## Abstract

Although there is an urgent demand, it is still a tremendous challenge to use the coherent optical communication technology to the satellite-to-ground data transmission system especially at large zenith angle due to the influence of atmospheric turbulence. Adaptive optics (AO) is a considerable scheme to solve the problem. In this paper, we integrate the adaptive optics (AO) to the coherent laser communications and the performances of mixing efficiency as well as bit-error-rate (BER) at different zenith angles are studied. The analytical results show that the increasing of zenith angle can severely decrease the performances of the coherent detection, and increase the BER to higher than 10^{−3}, which is unacceptable. The simulative results of coherent detection with AO compensation indicate that the larger mixing efficiency and lower BER can be performed by the coherent receiver with a high-mode AO compensation. The experiment of correcting the atmospheric turbulence wavefront distortion using a 249-element AO system at large zenith angles is carried out. The result demonstrates that the AO system has a significant improvement on satellite-to-ground coherent optical communication system at large zenith angle. It also indicates that the 249-element AO system can only meet the needs of coherent communication systems at zenith angle smaller than 65̊ for the 1.8m telescope under weak and moderate turbulence.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

In recent years, the technology of free-space optical communication (FSOC) has gained importance due to high bandwidth and data rate requirements [1]. At present, FSOC technology is mainly applied to satellite communication system since the traditional wireless microwave communication technology has been unable to meet the needs of satellite communications. Many institutes and universities have successively studied the theories and carried out in-orbit experiments including inter-satellite links, low earth orbit (LEO) satellite-to-ground links, synchronous orbit satellite-to-ground links and deep-space prober-to-ground links [2–9]. However, there still are many unsolved problems. The technology of achieving high data rate optical communications at large zenith angle is one of them. On the one hand, for a LEO satellite-to-ground optical communication system, the available time for data transmission is limited due to the fast angular velocity of the satellite terminal. A feasible way to increase the data transmission time is using the technology of high date rate laser communication at large zenith angle. On the other hand, the zenith angle of the synchronous satellite is large and unchangeable when the ground station is located in a high-altitude area. Therefore, the large zenith angle and high data rate optical communication technologies play an important role in the satellite-to-ground optical data transmission systems.

For the long-range and high-speed communication link, e.g. the link between the synchronous satellite and the ground station, the received signal photons per bit is limited, which results in difficulties to establish a high-speed free-space communication link with the common non-coherent intensity modulation / direct detection (IM/DD) scheme. The coherent free-space laser communications, with its extremely high sensitivity, have been paid more and more attention and have high potential to be used in practice in the future [10,11]. However, with the increasing of zenith angle, turbulence influence in the atmosphere which affects the optical beam quality of the carrier light becomes more serious especially on the coherent receivers. Adaptive optics (AO) is a means for real time compensation of the phase distortions caused by turbulence [12]. It consists of using an active optical element such as a deformable mirror to correct the instantaneous wavefront distortions and has been used in numerous areas, such as astronomy observation [13]. Many researchers have demonstrated that the AO is also a powerful tool to improve the performance of the non-coherent laser communications [14–17]. Some researchers have also pointed out that the AO can be utilized in the coherent laser communication system to improve its performance [18–21]. However, detailed results of satellite-to-ground coherent optical communication at large zenith angle with AO technology have not been reported to our knowledge.

In the next few sections, after theoretical analysis of mixing efficiency, BER, and atmospheric turbulence, various simulative results of mixing efficiency and BER in a coherent optical receiver with different modes AO correction are presented. Then the verification experiment of coherent optical communication using a 249-element AO unit is carried out at large zenith angle and the mixing efficiency and BER of the communication system are studied.

The purpose of this paper is to present the evaluation as well as the experimental verification of the performance improvement using AO technology on satellite-to-ground coherent optical communication systems at large zenith angle. The AO system design should achieve high data rate satellite-to-ground coherent optical communication at large zenith angle.

