1}(t)({I{}_1(t){s_1}(t) + {n_{U - BG}}} )+ {{{n_{ASE}}} / {\sqrt 2 }}\\ &\approx I_1^{ - 1}(t){I_1}(t){s_1}(t) + I_1^{ - 1}(t){{{n_{U - BG}}} / {\sqrt 2 }} + {{{n_{ASE}}} / {\sqrt 2 }}\,\\ &\approx {s_1}(t) + {{{n_{ASE}}} / {\sqrt 2 }}. \end{aligned}$$

 figure: Fig. 1.

Fig. 1. Block diagram of the proposed optical adaptive power transmission. LD: laser diode, PBC: polarization beam combiner, PBS: polarization beam splitter, EDFA: erbium-doped fiber amplifier, OBPF: optical band pass filter, PD: photodiode, FTD: fixed threshold decision.

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 figure: Fig. 2.

Fig. 2. Principles of optical channel inversion using APC-EDFA.

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${n_{U - BG}}$ can be significantly reduced using an OBPF with very narrow bandwidth, therefore, it is neglected in this study [6]. The scintillation effect is effectively mitigated by APC-EDFA due to the high similarity between ${I_1}^{ - 1}$ and $I_c^{ - 1}$. As to the downstream transmission, ${s_2}(t)$ is transmitted with intensity variation of $I_c^{ - 1}$. Then, it suffers intensity fluctuation of ${I_2}(t)$ from the turbulence channel. As to the horizontal and short distance vertical FSO links, upstream and downstream signals share a similar scintillation effect with a high channel reciprocity, thus, ${I_2}^{ - 1}$ is similar to $I_c^{ - 1}$ as well [11– 13]. The received downstream signal ${r_2}(t)$ is given by

$$\begin{aligned} {r_2}(t) &= {I_2}(t){s_2}^{\prime}(t)\, + {n_{D - BG}}\\ &\approx {I_2}(t)\left( {I_c^{ - 1}(t)\left( {{s_2}(t) + I_1^{ - 1}(t){{{n_{U - BG}}} / {\sqrt 2 }}} \right) + {{{n_{ASE}}} / {\sqrt 2 }}} \right) + {n_{D - BG}}\\ &\approx {I_2}(t)\left( {I_2^{ - 1}(t)\left( {{s_2}(t) + I_1^{ - 1}(t){{{n_{U - BG}}} / {\sqrt 2 }}} \right) + {{{n_{ASE}}} / {\sqrt 2 }}} \right) + {n_{D - BG}}\\ &\approx {I_2}(t)\left( {I_2^{ - 1}(t){s_2}(t) + I_2^{ - 1}(t)I_1^{ - 1}(t){{{n_{U - BG}}} / {\sqrt 2 }} + {{{n_{ASE}}} / {\sqrt 2 }}} \right) + {n_{D - BG}}\\ &\approx {I_2}(t)I_2^{ - 1}(t){s_2}(t) + {I_2}(t)I_2^{ - 1}(t)I_1^{ - 1}(t){{{n_{U - BG}}} / {\sqrt 2 }} + {{{I_2}(t){n_{ASE}}} / {\sqrt 2 }} + {n_{D - BG}}\\ &\approx {s_2}(t) + {{{I_2}(t){n_{ASE}}} / {\sqrt 2 }}, \end{aligned}$$
where ${n_{D - BG}}$ is the background noises of the downlink, and it is neglected as well. The scintillation effect on the received downstream signal is effectively suppressed by the adaptive power transmission with a transmitted power efficiency. Both upstream and downstream signals are detected by PDs and decided using FTD. Consequently, the scintillation effect is effectively mitigated by the proposed adaptive power transmission technique with optimized ${f_{EDFA}}$ and power ratio between ${r_1}(t)$ and ${s_2}(t)$ without the estimation of CSI knowledge for FSO links.

3. Channel analysis

In the atmospheric channel, the variation of temperature and pressure of atmospheric causes the turbulence effect. Turbulence effect is classified into three types of effects: beam wander, beam spreading, and beam scintillation effects. Among these effects, the scintillation effect is the major issue of system distortion, which can cause the intensity fluctuation [1]. The degree of scintillation effect is measured by the scintillation index $\sigma _I^2$. In this work, the turbulence channel with time-varying intensity fluctuation characteristics is modeled for the weak turbulence channel. It is derived from the power spectrum density (PSD) of the log-amplitude fluctuation, which is given by

$${W_A}(f) = 0.528{\pi ^2}{k^2}\;\int\limits_0^L {C_n^2(h)} \int_{\frac{{2\pi f}}{{v(h)}}}^\infty {{{[{{(\mathrm{\kappa }v(h))}^2} - {{(2\pi f)}^2}]}^{\frac{{ - 1}}{2}}}} {\mathrm{\kappa }^{\frac{{ - 8}}{3}}}{\sin ^2}(\frac{{{\mathrm{\kappa }^2}\gamma h}}{{2k}})F(\gamma \mathrm{\kappa })d\mathrm{\kappa }dh,$$
where A is the log-amplitude, L is the link distance, h is the altitude, $C_n^2$ is Hufnagel-Valley model based refractive-index structure parameter, v is Bufton model based wind speed, k is the optical wave number, λ is the wavelength, $\gamma $ is the propagation parameter, $\kappa $ is the spatial wave number, and F is the aperture filter function [6]. The time-varying intensity fluctuated channel is modeled after phase modulation, inverse Fourier transform, and First-order Rytov approximation [16].

