## Abstract

In this paper, experimental results related to the received-power fluctuations in a LEO satellite-to-ground laser-communication link using the Small Optical TrAnsponder (SOTA) are presented. The data is compared to the theoretical expectations based on the Hufnagel-Valley model. The discrepancies in the results are discussed by spectrum analysis and by a comparison with the Differential Image Motion Monitor (DIMM) measurements of the Fried parameter. Finally, the experimentally-derived coherence time is shown and discussed.

© 2017 Optical Society of America

## 1. Introduction

Satellite laser communications are gaining more attention as a promising alternative to Radio-Frequency (RF) based communications providing much wider bandwidths with lower size, weight and power consumption compared to the analogical RF solutions. While the advantages of the technology in inter-satellite scenarios are clear, direct satellite-to-ground links can further increase its possible applications, for example, high-speed optical feeder links [1], relay links [2, 3] for geosynchronous satellites, or ultra-high-speed optical link between Low-Earth Orbit (LEO) micro satellites and ground [4–6]. When the laser beam propagates through the atmosphere though, there are several important factors that can severely affect and even terminate the communication link.

For every future satellite-to-ground link design, it is essential to know the main atmospheric-turbulence parameters –– the scintillation index, the Fried parameter and the Greenwood frequency (reciprocal to the coherence time) – since they will have a significant impact on the link budget. For FEC and interleaver testing simulators with fading generators requiring the received optical power Probability Density Function (PDF) and coherence time are built [7, 8]. Often the only available data is the scintillation index, measured or theoretically derived by the Hufnagel Valley model [9], and the PDF, which for simple scenarios is considered to be the lognormal distribution.

In order to increase the knowledge for the LEO satellite-to-ground beam propagation through the atmosphere, the National Institute of Information and Communications Technology (NICT), Japan, developed the Small Optical TrAnsponder (SOTA), which has a total mass under 6 kg and was designed to be installed on a 50-kg class microsatellite [10]. The received power fluctuations PDF and partially the scintillation index measurements have been already discussed in [11]. This paper concludes the experiment results analysis by a deeper discussion on the scintillation index and the relationship among the later, the Fried parameter and the coherence time, including frequency domain processing and analysis, and theory-versus-experiment data comparison considering the implementation specifics.

The paper is organized as follows. Section 2 provides the theoretical background with the relationships between the atmospheric-turbulence parameters. In Section 3, the experimental setup is introduced. Section 4 consists of the experimental results and the comparison with the theory and finally Section 5 concludes the paper.

## 2. Theoretical background

When a laser beam propagates through the atmosphere, its wavefront gets distorted and spatial and temporal fluctuations of the beam irradiance occur. For big receiving apertures, the spatial wavefront fluctuations are an obstacle to effectively concentrate light in the small-size receiver (photodiode, fiber, etc.).

The phase aberrations of the laser-beam wavefront in the receiving plane are characterized by the Fried parameter, *r _{0}*, given in [cm], and describing the diameter of a circle over which the root-mean-square-wavefront aberration due to atmospheric optical turbulence is equal to 1 radian [12]. There are techniques, such as Adaptive Optics (AO) [13], that allow wavefront correction. The temporal fluctuations of the received signal due to atmospheric turbulence can potentially lead to errors due to false ‘0’ or ‘1’ decisions and their strength is described with the scintillation index,

*σ*. Of particular importance is the length of the fades under a designated threshold since such fades lead to long (up to several milliseconds) burst errors that are hard to correct without using long interleaver in combination with Forward Error Correction (FEC) codes. To be able to estimate a particular interleaver/FEC performance under atmospheric turbulence the parameter coherence time, τ

_{I}^{2}_{0}, is also necessary.

#### 2.1 Scintillation index

The scintillation index is defined as the normalized variance of the received power (intensity) fluctuations and can be derived from experimental data [9]:

where*I*is the intensity in the receiver and

*σ*

_{χ}^{2}is the log-amplitude variance.