## 2. The theories

#### 2.1 The mixing efficiency of coherent detection

In the coherent detection technique, a continuous-wave (CW) is combined with the optical signal coherently before it falls on the photo-detector (PD). The CW light is generated locally at the receiver using a narrow-linewidth laser, called the local oscillator (LO). Considering the principle of coherent detection, the optical power of the combined beam is given by [22]

*K*is a constant of proportionality. ${A}_{S}$ and ${A}_{LO}$ represent the optical magnitudes of signal light and LO beam at the PD plane respectively. When $\Delta \omega $ equals to zero, it is called homodyne detection. Otherwise, it is called heterodyne detection. In this paper, we only study the homodyne detection because the atmospheric turbulence has the similar influence on homodyne and heterodyne detection. The effective photocurrent ($I=RP$, where

*R*is the detector responsivity) of the homodyne detection is given byandWhere $\text{\eta}$ is the quantum efficiency of the PD, $\upsilon $ and

*h*represent the frequency of the carrier wave and Planck constant, respectively. The advantage of coherent detection for lightwave systems can be analyzed by considering the signal-to-noise ratio (SNR) of the receiver current. The receiver current fluctuates because of shot noise and thermal noise which are the two fundamental noise mechanisms responsible for current fluctuations in all optical receivers even when the incident optical power is constant. The variance of current fluctuations is given by [23]wherewhere ${\sigma}_{S}^{2}$ is the variance of shot noise and ${\sigma}_{S}^{2}$ is the variance of thermal noise. $\Delta f$ is the effective noise bandwidth of the receiver, ${I}_{d}$ is the dark current. ${k}_{B}$ is the Boltzmann constant, $T$ is the absolute temperature. ${R}_{L\text{}}$ is the load resistor. The SNR is obtained by dividing the average signal power by the average noise power, and it is given by

For the coherent detection, the optical power of LO laser can be chosen extremely high at the receiver, that means

Thus, according to Eq. (2), Eq. (3), Eq. (6), and Eq. (7), the SNR can be expressed asIt can be clearly seen from Eq. (8) that the phase difference $\text{\Delta \phi}$ effects the signal-to-noise rate. The LO laser is a local beam which can be seen as a plane light. If $\text{\Delta \phi}$ equals to zero, the SNR without turbulence can by expressed as

However, due to the influence of the turbulence channel, the wavefront of the signal beam is distorted. We define the mixing efficiency of the coherent detection

Under the assumption that no other wavefront distortions are present in the system, the mixing efficiency is the ratio of the actual SNR under atmospheric turbulence over the SNR without atmospheric turbulence. It can be used for evaluating the influence of the turbulence channel to the coherent detection. Equation. (10) also indicates that the mixing efficiency is determined by the spatial amplitude distribution and spatial phase distribution difference $\text{\Delta \phi}$ between the signal beam and the LO beam. For a turbulence channel, we mostly focus on the influence of phase distribution difference. The mixing efficiency as a function of phase distribution difference is shown in Fig. 1 by statistics of 1000 calculating results.

Generally, it is not easy to measure the mixing efficiency of a coherent optical communication system. However, the Strehl Ratio (SR) of the incident light is much more convenient to acquaint. For a relatively small wavefront aberration, the RMS of the wavefront aberration is related to the SR through [24]

Where $\text{\sigma}$ is the root-mean-square (RMS) of the wavefront aberration which is in the unit of wavelength. The curve in Fig. 1 shows the SR as a function of phase wavefront. It’s shown thatIt is indicates that the mixing efficiency nearly equals to the Strehl ratio of the far-field of the incident signal beam for the coherent detection. The deviation is smaller than 4% when the SR is larger than 0.36. This conclusion is very useful for the evaluation of the coherent optical receiver after the correction of the adaptive optics.

#### 2.2 The BER of coherent detection

In the field of optical communications, it is very useful to express the SNR in terms of the number of photons received within a single bit, ${N}_{p}$. At the bit rate $B\approx 2\Delta f$, the signal power ${{\displaystyle \int}}^{\text{}}{A}_{S}^{2}dU$ is related to ${N}_{p}$ as

thus, the SNR is given by a simple expressionThe BER of coherent detection is [22]

where the function*erfc*is the complementary error function. For the synchronous binary phase shift keying (BPSK) coherent receiver R can be expressed as

Equation (14) to Eq. (16) then provide the following expression of the BER of BPSK coherent detection

From Eq. (17), it is obviously shown that the BER is determined by the received signal optical power per bit ${N}_{p}$ and the mixing efficiency $\gamma $. In order to obtain a higher incident optical power, larger diameter of telescope is required. However, with increasing the diameter of the receiving telescope, the impact of atmospheric turbulence becomes serious and decreases the mixing efficiency of the coherent receiver. It is studied in section 2.3.

#### 2.3 The turbulence in satellite-to-ground channel

The analysis of satellite-to-ground laser communication system requires a good appreciation of the characteristics of the wavefront aberrations caused by turbulence channel. Since the aberrations are random, they can only be described statistically using statistical estimates such as variances, or covariances. The turbulence strength is discussed by the statistics of their evolution, mean value and standard deviation for a given telescope.

