## Abstract

In a ground-to-satellite communication system with a preset EDFA, the EDFA’s performance will be affected by space environment. With 250 Gy radiation, the EDFA’s gain decreases by 2 dB from 19.97 dB at $20\xb0\text{C}$. The BER increases by 2.5 orders of magnitude from 10^{−10}, and increases more with more radiation. The situation aggravates when the temperature rises by $73\xb0\text{C}$. The laser’s divergence-angle and transmitter radius have optimal values to make the lowest BER and increasing receiver diameter makes lower BERs, so setting these parameters with appropriate values will compensate the degradation caused by EDFA.

© 2014 Optical Society of America

## 1. Introduction

In the 1990s, the erbium-doped fiber amplifier (EDFA) was firstly applied into the optical fiber transmission system as a new device. With EDFA’s wide application, the optical fiber communication technology revolutionized rapidly. Thanks to its advantages like low weight, high signal amplification, wide bandwidth, etc, it greatly attracts the industry’s attention. With the development of several important space optical communication programs which are carried out by the National Aeronautics and Space Administration (NASA) and the European Space Agency (ESA) [1–4], many key ground optical communication devices and techniques have been introduced to the field of satellite optical communication. In particular, EDFA is introduced to satellite optical communications to solve the conflict between the input power and modulation rate.

However, during the satellites’ stay in orbit, their components will face a harsh radiation environment meaning that the performance of EDFA will inevitably be affected. Investigations on the characteristics of EDFA in radiation are carried out by several research groups [5]. A. Gusarov’s group found that direct nanoparticle deposition technology allows improving the EDFA’s radiation resistance by increasing the concentration of ${{\displaystyle \text{Er}}}^{3+}$ ions [6]. T.S. Rose’s group proposed that the radiation-induced loss determined from amplifier measurements can be substantially less than that determined from passive transmission spectra in certain fibers where the damage is significant [7]. O. Berne’s group demonstrated that the gain of EDFA will reduce about 10 dB at 3000 Gy dose of radiation, as is shown in [8]. However, O. Berne proposed that space radiation has little effect on EDFA because the EDFA is protected by an aluminum plate which means it actually suffers only 60 Gy dose of radiation. But the truth is that aluminum plates only prevent electronic radiation but show little resistance to radiation caused by other high energy particles like Gamma particles. Therefore, the impact of radiation on EDFA still cannot be ignored. What should be clarified is that these published papers on EDFA in radiation only focus on the characteristics of EDFA outside a whole communication system. To make these investigations more practical, it is unavoidable to investigate the EDFA’s effect on a whole communication system. That is what we will do in this paper.

To study the performance of a ground-to-satellite optical communication system, it is not accurate enough to only take the effect of EDFA into account. In a practical laser link, its performance will be significantly affected by the effect of atmospheric turbulence [9, 10]. Here, we take the random wander and scintillation into account to build a real channel from ground to satellites [11].

The main idea of this letter is to use the propagation equations with radiation-induced background losses at pump and signal wavelength to obtain the evolution of the gain of EDFA with increasing radiation dose. It is agreed that the input power of the laser link strongly affects the BER performance, so the influence of the space radiation on EDFA will be reflected. By adding the factor of atmospheric turbulence we may get more accurate performance of the whole system. Here, we only analyze the BER performance of the on-off keying (OOK) modulation scheme. By certain numerical simulation tests, the relationships between BER and laser divergence angle, receiver diameter, and transmitter laser radius are obtained to choose the optimal system parameters and configuration.

## 2. Theory

People have found that the performance of optical fiber devices will be deteriorated when suffering radiation because of the color center effect. To describe the characteristics of EDFA in radiation, we use the theoretical model proposed in [8]. The model is an improved one based on Jackson’s model [12], which introduces additional radiation-induced background losses for pump and signal. The propagation equations of pump and signal are written as follows [8],

To obtain the accurate radiation-induced losses, we use a power law to describe the effects of dose and dose rate on 1310 nm absorption [13]

Then, it is possible to predict the radiation-induced losses at pump and signal wavelengths by the equation below [8]For an OOK scheme, the BER, with the assumption of equal possibilities of sending “1” and “0”, under the effect of detector noise is [14]