*σ*

_{I}^{2}is often evaluated in terms of Rytov variance [14]:

*k*is the wavenumber,

*ζ*is the zenith angle, and h is the altitude (h

_{0}is the altitude of the OGS over the sea level). The refractive index structure parameter

*C*

_{n}^{2}(h) profile is a fundamental parameter in the presented analysis. It is often described with the Hufnagel-Valley (HV) model [9], in which the wind profile is given by the Bufton wind model [9].

The typical receiving optical antenna for satellite-to-ground communications is a telescope with relatively big size (0.2 m to 1 m diameter), which requires to take into account the aperture averaging effect –a decrease of the received power fluctuation levels with the increase of the receiver aperture size [9].

#### 2.2 Fried parameter

The Fried parameter is a quantitative measure of the quality of the optical transmission through the atmosphere and is defined as [15]:

The Fried parameter is a function of wavelength, and typically is referenced at a wavelength of 500 nm at zenith and then scaled according to the desired zenith angle and optical link wavelength. In the provided analysis, the chosen wavelength is 1550 nm since this is often considered to be the wavelength of interest for satellite-to-ground laser communications and the SOTA experiments are performed at this wavelength.

Fried parameter can be measured by using a Differential Image Motion Monitor (DIMM) –a telescope system with a mask at the front forming two separated sub apertures with a diameter *D _{A}* at a distance

*d*. By attaching one or two prisms over the sub apertures, two separated spots are formed in the image sensor. The measured variances of the differential motions of the two images –

_{L}*σ*(the projection parallel to the line connecting the apertures) and transverse

_{L}*σ*(the projection perpendicular to the connecting line) – are related to the Fried parameter [15].

_{T}The main advantage of the DIMM-measurement method is the fact that it only measures the angular difference between the two images and remains unaffected by any motion different than the atmospheric turbulence, including implementation issues such as erratic motion of the telescope.

#### 2.3 Coherence time

The coherence time *τ _{0}* represents the time duration when the signal shows a high-amplitude correlation. It is related to the Fried parameter as [16]:

Where

The coherence time can also be calculated directly from the autocovariance function of the received power. A method of calculation is shown in [17].

## 3. Experimental setup

NICT conducted LEO satellite-to-ground laser-communication experiments with SOTA for over two years. Figure 1(a) shows the optical part of SOTA with its position on the SOCRATES satellite. SOTA consists of two parts –optical and control (not shown), with total weight under 6 kg and power consumption under 40 W. The optical part consists of a two-axis gimbal and the elevation stepper motor is visible in the left. There are four transmit beams with different wavelengths. The 5-cm mirror serves both as transmitter antenna for the 1550-nm wavelength and as receiver of the OGS beacon. Under the 5-cm Rx on the right side the coarse tracking and acquisition sensor can be seen. The fine-tracking sensor with a fast steering mirror are behind the 5-cm antenna. While SOTA allows experiments using different wavelengths, the main focus of this work is the 1550-nm wavelength, which is considered to be one of the most promising candidates for future satellite lasercom networks.

The OGS setup is shown in Fig. 1(b). The top-right image shows the 1-meter telescope dome from outside. At the right of the same picture, a part of the 1.5-meter telescope dome is visible. The distance between both telescopes is about 10 meters. Since the SOTA 1550-nm beam divergence is 223 μrad and the distance between the satellite and the ground is about 600 km at 90-degree elevation angle, the beam spot on the ground is in the order of 130-meter diameter and that allows the parallel receiving of the same signal from the satellite in both telescopes. On Fig. 1(b), the left picture shows the 1-meter telescope with the receiver bench on the right nasmyth. Parallel to it on the circled optical bench the 5-cm receiver, the DIMM and the beacon are mounted, shown separately in the bottom-right picture. The main purpose of the 5-cm receiver in parallel is to observe the aperture averaging effect compared to the big telescopes. The received-power fluctuations from all the apertures were recorded at a 20-kHz sampling rate.