The parameters from Table 1 were used to generate a turbulence channel for long-distance terrestrial FSO communication. Figure 3 illustrates the verification of the modeled turbulence channel under $\sigma _I^2$ of 0.0596 and 0.2506. Different degrees of intensity fluctuations were observed in Fig. 3(a). Various temporal spectrums with low frequency features were obtained in Fig. 3(b). The PDF of the modeled turbulence channel fit well with lognormal distribution in Fig. 3(c). Therefore, the turbulence channel was effectively modeled, and it was applied in the following discuss.

 figure: Fig. 3.

Fig. 3. Verification of the modeled turbulence channel under $\sigma _I^2$ of 0.0596 and 0.2506. (a) intensity variation, (b) frequency, and (c) PDF. PSD: power spectrum density, PDF: probability density function.

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Tables Icon

Table 1. Parameters of turbulence channel

4. Simulation and results

We simulated the proposed technique using the modeled turbulence channel. Parameters of EDFA in Table 2 were used in simulation. We assumed upstream and downstream signals suffered a same scintillation effect for simplicity. Capability of adaptive power transmission was analyzed under various dynamic gain frequencies of APC-EDFA and different average power ratios between upstream and downstream signals before APC-EDFA. The data rate was set to 1.25 Gb/s.

Tables Icon

Table 2. Parameters of EDFA

Figure 4 shows the correlation coefficient of the scintillation effect between the received upstream signal ${r_1}(t)$ and combined signal $c(t)$. The correlation coefficient was dramatically improved with the increase of average power ratio between upstream signal ${r_1}(t)$ and downstream signal ${s_2}(t)$ before APC-EDFA.

 figure: Fig. 4.

Fig. 4. Correlation coefficient of the scintillation effect between the received upstream signal ${r_1}(t)$ and combined signal $c(t)$. ${P_{Up}}:{P_{Down}}$: average power ratio between received upstream signal ${r_1}(t)$ and transmitted downstream signal ${s_2}(t)$ before APC-EDFA.

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Figure 5 illustrates the bit-error-rate (BER) performance of the upstream signal detection under various dynamic gain frequencies of APC-EDFA and different average power ratios between received upstream signal ${r_1}(t)$ and transmitted downstream signal ${s_2}(t)$ before APC-EDFA. BERs were calculated using FTD under various signal-to-noise ratios (SNRs). As to the turbulence channel with $\sigma _I^2$ of 0.0596, the scintillation effect was effectively mitigated by APC-EDFA with ${f_{EDFA}}$ of 0.1, 1, and 10 kHz and ${P_{Up}}:{P_{Down}}$ of 50:1, 20:1, 10:1, 4:1, 2:1, and 1:1. As to the turbulence channel with $\sigma _I^2$ of 0. 2506, the scintillation effect was suppressed by APC-EDFA with ${f_{EDFA}}$ of 1 and 10 kHz and ${P_{Up}}:{P_{Down}}$ of 50:1, 20:1, 10:1, and 4:1. Higher ${f_{EDFA}}$ of APC-EDFA and larger ${P_{Up}}:{P_{Down}}$ were required as to the turbulence channel with $\sigma _I^2$ of 0. 2506 due to the higher frequency components of temporal spectrum and larger degree of intensity fluctuation. Therefore, the scintillation effect was effectively mitigated by the proposed technique with higher ${f_{EDFA}}$ of APC-EDFA and larger ${P_{Up}}:{P_{Down}}$ as to the upstream signal detection.

 figure: Fig. 5.

Fig. 5. BER performance of the upstream signal detection under various ${P_{Up}}:{P_{Down}}$. (a) $\sigma _I^2$ of 0.0596 and ${f_{EDFA}}$ of 0.1 kHz, (b) $\sigma _I^2$ of 0.0596 and ${f_{EDFA}}$ of 1 kHz, (c) $\sigma _I^2$ of 0.0596 and ${f_{EDFA}}$ of 10 kHz, (d) $\sigma _I^2$ of 0.2506 and ${f_{EDFA}}$ of 0.1 kHz, (e) $\sigma _I^2$ of 0.2506 and ${f_{EDFA}}$ of 1 kHz, and (f) $\sigma _I^2$ of 0.2506 and ${f_{EDFA}}$ of 10 kHz. ${f_{EDFA}}$: dynamic gain frequency of APC-EDFA.