For an avalanche photodiode (APD) detector in the laser link with a preset EDFA in space, the mean values ${{\displaystyle m}}_{0}$, ${{\displaystyle m}}_{1}$ and variances ${{\displaystyle \sigma}}_{0}^{2}$, ${{\displaystyle \sigma}}_{1}^{2}$ of noise can be [15]

Considering the influence of atmospheric turbulence, the actual BER should be the ensemble average of the BER at all values of $I$. Therefore, the final BER of OOK should be [14]

_{$P(r)$}is the probability density function (PDF) of beam wander at the receiving point following a Rayleigh distribution [16] when a laser beam propagates in the atmosphere, the expression is

_{${{\displaystyle P}}_{r}(I)$}is the PDF of intensity $I$ at the receiving point following a log normal distribution under weak turbulence conditions, which is [11]

For these two PDFs, ${{\displaystyle \sigma}}_{r}^{2}$ and ${{\displaystyle \sigma}}_{I}^{2}(r,L)$ are the respective variances, which are given by [11]

## 3. Simulation

Based on the theory introduced above, we start numerical simulation with 1550nm signal and 980nm pump, and other conditions are also mentioned below. Parameters for EDFA are from [8], where ${{\displaystyle \alpha}}_{p}=2.9\text{dB/m}$, ${{\displaystyle \alpha}}_{s}=1.3\text{dB/m}$, ${{\displaystyle \alpha}}_{p}^{\text{'}}=0.025\text{dB/m}$, ${{\displaystyle \alpha}}_{s}^{\text{'}}=0.004\text{dB/m}$, ${{\displaystyle g}}_{s}=1.134\text{dB/m}$, and the length of EDF is $l=24\text{m}$. As for the other parts of the laser link, we take the values below, $\eta =0.7$, ${{\displaystyle G}}_{A}=10\text{dB}$, $F={{\displaystyle {{\displaystyle G}}_{A}}}^{0.7}$, ${{\displaystyle I}}_{b}=10\text{nA}$, ${{\displaystyle I}}_{dc}=1\text{nA}$, $R=50\Omega $, $T=300\text{K}$, $h={{\displaystyle 6.626\times 10}}^{-34}$, $e={{\displaystyle 1.602\times 10}}^{-19}\text{C}$, ${{\displaystyle k}}_{b}={{\displaystyle 1.381\times 10}}^{-23}$, ${{\displaystyle \tau}}_{T}={{\displaystyle \tau}}_{R}=1$, ${{\displaystyle n}}_{sp}=0.75$, ${{\displaystyle B}}_{o}=10\text{GHz}$, ${{\displaystyle B}}_{e}=40\text{MHz}$, $\alpha =1$, $\delta \nu ={{\displaystyle B}}_{o}$, ${{\displaystyle P}}_{in}=10\text{mW}$, ${{\displaystyle P}}_{p}=2\text{W}$, ${{\displaystyle D}}_{r}=0.2\text{m}$, $\zeta =0$, $\theta =30\text{\mu rad}$, $H=38000\text{km}$, ${{\displaystyle h}}_{0}=100\text{m}$.

In order to get an appropriate output power (about 1 W) of the laser, we modify the parameters in [8]. We use the 2W pump for EDFA, and this does not affect the overall parameters.

The ${{\displaystyle \alpha}}_{RAD}$ of 1550nm and 980nm is obtained from Eq. (5) with the ${{\displaystyle \alpha}}_{RAD}$ of 1310nm cited from [8], and the gain of EDFA obtained from Eqs. (1) and (2) versus Dose of radiation are shown in Fig. 1. The parameter $c$ in Eq. (4) is variable at different temperature, which is testified in [8] that $c={{\displaystyle 0.19\times 10}}^{-3}$ and $c={{\displaystyle 0.30\times 10}}^{-3}$ for $20\xb0\text{C}$ and $73\xb0\text{C}$, respectively. And, the parameter $f$ and the dose rate $R$ are given by $f=0.77$, $R=269\text{Gy/h}$ [8].