The SOCRATES satellite is in a Sun-synchronous near circular orbit and it is visible from the OGS for a short period of time (several minutes), called pass. The experiment flow is as follows. SOTA will receive in advance commands for the time to switch the tracking and acquisition system on and for initial gimbal coordinates. The satellite orbit information is given to both telescopes to predefine their movement during the pass. At a given time, the strong beacon is switched on. Once it hits SOTA, tracking and acquisition start and the downlink signal is sent from SOTA and received in the telescopes. There is no fast steering mirror in the NICT OGS, but different implementations with fast steering mirror at the German Space Agency (DLR) [5] and Centre National d'Etudes Spatiales (CNES) [6] were used for SOTA experiments.

## 4. Results

The data from the experiment on 2016/5/5 is shown in Fig. 2. The theoretical fitting is performed on the experimental data by applying the HV model using the wind measurements from the NICT weather-monitoring system. Thus, the only changing parameter for the fitting is the ground scintillation, represented by C_{n}^{2}(0) in the HV model. Similar results were received in all communication passes available but for simplicity only one experiment is shown in this paper. There are several discrepancies between the measurements and theory. First, the 1-meter telescope and the 1.5-meter telescope results look similar with scintillation indices of about 0.05 to 0.1. Such values are much higher than the theoretically expected ones. Second, it can be seen that the 5-cm telescope scintillation index changes as expected with the change of the elevation angle. However, the scintillation indices for the 1-meter and the 1.5-meter telescopes are relatively constant and for the later, it can be speculated that the scintillation index increases in contradiction with the theoretical expectations. Third, it appears that there is no aperture-averaging effect when the 1-meter and the 1.5-meter telescope results are compared.

The first two points have been partially discussed in [11] and explained with the increasing tracking and pointing errors for high-elevation angles, and respectively, high slew rates and the discussion continues in this work.

It can be seen that for low-elevation angles in the beginning of the experiment the theoretical aperture-averaging effect is similar to the experimental one (Fig. 3). However, with the increase of the elevation angle, the experimental values change drastically and they reach even lower values for the ratio 1.5-meter/5-cm receiver compared to the 1-meter/5-cm one.

One neutral reference to compare the results would be the Fried parameter measurement from the DIMM, since it is not affected by the implementation-related movements. By inserting the best-fit parameters into the HV model and into the integral in Eq. (3), the expected values for the Fried parameter can be calculated. Figure 4 shows the comparison between the actual DIMM measurements and the expected *r _{0}* from the scintillation-index fitting for the experiment as derived for Fig. 2. While the actually measured

*r*mean value is over 10 cm, the expected theoretical values by using Eq. (3) and the best fit parameters predict around 2 cm for the 5-cm receiver and under 1-cm values for the 1-meter and the 1.5-meter telescope.

_{0}To summarize the results above, there are two main anomalies with the experimental results as opposed to the theoretical expectations. First, the scintillation-index values are much higher than expected. Second, the aperture-averaging effect seems to be very small and even negligible for higher elevation angles. To explain that, Fig. 5 shows the spectrograms for all four parallel apertures data from 2016/5/5, where the y-axis is the PSD, calculated for each experiment second on the x-axis. Although just one experiment is shown here, the same effect has been observed in all the other experiments. The magnitudes on all four graphs have been equalized so that the levels can be easily compared. While there are some common noises for higher frequencies, the particular effect to be discussed is clearly noticed on frequencies up to 200 Hz and this limit has been adopted for the graphs. It can be seen how the PSD magnitude changes with the size of the telescope –for both 5-cm receivers the magnitude is much stronger compared to the 1-meter receiver due to the aperture averaging effect. It is also visible that the 1.5-meter receiver has the lowest magnitudes, respectfully atmospheric-turbulence contribution compared to the other apertures. However, it is interesting to notice that there are non-random contributions, a number of harmonics, which frequency and magnitude changes with the elevation angle. They go almost unnoticed for the 5-cm receivers because of the stronger atmospheric-turbulence effect and their contribution is not that significant. However, with the aperture effect taking place, the atmospheric-turbulence effect weakens and the non-random harmonics become the dominant contribution.

