Free-space optical communication has the advantages of size, weight, and power (SWaP) and has prospects for broad application.

With the rapid development of space Internet technologies based on giant constellations such as Starlink and Oneweb, free-space optical communication has received more and more attention and has become the inevitable choice of satellite Internet backbone links^[1–7]. The beam divergence of the laser terminal is tens of µrad, so it needs high-accuracy pointing to reduce the pointing error loss. Typically, the root mean square (RMS) pointing error of an optical terminal is about one-tenth of the beam divergence. However, due to the presence of the micro-vibration of the satellite platform, referred to as the European Space Agency (ESA) micro-vibration spectrum or the National Space Development Agency of Japan (NASDA) micro-vibration spectrum, the pointing error would be greater than the laser beam divergence^[8–10]. In order to ensure the stability and reliability of the communication link, it is necessary for the communication terminal to have a high-precision pointing, acquisition, and tracking (PAT) technology^[11–13]. It is a significant engineering challenge to achieve accurate pointing between two laser terminals. The existing space laser communication terminals mainly use the compound-axis control system of coarse tracking and fine tracking cooperation. They use the coarse tracking unit for coarse pointing and tracking, and use the fine tracking unit to suppress coarse tracking residuals. Between them, the coarse tracking unit has a large range of motion, low bandwidth, and limited precision, and the fine tracking unit has high precision and high bandwidth but a small range of motion^[14,15].

In 2002, the ESA successfully achieved bidirectional laser communication between the geostationary orbit (GEO) satellite ARTEMIS and the low earth orbit (LEO) satellite SPOT4^[16,17]. A direct-driven stepper motor is used as the coarse tracking mechanism, and two mirrors driven by electromagnetic actuators are used as the fine tracking assembly. The independent avalanche photodetector (APD) is used as the communication detector. In order to quickly realize beam acquisition, a beacon with a beam divergence of 750 µrad is used for initial acquisition at the stage of laser link establishment. In 2008, the German LEO satellite TerraSAR-X and the U.S. satellite NFIRE realized bidirectional coherent communication with a bit rate of 5.6 Gbps^[18,19]. Here, the scheme of beaconless acquisition is adopted. In order to establish a laser link, the terminal needs to go through three phases, which greatly increases the complexity of the acquisition and tracking algorithm. In 2019, Lu et al. reported an inter-satellite laser communication terminal based on double Risley prisms beam steering. In this experiment, we adopted a beaconless acquisition and tracking scheme, and the platform micro-vibration below 5 Hz could be effectively suppressed^[20].

The beaconless scheme is a tendency for the SWaP terminal. There are two feasible schemes to realize beam position detection and tracking: the split-signal laser and the corresponding position detector, or communication and tracking multiplex detector. In 2019, Zhao et al. reported a coherent tracking system based on fiber nutation for inter-satellite beaconless laser communication. The receiving field of view (FOV) is only 300 µrad, and a larger FOV will bring more power loss^[21,22]. The FOV of beam position detection mainly depends on the initial pointing deviation of the terminal, which is generally in the order of mrad. Therefore, in order to simplify the scanning, acquisition, and tracking algorithm of laser terminals in orbit, the FOV of beam position detection is preferably selected in the order of mrad.

In this paper, we propose a laser communication system based on a compound-axis tracking scheme. The contents are organized in the following way. First, we introduce the overall structure of the proposed laser terminal. Second, we discuss the key features of the terminal. Third, we present the ground test results and in-orbit experimental results. Finally, we summarize the performance of the terminal and discuss prospects for the terminal application scenarios.

The structure of the beaconless laser communication terminal is shown in Fig. 1. The communication signal is loaded on the intensity of the seed laser through the electro-optic modulator (EOM) to realize intensity modulation. The seed laser-carried signal is amplified by an erbium-doped fiber amplifier (EDFA) and collimated into space. Point-ahead fast steering mirror (FSM) is used to lead pointing caused by the relative axial movement. Dichroic mirrors are used for beam splitting the transmit and receiver lasers, which have different center wavelengths. Fine tracking FSM is the actuator of the fine tracking closed-loop system. The beam expansion ratio of the telescope is 12, and the effective beam diameter is 80 mm. Finally, the divergence angle of the transmitting beam is 60 µrad.