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Figure 6 depicts the BER performance of the downstream signal detection. As to the turbulence channel with $\sigma _I^2$ of 0.0596, the scintillation effect was suppressed by APC-EDFA with ${f_{EDFA}}$ of 0.1, 1, and 10 kHz and ${P_{Up}}:{P_{Down}}$ of 50:1, 20:1, 10:1, and 4:1. A larger ${P_{Up}}:{P_{Down}}$ was required to have a high accuracy of the optical channel inversion from APC-EDFA comparing with the upstream signal detection in Fig. 5. As to the turbulence channel with $\sigma _I^2$ of 0. 2506, the scintillation effect was mitigated by APC-EDFA with ${f_{EDFA}}$ of 1 and 10 kHz and ${P_{Up}}:{P_{Down}}$ of 50:1, 20:1, and 10:1. A much larger ${P_{Up}}:{P_{Down}}$ was required to improve the accuracy of optical channel inversion from APC-EDFA due to the larger intensity fluctuation comparing with the downstream signal detection with $\sigma _I^2$ of 0.0596. Figure 7 shows the proposed adaptive power transmission under $\sigma _I^2$ of 0.2506, ${f_{EDFA}}$ of 10 kHz, and ${P_{Up}}:{P_{Down}}$ of 50:1. The channel information from the received upstream signal was effectively transform to the transmitted downstream signal by APC-EDFA with the channel inversion characteristics. Therefore, there is no intensity fluctuation as to the received downstream signal at the receiver end. Consequently, as to the downstream signal transmission, the scintillation effect was effectively mitigated by the proposed adaptive power transmission technique with higher ${f_{EDFA}}$ of APC-EDFA and larger ${P_{Up}}:{P_{Down}}$ as well.

 figure: Fig. 6.

Fig. 6. BER performance of the downstream signal detection under various ${P_{Up}}:{P_{Down}}$. (a) $\sigma _I^2$ of 0.0596 and ${f_{EDFA}}$ of 0.1 kHz, (b) $\sigma _I^2$ of 0.0596 and ${f_{EDFA}}$ of 1 kHz, (c) $\sigma _I^2$ of 0.0596 and ${f_{EDFA}}$ of 10 kHz, (d) $\sigma _I^2$ of 0.2506 and ${f_{EDFA}}$ of 0.1 kHz, (e) $\sigma _I^2$ of 0.2506 and ${f_{EDFA}}$ of 1 kHz, and (f) $\sigma _I^2$ of 0.2506 and ${f_{EDFA}}$ of 10 kHz.

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 figure: Fig. 7.

Fig. 7. The proposed adaptive power transmission under $\sigma _I^2$ of 0.2506, ${f_{EDFA}}$ of 10 kHz, and ${P_{Up}}:{P_{Down}}$ of 50:1. (a) received upstream signal before APC-EDFA, (b) transmitted downstream signal after APC-EDFA, and (c) received downstream signal.

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Figure 8(a) shows the comparison between the proposed technique under ${f_{EDFA}}$ of 10 kHz and ${P_{Up}}:{P_{Down}}$ of 50:1 and ATD. A nearly similar BERs were observed as to the proposed adaptive downstream power transmission under various $\sigma _I^2$. BERs were closed to ATD under weak scintillation effect with $\sigma _I^2$ of 0.0596. However, the required SNRs were dramatically reduced in case of larger $\sigma _I^2$ due to the effect scintillation mitigation by the adaptive power transmission. Figure 8(b) shows the power efficiency of the proposed adaptive downstream power transmission under ${f_{EDFA}}$ of 10 kHz and ${P_{Up}}:{P_{Down}}$ of 50:1. The degree of transmitted optical power was significantly decreased with the increase of $\sigma _I^2$ values compared to ATD. Larger $\sigma _I^2$ has a higher degree of power efficiency and required SNR reduction. Therefore, the scintillation mitigation, transmitted power efficiency, and required SNR reduction were achieved by the proposed optical power transmission.

 figure: Fig. 8.

Fig. 8. Comparison between the proposed technique under ${f_{EDFA}}$ of 10 kHz and ${P_{Up}}:{P_{Down}}$ of 50:1 and ATD. (a) BER performance and (b) transmitted power efficiency. ATD: adaptive threshold decision.

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5. Conclusion

In summary, we proposed a novel optical adaptive power transmission using APC-EDFA for turbulence-tolerant FSO communications. EDFA in APC mode was used to have an optical channel inversion for the transmitted downstream signal according to the received upstream signal. The capability of scintillation mitigation was analyzed for both upstream and downstream signals detection. The power efficiency and required SNR reduction were discussed under various turbulence channels. Simulation results revealed that the scintillation effect was effectively mitigated by the proposed technique with the transmitted power efficiency and required SNR reduction without the estimation of CSI. Therefore, it is a highly potential technique for FSO communication systems.

Funding

Major Scientific and Technological Innovation Project of Shandong Province (2019JZZY010128); Natural Science Foundation of Liaoning Province (20180520022).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. H. Kaushal, V. K. Jain, and S. Kar, Free Space Optical Communication (Springer, 2017).

2. A. S. Hamza, J. S. Deogun, and D. R. Alexander, “Classification framework for free space optical communication links and systems,” IEEE Commun. Surv. Tutorials 21(2), 1346–1382 (2019). [CrossRef]  

3. K. Yoshisada, T. Morio, T. Yoshihisa, and T. Hideki, “The Uplink Data Received by OICETS,” J. NICT 59(1/2), 117–123 (2012).