The radiation-induced losses of 1550nm and 980nm grow with the increasing dose of radiation, leading to degradation of the gain of EDFA. The gain of EDFA with 250Gy radiation is 2dB lower than that with no radiation when the temperature is $20\xb0\text{C}$. In addition, the radiation-induced loss of 1550nm at $73\xb0\text{C}$is always higher than that at $20\xb0\text{C}$and achieves the largest gap, 0.14dB/m, when the radiation dose reaches 3000Gy. For the radiation-induced loss of 980nm, the largest gap is 0.42dB/m at the dose of 3000Gy. Hence, the gain of EDFA also degrades for about 4.65dB. This figure shows that the rise of temperature will aggravate the negative impact of radiation on EDFA.

In Fig 2. the impacts of radiation and temperature on BER performance are clearly illustrated. At $20\xb0\text{C}$, the BER rises constantly when the dose of radiation rises, and it increases 2.5 orders of magnitude with 250Gy radiation than that with no radiation. Due to the rising temperature, BER at $73\xb0\text{C}$ increases much more with the increasing dose than that at $20\xb0\text{C}$. Particularly, the largest gap between the two conditions appears at the dose of 1250Gy, reaching 2 orders of magnitude. And the gap gradually decreases after that mainly because the influence of radiation on EDFA has reached the saturation.

To find an optimal configuration for the laser link in radiation environment, we investigate some of the most relevant parameters in different dose of radiation.

Figure 3 shows the evolution of the BER performance with the rising divergence-angle which ranges from 5$\text{\mu rad}$ to 80$\text{\mu rad}$. Analyze the curve which is produced with no radiation, we find that the BER decreases firstly, reaches the minimum value at the point of 23.75$\text{\mu rad}$and then increases constantly. Similar results are obtained in other conditions, indicating that there is always an optimal value for the divergence-angle that makes the laser link the best BER performance. However, the optimal value is variable. It decreases by 7.5$\text{\mu rad}$from 23.75$\text{\mu rad}$ to 16.25$\text{\mu rad}$when the dose increases from 0Gy to 1000Gy. It enlightens us that, to obtain a better BER performance, we should low down the divergence-angle a little when the space radiation increases.

Figure 4 suggests that the increasing receiver diameter can decrease BER. With different dose of radiation, the trends of BER versus divergence-angle are the same. And the gap of adjacent curves almost keeps invariable when the divergence-angle increases. In an uplink, the receiver is installed at the satellite, so its diameter cannot be too large. However, BER is quite sensitive to the variation of the receiver diameter. So increasing the diameter is also helpful for BER improvement in radiation environment.

Figure 5 indicates that there are minimum values of BER for optimal ${{\displaystyle W}}_{0}$with different dose of radiation. Therefore, by choosing an optimal ${{\displaystyle W}}_{0}$, the BER performance can be enhanced. And, it is shown that the value of the optimal ${{\displaystyle W}}_{0}$ decreases 0.0575m from 0.14425m to 0.08675m when the dose increases from 0Gy to 1000Gy. In order to reduce the aggravation caused by increasing radiation dose, ${{\displaystyle W}}_{0}$ should be appropriately reduced.

## 4. Conclusion

In conclusion, we can see that the BER performance is greatly influenced by space radiation with the numerical simulations. Particularly, the rise of temperature will aggravate the impact of radiation on the BER performance which suggests that the EDFA cannot work at high temperature and a system of heat dissipation is essential. Besides, the BER performance is greatly sensitive to the receiver diameter. And, it is noticeable that the divergence-angle and the transmitter laser radius respectively have optimal values to get the minimum value of BER. In addition, the optimal values decline with the increasing dose of radiation.

Based on these conclusions, it is possible to set an optimal configuration for the laser link. On the premise that the basic parameters are invariable, the BER will increase when the dose of radiation increases. To minimize the value of BER, we can firstly choose the receiver of large diameter, then select the laser with optimal divergence-angle and optimal transmitter laser radius. Although the operations expounded above cannot be dynamically realized in space, they offer a guidance for selection of lasers and receivers that adapt to certain dose of radiation. Even more, several configurations of lasers and receivers corresponding to different doses of radiation can be set up, and a quasi self-adaptive system will be built eventually.

## Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant 61205045, Jiangsu Provincial Natural Science Foundation of China under Grant BK2011555, Suzhou Province Science and Technology development Program of China under Grant SYG201307, National Natural Science Foundation of China under Grant 61377086, National Basic Research Program of China (973 Program) under Grant 2010CB327803.

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