The incident laser is received by a telescope and reflected by fine tracking FSM. The power splitting ratio of the splitter is 96:4. 4% of the received power is reflected into the CMOS camera for calculating the receiving beam position. The remaining received power is coupled into the fiber for amplification and photoelectric detection. The pyramid is used for in-orbit self-calibration of the transceiver optical axis.

In the acquisition stage, the terminal needs to calculate the initial pointing according to the orbit and attitude ephemeris data broadcast by the satellite platform. In the satellite body coordinate system, the initial pointing vector is $$\overrightarrow{P}=R_{\text{jizhun}}^{\text{terminal}}\times R_{\text{body}}^{\text{jizhun}}\times R_{j2000}^{\text{body}}({\overrightarrow{P}}_T-{\overrightarrow{P}}_B),$$(1)and $$\mathrm{Az}=a\sin \left(\frac{P_y}{\sqrt{P_x^2+P_y^2}}\right),$$(2)$$\mathrm{El}=a\tan \left(\frac{P_z}{\sqrt{P_x^2+P_y^2}}\right),$$(3)where $R_{j2000}^{\text{body}}$, calculated by position vectors and attitudes, is the rotation matrix from the J2000 inertial coordinate to the satellite body coordinate. $R_{\text{body}}^{\text{jizhun}}$ and $R_{\text{jizhun}}^{\text{terminal}}$, measured by theodolite, represent the rotation matrix from the satellite to the terminal reference prism and from the terminal reference prism to the terminal pointing coordinate, respectively. $\overrightarrow{P}$, expressed as $\overrightarrow{P}(P_x,P_y,P_z)$, is the pointing vector in the terminal pointing coordinate system. Az and El are the pointing azimuth and elevation angles, respectively.

Generally, the frequency of the position vector and attitude broadcast by the satellite is about 1 Hz. In order to improve the pointing accuracy of the terminal, it needs to process the position vectors and attitude data with an interpolation algorithm. The position interpolation algorithm is expressed as $${\overrightarrow{P}}_B(t)={\overrightarrow{P}}_B(t_1)+\overrightarrow{\upsilon }(t_1)\times (t-t_1)+0.5\times \frac{\overrightarrow{\upsilon }(t_1)-\overrightarrow{\upsilon }(t_0)}{t_1-t_0}\times {(t-t_1)}^2,$$(4)$$\overrightarrow{\upsilon }(t)=\overrightarrow{\upsilon }(t_1)+\frac{\overrightarrow{\upsilon }(t_1)-\overrightarrow{\upsilon }(t_0)}{t_1-t_0}\times (t-t_1),$$(5)where $\overrightarrow{\upsilon }(t_1)$ and $\overrightarrow{\upsilon }(t_0)$ are the velocity vectors of the satellite broadcast at times $t_1$ and $t_0$. ${\overrightarrow{P}}_B(t_1)$ is the position vector at time $t_1$. ${\overrightarrow{P}}_B(t)$ and $\overrightarrow{\upsilon }(t)$ are the calculated interpolation data at time $t$. Figure 2 shows the position and velocity interpolation algorithm error. When the interpolation time is 10 s, the position and velocity errors of the $x$- and $y$-axes are very small and almost stable, while the position and velocity errors of the $z$-axis increase. The largest error is less than 100 m and 0.5 m/s, respectively.

Similarly, the attitude data obtained from the satellite also needs to be interpolated, and the interpolation algorithm is $$\theta =|\overrightarrow{\omega }|\mathrm{\Delta }t,$$(6)$$q_m=[\cos \left(\frac{\theta }{2}\right),\frac{{\omega }_x}{|\overrightarrow{\omega }|}\sin \left(\frac{\theta }{2}\right),\frac{{\omega }_y}{|\overrightarrow{\omega }|}\sin \left(\frac{\theta }{2}\right),\frac{{\omega }_z}{|\overrightarrow{\omega }|}\sin \left(\frac{\theta }{2}\right)],$$(7)and $$Q=\left(\begin{array}{c}\cos (\alpha /2)\times \cos (\beta /2)\times \cos (\gamma /2)-\sin (\alpha /2)\times \sin (\beta /2)\times \sin (\gamma /2)\\ \cos (\alpha /2)\times \sin (\beta /2)\times \cos (\gamma /2)-\sin (\alpha /2)\times \cos (\beta /2)\times \sin (\gamma /2)\\ \sin (\alpha /2)\times \cos (\beta /2)\times \cos (\gamma /2)+\cos (\alpha /2)\times \sin (\beta /2)\times \sin (\gamma /2)\\ \sin (\alpha /2)\times \sin (\beta /2)\times \cos (\gamma /2)+\cos (\alpha /2)\times \cos (\beta /2)\times \sin (\gamma /2)\end{array}\right),$$(8)where $\overrightarrow{\omega }$ expressed as $\overrightarrow{\omega }({\omega }_x,{\omega }_y,{\omega }_z)$ is the broadcast attitude angular velocity in the J2000 inertial coordinate. $\alpha ,\beta ,\text{and}\gamma$ are the broadcast pitch angle, roll angle, and raw angle, respectively, in the 312 rotation order. $Q$ is the corresponding quaternion. $Q_{\mathrm{\Delta }t}=Q*q_m$ is the quaternion corresponding to the interpolation time $\mathrm{\Delta }t$. Figure 3 shows the attitude interpolation error with interpolation time $\mathrm{\Delta }t=1$. The total RMS of the attitude error is less than 0.006 deg (about 105 µrad). The divergence angle of the transmitting beam is on the same order of magnitude, effectively ensuring the rapid establishment of inter-satellite laser linkage.