4. S. Constantine, L. E. Elgin, M. L. Stevens, J. A. Greco, K. Aquino, D. D. Alves, and B. S. Robinson, “Design of a high-speed space modem for the lunar laser communications demonstration,” Proc. SPIE 7923, Free-Space Laser Communication Technologies XXIII, 792308, (2011).

5. M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Commun. Surv. Tutorials 16(4), 2231–2258 (2014). [CrossRef]  

6. H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Commun. Surv. Tutorials 19(1), 57–96 (2017). [CrossRef]  

7. H. Shen, L. Yu, and C. Fan, “Temporal spectrum of atmospheric scintillation and the effects of aperture averaging and time averaging,” Opt. Commun. 330(1), 160–164 (2014). [CrossRef]  

8. I. B. Djordjevic and T. Goran, “On the communication over strong atmospheric turbulence channels by adaptive modulation and coding,” Opt. Express 17(20), 18250–18262 (2009). [CrossRef]  

9. T. Xuan, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Power adaptation based on truncated channel inversion for hybrid FSORF transmission with adaptive combining,” IEEE Photonics J. 7(4), 1–12 (2015). [CrossRef]  

10. H. Safi, A. A. Sharifi, M. T. Dabiri, I. S. Ansari, and J. Cheng, “Adaptive Channel Coding and Power Control for Practical FSO Communication Systems Under Channel Estimation Error,” IEEE Trans. Veh. Technol. 68(8), 7566–7577 (2019). [CrossRef]  

11. R. R. Parenti, J. M. Roth, J. H. Shapiro, F. G. Walther, and J. A. Greco, “Experimental observations of channel reciprocity in single-mode free-space optical links,” Opt. Express 20(19), 21635–21644 (2012). [CrossRef]  

12. J. H. Shapiro and A. L. Puryear, “Reciprocity-enhanced optical communication through atmospheric turbulence-Part I: Reciprocity proofs and far-field power transfer optimization,” J. Opt. Commun. Netw. 4(12), 947–954 (2012). [CrossRef]  

13. A. L. Puryeara, J. H. Shapirob, and R. R. Parenti, “Reciprocity-enhanced optical communication through atmospheric turbulence-Part II: Communication architectures and performance,” J. Opt. Commun. Netw. 5(8), 888–900 (2013). [CrossRef]  

14. P. C. Becker, A. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers (Academic, 1999).

15. Y. Ben-Ezra, M. Haridim, and B. I. Lembrikov, “All-Optical AGC of EDFA Based on SOA,” IEEE J. Quantum Elect. 42(12), 1209–1214 (2006). [CrossRef]  

16. W. H. Shin, J. Y. Choi, and S. K. Han, “Fixed threshold on-off keying differential detection for satellite optical communications,” Opt. Express 27(2), 1590–1596 (2019). [CrossRef]  

References

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  • |

  1. H. Kaushal, V. K. Jain, and S. Kar, Free Space Optical Communication (Springer, 2017).
  2. A. S. Hamza, J. S. Deogun, and D. R. Alexander, “Classification framework for free space optical communication links and systems,” IEEE Commun. Surv. Tutorials 21(2), 1346–1382 (2019).
    [Crossref]
  3. K. Yoshisada, T. Morio, T. Yoshihisa, and T. Hideki, “The Uplink Data Received by OICETS,” J. NICT 59(1/2), 117–123 (2012).
  4. S. Constantine, L. E. Elgin, M. L. Stevens, J. A. Greco, K. Aquino, D. D. Alves, and B. S. Robinson, “Design of a high-speed space modem for the lunar laser communications demonstration,” Proc. SPIE 7923, Free-Space Laser Communication Technologies XXIII, 792308, (2011).
  5. M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Commun. Surv. Tutorials 16(4), 2231–2258 (2014).
    [Crossref]
  6. H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Commun. Surv. Tutorials 19(1), 57–96 (2017).
    [Crossref]
  7. H. Shen, L. Yu, and C. Fan, “Temporal spectrum of atmospheric scintillation and the effects of aperture averaging and time averaging,” Opt. Commun. 330(1), 160–164 (2014).
    [Crossref]
  8. I. B. Djordjevic and T. Goran, “On the communication over strong atmospheric turbulence channels by adaptive modulation and coding,” Opt. Express 17(20), 18250–18262 (2009).
    [Crossref]
  9. T. Xuan, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Power adaptation based on truncated channel inversion for hybrid FSORF transmission with adaptive combining,” IEEE Photonics J. 7(4), 1–12 (2015).
    [Crossref]
  10. H. Safi, A. A. Sharifi, M. T. Dabiri, I. S. Ansari, and J. Cheng, “Adaptive Channel Coding and Power Control for Practical FSO Communication Systems Under Channel Estimation Error,” IEEE Trans. Veh. Technol. 68(8), 7566–7577 (2019).
    [Crossref]
  11. R. R. Parenti, J. M. Roth, J. H. Shapiro, F. G. Walther, and J. A. Greco, “Experimental observations of channel reciprocity in single-mode free-space optical links,” Opt. Express 20(19), 21635–21644 (2012).
    [Crossref]
  12. J. H. Shapiro and A. L. Puryear, “Reciprocity-enhanced optical communication through atmospheric turbulence-Part I: Reciprocity proofs and far-field power transfer optimization,” J. Opt. Commun. Netw. 4(12), 947–954 (2012).
    [Crossref]
  13. A. L. Puryeara, J. H. Shapirob, and R. R. Parenti, “Reciprocity-enhanced optical communication through atmospheric turbulence-Part II: Communication architectures and performance,” J. Opt. Commun. Netw. 5(8), 888–900 (2013).
    [Crossref]
  14. P. C. Becker, A. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers (Academic, 1999).
  15. Y. Ben-Ezra, M. Haridim, and B. I. Lembrikov, “All-Optical AGC of EDFA Based on SOA,” IEEE J. Quantum Elect. 42(12), 1209–1214 (2006).
    [Crossref]
  16. W. H. Shin, J. Y. Choi, and S. K. Han, “Fixed threshold on-off keying differential detection for satellite optical communications,” Opt. Express 27(2), 1590–1596 (2019).
    [Crossref]