Kolmogorov [25] studied the mean-square velocity difference between two points in space divided by a displacement vector ** r** and related the velocity structure to the index-of-refraction structure. The index-of-refraction structure function is defined as [26]

*h*is the height above sea level in meters. $\text{\omega}$ is the wind speed. If the site is at sea level, $\text{\omega}$ and

*A*are given byand

Figure 2 illustrates the HVB model refractive-index structure value as a function of altitude. It can be seen that most of the atmospheric turbulence occurs under an altitude of 10 km.

In a study of an optical heterodyne communications receiver, Fried found that the maximum allowable diameter of a collector before atmospheric distortion seriously limits performance is the coherence length [28]

In this expression, $L$ is the path length, $\theta $ is the zenith angle. The coherence length characterizes the effect of seeing at a particular wavelength. According to Eq. (17), ${r}_{0}$ increases as the $6/5$ power of wavelength. We analyze the coherence length in satellite-to-ground link with different zenith angle in the 1550 nm waveband. As shown in Fig. 3, the coherence length decreases rapidly when the zenith angle is larger than $60\xb0$.

## 3. The simulative results

For this simulative study, we make a number of assumptions about the AO system. As this paper does not investigate the high-bandwidth control, reduce anisoplanatism or reduce the noise of the AO system, we assume that the control bandwidth is unlimited, the noise of the AO and the isoplanatic errors are neglectable. That is, our study focuses on the spatial-phase-control effects of the AO system. Since the AO system don’t have the ability to correct the optical intensity scintillation, we also assume that the amplitude distributions of the received optical signal and the LO laser are uniform. Besides, we use Zernike polynomials to describe the atmospheric turbulence wavefront. A review of the properties of the Zernike modes relevant to the description of atmospherically turbulence wavefront can be found in a paper by Noll [29]. The number of Zernike modes used to generate the turbulent wavefront is 231 and the diameter of the telescope is 1800 mm. The residual turbulent wavefront error is generated using the residual Zernike coefficients. The grid number of the turbulent wavefront is $256\times 256.$

The mixing efficiency of coherent detection over different zenith angle is shown in Fig. 4. With only tip & tilt correction, the mixing efficiency is smaller than 0.03 when the zenith angle equals to 0. This simulative result is due to the relatively large diameter of the simulative telescope, which the tip/tilt is averaged and mainly occurs in the sub-apertures, thus in higher aberration orders. When the zenith is greater than 10 degrees, the mixing efficiency is nearly 0. Therefore, if the coherent system is only with tip & tilt correction, no matter how high the altitude angle of the satellite terminal is, the coherent receiver cannot work well.

With AO correction of 15 modes, the mixing efficiency increases to 0.48 or 0.05 when the zenith angle equals to 0 or 80 degrees, respectively. When the zenith angle of the satellite terminal is small ($\text{smaller}\text{than}50\xb0$), the coherent receiver can obtain a mixing efficiency larger than 0.3. It is indicated that the coherent detection can be realized with low-order AO correction when the zenith angle is small. However, when the zenith angle is large (larger than $\text{}50\xb0$), higher orders aberration correction is needed. For example, with AO correction of 65 modes, the mixing efficiency is 0.65 even the zenith angle equals to 80 degrees. This conclusion is favorable to design AO systems for satellite-to-ground laser communication systems.

Before discussion of the BER improvement by AO system, the BER degradation due to turbulent channel without AO correction is studied. The quantum efficiency of the PD is deemed to be 1 in this paper. It is shown in Fig. 5 that, in the condition of 80 degrees of zenith angle, the BER reaches 0.5 even though the number photons per bit equals to 100. When the zenith angle equals to 0 degrees, the BER reaches 10^{−3} when the number photons per bit equals to 100, which is not acceptable in a coherent detection system. It is indicated that the AO system is needed urgently when the zenith angle is large.

The BER performances of coherent receivers with AO correction over different zenith angles are illustrated in Fig. 6. The simulation is presented using zenith angles at 0 degree (a), 30 degrees (b), 60 degrees (c), and 80 degrees (d) as well as simulating the coherent system with tip & tilt, 15 modes, 35 modes, and 65 modes corrections. All the BER values are larger than 10^{−2} when the system is only with tip & tilt correction. When the zenith angle equals to zero, BER improves significantly when correcting the turbulence with 15 modes. However, when the zenith angle equals to 80 degrees, the BER is unacceptable when correcting the turbulence of 15 modes, higher aberration correction is needed.