Table 1 shows the main parameters of the terminal, according to the calculation formula of the inter-satellite laser link. Figure 4 shows the relationship between the link margin and the communication distance. It can be seen from the figure that with the increase of distance, the link margin rapidly decreases, and at a link distance of 3000 km, the margin is about 3 dB.

The micro-vibration characteristics of satellite platforms can have an impact on laser pointing, leading to unstable laser linkage. The National Aeronautics and Space Administration (NASA) and the ESA have conducted in orbit tests on the micro-vibration characteristics of satellite platforms. Using the frequency domain analysis of the micro-vibration data, the vibrations are mainly concentrated within 100 Hz, and the vibration amplitude decreases with the increase of the frequency domain. We adopt a composite-axis tracking control system to effectively suppress micro-vibration interference. An equivalent working model of the control system is shown in Fig. 5.

The position detector is a CMOS camera with variable readout frame rates. In the control system, it is regarded as a delay unit $D(s)$ and is expressed as $$D(s)=e^{-s\tau },$$(9)where $\tau$ is the delay time of the CMOS camera. In the case of ignoring high-frequency resonance, the fine FSM transfer function is equivalent to a first-order function $C(s)$ and can be expressed as $$C(s)=\frac{A}{B\times s+1},$$(10)where $A$ and $B$ are the coefficients of the fine FSM transfer function $C(s)$, which can be determined by fitting the amplitude frequency response curve. The fine controller $G(s)$ adopts the classical proportional integral (PI) control strategy with leading phase compensation, $$G(s)=\frac{K_{p}s+K_i}{s}\times \frac{s+1/T_c}{s+1/\alpha T_c}(0<\alpha <1).$$(11)

The closed-loop transfer function $H(s)$ of the beam pointing is $$H(s)=\frac{A(K_{p}s+K_i)(s+1/T_c)e^{-s\tau }}{s(1+Bs)(s+1/\alpha T_c)+A(K_{p}s+K_i)(s+1/T_c)e^{-s\tau }}.$$(12)

In our study, $\tau$ equals 3 ms. The coefficients $A$ and $B$ are 61.5 and 5.7 × 10⁻⁴, respectively. The ESA measured the vibration spectrum of different satellites and obtained the vibration spectrum function $V(f)$ as follows^[23]: $$V(f)=\frac{160}{1+f^2}\mathrm{\mu }{\mathrm{rad}}^2/\mathrm{Hz}.$$(13)

By optimizing the controller parameters, Fig. 6(a) shows the amplitude frequency curve of the closed-loop transfer function. The theoretical tracking bandwidth is about 70 Hz. Figure 6(b) is the residual micro-vibration spectral density. As shown in the figure, the power spectral density of ESA is effectively suppressed in the frequency band below 50 Hz. Taking 1 Hz frequency as an example, the difference in spectral density before and after suppression is greater than two orders of magnitude. It can effectively suppress the micro-vibration.