2019 (3)

A. S. Hamza, J. S. Deogun, and D. R. Alexander, “Classification framework for free space optical communication links and systems,” IEEE Commun. Surv. Tutorials 21(2), 1346–1382 (2019).
[Crossref]

H. Safi, A. A. Sharifi, M. T. Dabiri, I. S. Ansari, and J. Cheng, “Adaptive Channel Coding and Power Control for Practical FSO Communication Systems Under Channel Estimation Error,” IEEE Trans. Veh. Technol. 68(8), 7566–7577 (2019).
[Crossref]

W. H. Shin, J. Y. Choi, and S. K. Han, “Fixed threshold on-off keying differential detection for satellite optical communications,” Opt. Express 27(2), 1590–1596 (2019).
[Crossref]

2017 (1)

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Commun. Surv. Tutorials 19(1), 57–96 (2017).
[Crossref]

2015 (1)

T. Xuan, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Power adaptation based on truncated channel inversion for hybrid FSORF transmission with adaptive combining,” IEEE Photonics J. 7(4), 1–12 (2015).
[Crossref]

2014 (2)

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Commun. Surv. Tutorials 16(4), 2231–2258 (2014).
[Crossref]

H. Shen, L. Yu, and C. Fan, “Temporal spectrum of atmospheric scintillation and the effects of aperture averaging and time averaging,” Opt. Commun. 330(1), 160–164 (2014).
[Crossref]

2013 (1)

2012 (3)

2009 (1)

2006 (1)

Y. Ben-Ezra, M. Haridim, and B. I. Lembrikov, “All-Optical AGC of EDFA Based on SOA,” IEEE J. Quantum Elect. 42(12), 1209–1214 (2006).
[Crossref]

Alexander, D. R.

A. S. Hamza, J. S. Deogun, and D. R. Alexander, “Classification framework for free space optical communication links and systems,” IEEE Commun. Surv. Tutorials 21(2), 1346–1382 (2019).
[Crossref]

Alves, D. D.

S. Constantine, L. E. Elgin, M. L. Stevens, J. A. Greco, K. Aquino, D. D. Alves, and B. S. Robinson, “Design of a high-speed space modem for the lunar laser communications demonstration,” Proc. SPIE 7923, Free-Space Laser Communication Technologies XXIII, 792308, (2011).

Ansari, I. S.

H. Safi, A. A. Sharifi, M. T. Dabiri, I. S. Ansari, and J. Cheng, “Adaptive Channel Coding and Power Control for Practical FSO Communication Systems Under Channel Estimation Error,” IEEE Trans. Veh. Technol. 68(8), 7566–7577 (2019).
[Crossref]

Aquino, K.

S. Constantine, L. E. Elgin, M. L. Stevens, J. A. Greco, K. Aquino, D. D. Alves, and B. S. Robinson, “Design of a high-speed space modem for the lunar laser communications demonstration,” Proc. SPIE 7923, Free-Space Laser Communication Technologies XXIII, 792308, (2011).

Becker, P. C.

P. C. Becker, A. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers (Academic, 1999).

Ben-Ezra, Y.

Y. Ben-Ezra, M. Haridim, and B. I. Lembrikov, “All-Optical AGC of EDFA Based on SOA,” IEEE J. Quantum Elect. 42(12), 1209–1214 (2006).
[Crossref]

Cheng, J.

H. Safi, A. A. Sharifi, M. T. Dabiri, I. S. Ansari, and J. Cheng, “Adaptive Channel Coding and Power Control for Practical FSO Communication Systems Under Channel Estimation Error,” IEEE Trans. Veh. Technol. 68(8), 7566–7577 (2019).
[Crossref]

Choi, J. Y.

Constantine, S.

S. Constantine, L. E. Elgin, M. L. Stevens, J. A. Greco, K. Aquino, D. D. Alves, and B. S. Robinson, “Design of a high-speed space modem for the lunar laser communications demonstration,” Proc. SPIE 7923, Free-Space Laser Communication Technologies XXIII, 792308, (2011).

Dabiri, M. T.