It is out of the scope of this manuscript to discuss in detail the source of these harmonics. Furthermore, they are not random and are completely implementation-specific. In order to provide clear results that can be compared to the theory, these effects must be removed. Also, such implementation contributions with different characteristics are to be expected in other experiments with different telescopes and LEO satellites and their effect is not negligible. To prove the concept that these contributions do actually prevent the results to show good agreement with the theory, a simple filtering has been performed. The spectrogram for 1-meter telescope is analyzed to separate their frequencies. For simplicity, only several harmonics have been chosen in a limited-time interval where they are relatively linear. The left side of Fig. 6 shows the center frequencies that have been defined to be filtered. These six band stop notch filters, together with a low-pass filter removing the non-scintillation contributions over 2 kHz have been applied to the raw received optical signal. The resulting spectrogram is shown in the right side of Fig. 6.

While the filtering method is far from perfect, it is useful to prove the concept that the harmonics due to implementation have a strong effect on the received-power fluctuations. In a future research, an improved filtering will be performed for more accurate results. Figure 7 shows a comparison of the scintillation index of the 1-meter receiver data before and after filtering. There is a decrease in the scintillation index after the filtering and although speculative, it can be said that some relation between the elevation angle and the scintillation index is observed.

The experimentally-derived coherence time for the two dates (2016/4/5 and 2016/5/5) and all four apertures are shown in Fig. 8 and Fig. 9, respectively. There are two points of interest. First, the big difference in the values for the coherent time between the small apertures and the big telescopes. The main reason is the temporal averaging effect, explained in detail in [18]. Second, while the scintillation is weaker for the experiment on 5th of April, the coherence time is longer for the same date, compared to 5th of May. The main reason is the wind component in the HV model. If the Bufton wind model is used, there are three components to be considered. The slew rate creates a pseudo wind that will increase with the higher-elevation angles due to the Altazimuth telescope, which has been used. The other two components in the model are given assuming that the wind direction is normally horizontal above the ground. In respect of the receiver aperture though, as discussed in [19], the wind must be perpendicular to the propagation path${v}_{\perp}={v}_{\mathrm{mod}el}\mathrm{cos}(\zeta )$. This defines stronger wind speed, respectfully shorter coherence time, for higher elevation angles. Apart from that, the ground wind speed for 5th of April was 0.6 m/s, while on 5th of May it was 1.8 m/s, which also contributes for lower values on the second date.

## 5. Conclusion

When a satellite laser communication link is designed, the interleaver and FEC are chosen based solely on scintillation theory. However, as shown in this paper, scintillation theory provides the ideal-case scenario and each real implementation will insert additional noise and fluctuation components to be considered. The statistics for four different apertures, gathering the received optical power from SOTA in parallel have been presented and discussed. The abnormally-high scintillation-index values, especially for the bigger apertures and the small aperture-averaging effect have been compared to the theoretically expected ones by fitting or calculation from widely accepted theoretical models. The spectrograms clearly showed that the relatively-constant implementation contributions are slightly noticeable for small apertures due to the strong scintillation effect, but with the increase of the telescope size, and respectfully, the aperture-averaging effect these contributions become dominant preventing the expected scintillation index drop for higher-elevation angles and maintaining high values. To support these claims, DIMM measurements of the Fried parameter, which are independent on any vibration movements apart from the movements due to scintillation itself. A novel concept for filtering of the non-random effects, visible from the spectrograms has been proposed in order to mitigate the pointing and tracking errors, vibrations, etc. Finally, the statistics for the coherence times is presented with a short discussion on the temporal averaging effect for bigger receiving apertures and strong influence of the wind over scintillation in the time domain has been provided.

## Acknowledgment

The authors would like to express their appreciation to all the members of National Institute of Information and Communications Technology (NICT), NEC Corporation, Nishimura Co. Ltd, and the satellite-bus maker Advanced Engineering Services Co. Ltd. (AES) for their consistent support during the preparation and execution of the tests. The authors would like to thank all the engineers of NEC (the prime contractor of the SOTA terminal) for their support in the tests.

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