In our study, the received signal laser is coupled into the optical fiber, and in order to reduce the sensitivity decrease caused by the connection flange and limited quantum efficiency of the detector at the receiving end, a low-noise EDFA is used to amplify the received optical signal. There are five kinds of noise components: thermal noise ${\sigma }_{\text{Th}}$, shot noise ${\sigma }_{\text{Shot-s}}$ caused by a signal laser, shot noise ${\sigma }_{\text{Shot-}\mathrm{ASE}}$ caused by amplified spontaneous emission (ASE), signal-to-ASE beat noise ${\sigma }_{\mathrm{S-ASE}}$, and ASE-to-ASE beat noise ${\sigma }_{\mathrm{ASE}-\mathrm{ASE}}$^[24]. Table 2 shows the related noise parameters and calculation results.

Receiving sensitivity is an important parameter for inter-satellite laser communication. The formula for the bit error rate (BER) can be expressed as$$\mathrm{BER}=\frac{1}{4}\times [\text{erfc}\left(\frac{{\mathrm{RGP}}_{\text{in}}}{\sqrt{{\sigma }_{\text{Th}}+{\sigma }_{\text{shot}\_\mathrm{ASE}}+{\sigma }_{\mathrm{ASE}\_\mathrm{ASE}}}}\right)+\mathrm{er}\mathrm{fc}\left(\frac{{\mathrm{RGP}}_{\text{in}}}{\sqrt{{\sigma }_{\text{shot}\_s}+{\sigma }_{\text{Th}}+{\sigma }_{s\_\mathrm{ASE}}+{\sigma }_{\text{shot}\_\mathrm{ASE}}+{\sigma }_{\mathrm{ASE}\_\mathrm{ASE}}}}\right)].$$(14)Figure 7 shows the relationship between the BER and the received optical power at a 10 Gbps communication rate. The corresponding received optical power is $-40.5\mathrm{dBm}$ under the BER of 3 × 10^-4. With RS (255,223) error-correction coding, the BER is below 10^-7. Compared with the theoretical curve, the receiver performance has a 1 dB penalty. Ideally, the spontaneous emission factor of the EDFA is 1, corresponding to a noise figure of 3 dB. For the actual EDFA, the noise figure is 4–5 dB, which is the main reason for the 1 dB difference.

In order to test the dynamic tracking and aiming performance of the laser communication terminals, we built a ground-based verification system for simulating the inter-satellite laser communication link. Figure 8 shows the satellite installation and the ground test photograph.

In the ground testing phase, we built an optical testing system and added a beam deflection device to specifically perturb the ground transmitting laser for simulating platform micro-vibrations. After receiving the jitter beam, the terminal begins to track and calculates the tracking error through statistical analysis. Figure 9 shows the tracking efficiency with disturbance frequency. The disturbance suppression bandwidth of the terminal is about 50 Hz. It can effectively suppress the fluctuation of the received optical power. The disturbance suppression bandwidth is lower than the theoretical value of 70 Hz, and it may be the deviation of the transfer function.

On August 4, 2020, the laser terminal installed in the $\mathrm{GMS}\text{-}\mathrm{\beta }$ satellite was launched. At present, the distance between the two satellites is about 900 km. Figure 10 shows the in-orbit tracking performance. According to the orbital data analysis, the tracking error ($3\sigma$) is 2.8 and 2.65 µrad, respectively. The corresponding tracking error loss is less than 0.5 dB. The reason why the tracking performance is better than expected may mainly be due to the smaller amplitude of the micro-vibrations on the satellite platform.

Figure 11 shows the communication BER at a 10 Gbps rate. According to the orbital communication data, the communication link is basically in error-free status after Reed–Solomon (RS) decoding. There are burst bit errors, which may be due to the high-frequency disturbance to the fine tracking loop when unloading the FSM position with the stepper motor. This can be alleviated by changing the unloading amplitude and speed of the motor.

In this study, we designed a compound-axis tracking space laser communication terminal based on single mirror beam steering. We theoretically analyzed the system performance. Through ground verification and in-orbit testing, the terminal’s ability to suppress micro-vibrations has reached 50 Hz, and the tracking error loss is less than 1 dB. The sensitivity of $-40.5\mathrm{dBm}$ was achieved while the BER was below 10^-7 at 10 Gbps. We conducted bidirectional link establishment communication tests 45 times, and the success rate of the link establishment was about 93%.

Through analysis of in-orbit data, platform micro-vibrations are the main factor causing instability and achieving ultra-high precision pointing is one of the main challenges in maintaining laser links. We innovatively adopted compound-axis tracking technology to achieve stable maintenance of the laser links. The results of these studies and experiments provide a feasible choice for high-speed inter-satellite interconnection of space Internet.