H. Safi, A. A. Sharifi, M. T. Dabiri, I. S. Ansari, and J. Cheng, “Adaptive Channel Coding and Power Control for Practical FSO Communication Systems Under Channel Estimation Error,” IEEE Trans. Veh. Technol. 68(8), 7566–7577 (2019).
[Crossref]

Deogun, J. S.

A. S. Hamza, J. S. Deogun, and D. R. Alexander, “Classification framework for free space optical communication links and systems,” IEEE Commun. Surv. Tutorials 21(2), 1346–1382 (2019).
[Crossref]

Djordjevic, I. B.

Elgin, L. E.

S. Constantine, L. E. Elgin, M. L. Stevens, J. A. Greco, K. Aquino, D. D. Alves, and B. S. Robinson, “Design of a high-speed space modem for the lunar laser communications demonstration,” Proc. SPIE 7923, Free-Space Laser Communication Technologies XXIII, 792308, (2011).

Fan, C.

H. Shen, L. Yu, and C. Fan, “Temporal spectrum of atmospheric scintillation and the effects of aperture averaging and time averaging,” Opt. Commun. 330(1), 160–164 (2014).
[Crossref]

Ghassemlooy, Z.

T. Xuan, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Power adaptation based on truncated channel inversion for hybrid FSORF transmission with adaptive combining,” IEEE Photonics J. 7(4), 1–12 (2015).
[Crossref]

Goran, T.

Greco, J. A.

R. R. Parenti, J. M. Roth, J. H. Shapiro, F. G. Walther, and J. A. Greco, “Experimental observations of channel reciprocity in single-mode free-space optical links,” Opt. Express 20(19), 21635–21644 (2012).
[Crossref]

S. Constantine, L. E. Elgin, M. L. Stevens, J. A. Greco, K. Aquino, D. D. Alves, and B. S. Robinson, “Design of a high-speed space modem for the lunar laser communications demonstration,” Proc. SPIE 7923, Free-Space Laser Communication Technologies XXIII, 792308, (2011).

Hamza, A. S.

A. S. Hamza, J. S. Deogun, and D. R. Alexander, “Classification framework for free space optical communication links and systems,” IEEE Commun. Surv. Tutorials 21(2), 1346–1382 (2019).
[Crossref]

Han, S. K.

Haridim, M.

Y. Ben-Ezra, M. Haridim, and B. I. Lembrikov, “All-Optical AGC of EDFA Based on SOA,” IEEE J. Quantum Elect. 42(12), 1209–1214 (2006).
[Crossref]

Hideki, T.

K. Yoshisada, T. Morio, T. Yoshihisa, and T. Hideki, “The Uplink Data Received by OICETS,” J. NICT 59(1/2), 117–123 (2012).

Jain, V. K.

H. Kaushal, V. K. Jain, and S. Kar, Free Space Optical Communication (Springer, 2017).

Kaddoum, G.

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Commun. Surv. Tutorials 19(1), 57–96 (2017).
[Crossref]

Kar, S.

H. Kaushal, V. K. Jain, and S. Kar, Free Space Optical Communication (Springer, 2017).

Kaushal, H.

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Commun. Surv. Tutorials 19(1), 57–96 (2017).
[Crossref]

H. Kaushal, V. K. Jain, and S. Kar, Free Space Optical Communication (Springer, 2017).

Khalighi, M. A.

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Commun. Surv. Tutorials 16(4), 2231–2258 (2014).
[Crossref]

Lee, C. G.

T. Xuan, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Power adaptation based on truncated channel inversion for hybrid FSORF transmission with adaptive combining,” IEEE Photonics J. 7(4), 1–12 (2015).
[Crossref]

Lembrikov, B. I.

Y. Ben-Ezra, M. Haridim, and B. I. Lembrikov, “All-Optical AGC of EDFA Based on SOA,” IEEE J. Quantum Elect. 42(12), 1209–1214 (2006).
[Crossref]

Morio, T.

K. Yoshisada, T. Morio, T. Yoshihisa, and T. Hideki, “The Uplink Data Received by OICETS,” J. NICT 59(1/2), 117–123 (2012).

Olsson, A. A.

P. C. Becker, A. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers (Academic, 1999).

Parenti, R. R.

Popoola, W. O.

T. Xuan, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Power adaptation based on truncated channel inversion for hybrid FSORF transmission with adaptive combining,” IEEE Photonics J. 7(4), 1–12 (2015).
[Crossref]

Puryear, A. L.

Puryeara, A. L.

Rajbhandari, S.

T. Xuan, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Power adaptation based on truncated channel inversion for hybrid FSORF transmission with adaptive combining,” IEEE Photonics J. 7(4), 1–12 (2015).
[Crossref]

Robinson, B. S.

S. Constantine, L. E. Elgin, M. L. Stevens, J. A. Greco, K. Aquino, D. D. Alves, and B. S. Robinson, “Design of a high-speed space modem for the lunar laser communications demonstration,” Proc. SPIE 7923, Free-Space Laser Communication Technologies XXIII, 792308, (2011).

Roth, J. M.

Safi, H.

H. Safi, A. A. Sharifi, M. T. Dabiri, I. S. Ansari, and J. Cheng, “Adaptive Channel Coding and Power Control for Practical FSO Communication Systems Under Channel Estimation Error,” IEEE Trans. Veh. Technol. 68(8), 7566–7577 (2019).
[Crossref]

Shapiro, J. H.