Depending on the above analysis of the simulative results, the performances of mixing efficiency and BER over different zenith angles are discussed carefully. With AO correction, both the mixing efficiency and BER performances increase significantly. The higher the modes that the AO system corrected, the better the mix efficiency and the lower BER value could be performed.

## 4. The experimental results

In order to verify the relationship between the zenith angle and performances of the coherent receiver. The experiment is carried out with a 249-element AO system incorporated with a 1.8 m telescope located on the Gaomeigu station of Yunnan astronomical observatory, China.The AO system uses the visible waveband with the central wavelength of 600 nm to detect the distorted wavefront, and uses the 1550 nm waveband to image the star observed in large zenith angles. The 1.8 m telescope and light path of the AO system are shown in Fig. 7(a) and Fig. 7(b), respectively. The AO system consists of a tip & tilt mirror (TM), a 249-element deformable mirror (DM), and a Hartmann-Shock wavefront sensor. Figure 7(c) shows the CCD image of the Hartmann-Shock wavefront sensor.

At about 20:00 to 23:00 on January 7, 2016, the star SAO015384 was observed. The zenith angle of the star changed from $58.8\xb0$ to $75.5\xb0$. CCD images in the 1550 nm waveband with or without AO correction are acquired in 12 frames per second. Figure 8 shows the star spot distributions in six different zenith angle. When the AO system is on, it is seen that the spread images of the star become a tiny bright point. The smaller the zenith angle, the higher the maximum intensity of the star becomes.

By acquainting the star images for 10 seconds, the curve of the star is illustrated in Fig. 9 over different zenith angles. SR of the star images are measured with the ration of encircled energy curve of the images to the diffraction limit at the first dark diffraction ring. The average SR of the 120 frames (10 seconds) star images are shown in Fig. 9. When the zenith equals to $75.5\xb0$ and the AO system is on, the average SR equals to 0.16, increases about 4.5 times compared with the average SR when the AO system is off. Meanwhile, the zenith angle influences the performance of the AO system significantly. With AO correction, the average SR is 0.521 when the zenith angle equals to $58.8\xb0$, increases almost 4.3 times compared with the average SR when the zenith angle equals to $75.5\xb0$.

According to Eq. (12), in a coherent detection optical communication system, the mixing efficiency of the coherent receiver is approximately equal to the Strehl ratio of the far-field of the incident beam. When the mixing efficiency is obtained, the BER can also be analyzed using Eq. (17). The number of photons per bit of received optical signal to calculate the BER value takes 12 (the received power is −45 dBm for a 5 gigabit per second (Gbps) links). Figure 10 and Fig. 11 illustrate the mixing efficiency and BER value of the experimental results, respectively.

In the experiment, the largest mixing efficiency obtained is 0.51 when the zenith angle equals to $58.8\xb0$, and the lowest BER value is under 10^{−6} with the same zenith angle. According to the analysis above, it is clearly that the zenith angle has a significantly influence on the coherent receiver and the AO system can greatly improve the performance of the coherent detection optical communication system in large zenith angle. However, when the zenith angle equals to $75.5\xb0$, the BER is higher than 10^{−3} with AO correction which is unacceptable. That means the 249-element AO system cannot meet the need for the zenith angle larger than $65\xb0$

## 5. Summary

In this paper, we have shown that the performances of the satellite-to-ground coherent optical communications under the large zenith angle can be greatly improved by the adaptive optics. Higher modes that the AO system corrected, larger mix efficiency and lower BER value could be performed. The experiment of observing stars at large zenith angles with the correction of a 249-element adaptive optics system have been carried out and the performances of the coherent communication system have been analyzed. The results show that, it is still a significant challenge to establish high-speed coherent optical communication links between satellites to ground stations at large zenith angle due to the influence of the atmospheric turbulence. When the zenith angle equals to $58.8\xb0$, the BER is nearly 10^{−7} with AO correction. However, when the zenith angle equals to $75.5\xb0$, the BER is higher than 10^{−3} with AO correction, which is unacceptable. In the free-space communication station that we investigated with 1.8 m telescope, the 249-element AO system cannot meet the requirement of coherent optical communication at the zenith angle larger than $65\xb0$. In order to achieve coherent optical communication at large zenith angle, the higher accuracy and reliability of AO system are required.

## Funding

Chinese Academy of Sciences (CAS) (CXJJ-16S021).

## Acknowledgments

We gratefully acknowledge the suggestions of Professor Wenhan Jian, the Academician of Chinese Academy of Engineering. We also want to acknowledge helpful suggestions from the reviewers and help from the editors.

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