Shapirob, J. H.

Sharifi, A. A.

H. Safi, A. A. Sharifi, M. T. Dabiri, I. S. Ansari, and J. Cheng, “Adaptive Channel Coding and Power Control for Practical FSO Communication Systems Under Channel Estimation Error,” IEEE Trans. Veh. Technol. 68(8), 7566–7577 (2019).
[Crossref]

Shen, H.

H. Shen, L. Yu, and C. Fan, “Temporal spectrum of atmospheric scintillation and the effects of aperture averaging and time averaging,” Opt. Commun. 330(1), 160–164 (2014).
[Crossref]

Shin, W. H.

Simpson, J. R.

P. C. Becker, A. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers (Academic, 1999).

Stevens, M. L.

S. Constantine, L. E. Elgin, M. L. Stevens, J. A. Greco, K. Aquino, D. D. Alves, and B. S. Robinson, “Design of a high-speed space modem for the lunar laser communications demonstration,” Proc. SPIE 7923, Free-Space Laser Communication Technologies XXIII, 792308, (2011).

Uysal, M.

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Commun. Surv. Tutorials 16(4), 2231–2258 (2014).
[Crossref]

Walther, F. G.

Xuan, T.

T. Xuan, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Power adaptation based on truncated channel inversion for hybrid FSORF transmission with adaptive combining,” IEEE Photonics J. 7(4), 1–12 (2015).
[Crossref]

Yoshihisa, T.

K. Yoshisada, T. Morio, T. Yoshihisa, and T. Hideki, “The Uplink Data Received by OICETS,” J. NICT 59(1/2), 117–123 (2012).

Yoshisada, K.

K. Yoshisada, T. Morio, T. Yoshihisa, and T. Hideki, “The Uplink Data Received by OICETS,” J. NICT 59(1/2), 117–123 (2012).

Yu, L.

H. Shen, L. Yu, and C. Fan, “Temporal spectrum of atmospheric scintillation and the effects of aperture averaging and time averaging,” Opt. Commun. 330(1), 160–164 (2014).
[Crossref]

IEEE Commun. Surv. Tutorials (3)

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” IEEE Commun. Surv. Tutorials 16(4), 2231–2258 (2014).
[Crossref]

H. Kaushal and G. Kaddoum, “Optical communication in space: challenges and mitigation techniques,” IEEE Commun. Surv. Tutorials 19(1), 57–96 (2017).
[Crossref]

A. S. Hamza, J. S. Deogun, and D. R. Alexander, “Classification framework for free space optical communication links and systems,” IEEE Commun. Surv. Tutorials 21(2), 1346–1382 (2019).
[Crossref]

IEEE J. Quantum Elect. (1)

Y. Ben-Ezra, M. Haridim, and B. I. Lembrikov, “All-Optical AGC of EDFA Based on SOA,” IEEE J. Quantum Elect. 42(12), 1209–1214 (2006).
[Crossref]

IEEE Photonics J. (1)

T. Xuan, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee, “Power adaptation based on truncated channel inversion for hybrid FSORF transmission with adaptive combining,” IEEE Photonics J. 7(4), 1–12 (2015).
[Crossref]

IEEE Trans. Veh. Technol. (1)

H. Safi, A. A. Sharifi, M. T. Dabiri, I. S. Ansari, and J. Cheng, “Adaptive Channel Coding and Power Control for Practical FSO Communication Systems Under Channel Estimation Error,” IEEE Trans. Veh. Technol. 68(8), 7566–7577 (2019).
[Crossref]

J. NICT (1)

K. Yoshisada, T. Morio, T. Yoshihisa, and T. Hideki, “The Uplink Data Received by OICETS,” J. NICT 59(1/2), 117–123 (2012).

J. Opt. Commun. Netw. (2)

Opt. Commun. (1)

H. Shen, L. Yu, and C. Fan, “Temporal spectrum of atmospheric scintillation and the effects of aperture averaging and time averaging,” Opt. Commun. 330(1), 160–164 (2014).
[Crossref]

Opt. Express (3)

Other (3)

P. C. Becker, A. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers (Academic, 1999).

H. Kaushal, V. K. Jain, and S. Kar, Free Space Optical Communication (Springer, 2017).

S. Constantine, L. E. Elgin, M. L. Stevens, J. A. Greco, K. Aquino, D. D. Alves, and B. S. Robinson, “Design of a high-speed space modem for the lunar laser communications demonstration,” Proc. SPIE 7923, Free-Space Laser Communication Technologies XXIII, 792308, (2011).

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (8)

Fig. 1.
Fig. 1. Block diagram of the proposed optical adaptive power transmission. LD: laser diode, PBC: polarization beam combiner, PBS: polarization beam splitter, EDFA: erbium-doped fiber amplifier, OBPF: optical band pass filter, PD: photodiode, FTD: fixed threshold decision.
Fig. 2.
Fig. 2. Principles of optical channel inversion using APC-EDFA.
Fig. 3.
Fig. 3. Verification of the modeled turbulence channel under $\sigma _I^2$ of 0.0596 and 0.2506. (a) intensity variation, (b) frequency, and (c) PDF. PSD: power spectrum density, PDF: probability density function.
Fig. 4.
Fig. 4. Correlation coefficient of the scintillation effect between the received upstream signal ${r_1}(t)$ and combined signal $c(t)$. ${P_{Up}}:{P_{Down}}$: average power ratio between received upstream signal ${r_1}(t)$ and transmitted downstream signal ${s_2}(t)$ before APC-EDFA.
Fig. 5.
Fig. 5. BER performance of the upstream signal detection under various ${P_{Up}}:{P_{Down}}$. (a) $\sigma _I^2$ of 0.0596 and ${f_{EDFA}}$ of 0.1 kHz, (b) $\sigma _I^2$ of 0.0596 and ${f_{EDFA}}$ of 1 kHz, (c) $\sigma _I^2$ of 0.0596 and ${f_{EDFA}}$ of 10 kHz, (d) $\sigma _I^2$ of 0.2506 and ${f_{EDFA}}$ of 0.1 kHz, (e) $\sigma _I^2$ of 0.2506 and ${f_{EDFA}}$ of 1 kHz, and (f) $\sigma _I^2$ of 0.2506 and ${f_{EDFA}}$ of 10 kHz. ${f_{EDFA}}$: dynamic gain frequency of APC-EDFA.
Fig. 6.
Fig. 6. BER performance of the downstream signal detection under various ${P_{Up}}:{P_{Down}}$. (a) $\sigma _I^2$ of 0.0596 and ${f_{EDFA}}$ of 0.1 kHz, (b) $\sigma _I^2$ of 0.0596 and ${f_{EDFA}}$ of 1 kHz, (c) $\sigma _I^2$ of 0.0596 and ${f_{EDFA}}$ of 10 kHz, (d) $\sigma _I^2$ of 0.2506 and ${f_{EDFA}}$ of 0.1 kHz, (e) $\sigma _I^2$ of 0.2506 and ${f_{EDFA}}$ of 1 kHz, and (f) $\sigma _I^2$ of 0.2506 and ${f_{EDFA}}$ of 10 kHz.
Fig. 7.
Fig. 7. The proposed adaptive power transmission under $\sigma _I^2$ of 0.2506, ${f_{EDFA}}$ of 10 kHz, and ${P_{Up}}:{P_{Down}}$ of 50:1. (a) received upstream signal before APC-EDFA, (b) transmitted downstream signal after APC-EDFA, and (c) received downstream signal.
Fig. 8.
Fig. 8. Comparison between the proposed technique under ${f_{EDFA}}$ of 10 kHz and ${P_{Up}}:{P_{Down}}$ of 50:1 and ATD. (a) BER performance and (b) transmitted power efficiency. ATD: adaptive threshold decision.

Tables (2)

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Table 1. Parameters of turbulence channel

Tables Icon

Table 2. Parameters of EDFA

Equations (6)

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

c ( t ) = I c ( t ) s c ( t ) + n U B G = r 1 ( t ) + s 2 ( t ) + n U B G = I 1 ( t ) s 1 ( t ) + s 2 ( t ) + n U B G ,
c ( t ) = G E D F A ( n T E D F A ) c ( t ) + n A S E = G E D F A ( n T E D F A ) I c ( t ) s c ( t ) + n A S E I c 1 ( t ) I c ( t ) s c ( t ) + n A S E ,
ρ I c 1 I 1 1 = C o v ( I c 1 , I 1 1 ) σ I c 1 σ I 1 1 ,
r 1 ( t ) I c 1 ( t ) ( I 1 ( t ) s 1 ( t ) + n U B G ) + n A S E / 2 I 1 1 ( t ) I 1 ( t ) s 1 ( t ) + I 1 1 ( t ) n U B G / 2 + n A S E / 2 s 1 ( t ) + n A S E / 2 .
r 2 ( t ) = I 2 ( t ) s 2 ( t ) + n D B G I 2 ( t ) ( I c 1 ( t ) ( s 2 ( t ) + I 1 1 ( t ) n U B G / 2 ) + n A S E / 2 ) + n D B G I 2 ( t ) ( I 2 1 ( t ) ( s 2 ( t ) + I 1 1 ( t ) n U B G / 2 ) + n A S E / 2 ) + n D B G I 2 ( t ) ( I 2 1 ( t ) s 2 ( t ) + I 2 1 ( t ) I 1 1 ( t ) n U B G / 2 + n A S E / 2 ) + n D B G I 2 ( t ) I 2 1 ( t ) s 2 ( t ) + I 2 ( t ) I 2 1 ( t ) I 1 1 ( t ) n U B G / 2 + I 2 ( t ) n A S E / 2 + n D B G s 2 ( t ) + I 2 ( t ) n A S E / 2 ,
W A ( f ) = 0.528 π 2 k 2 0 L C n 2 ( h ) 2 π f v ( h ) [ ( κ v ( h ) ) 2 ( 2 π f ) 2 ] 1 2 κ 8 3 sin 2 ( κ 2 γ h 2 k ) F ( γ κ ) d κ d h ,

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