Laser as the carrier-based satellite communication is a promising candidate to build the extremely high-bandwidth channel to support Gbps, or even Tbps-level data transmission, which has been applied into the mega constellations, such as Starlink1, Guowang (GW). With the data-rate dramatically increasing, the signal quality becomes more sensitive to the channel state, which is free-space in the laser inter-satellite communications. A misunderstanding on the free-space channel is no distortion happened in vacuum. Unfortunately, based on the real implementation, the clear distortion has been observed, even propagating only between the two satellites2. The distortion sources come from the two aspects: one is in the free-space channel; and the other is from the satellite platform itself. The free-space channel would avoid the distortion from the medium, e.g., the dispersion or the Kerr nonlinearity of fibers as in the fiber-optical communication systems, but the other distortions, such as the Sun radiation3, the Doppler frequency shift4,5, the propagating loss6 still existed. The distortion from the platform is also crucial to the signal’s quality. The random vibration would cause the misalignment between the two satellites, leading to the power variation when the detecting operation7,8. The power instability could bring the extra data-error. Moreover, the power recovery of optical signals through the Erbium-doped fiber amplifier (EDFA) also degrades the signal’s quality due to the amplifier spontaneous-emission noise (ASE). Therefore, the laser communication in outer space still needs to the compensation operation to be against the distortions, especially when the high-order modulation formats applied.

Because of the operational nature of the laser communications, the all-optical signal processing (AO-SP) technology is an optional to be used in the laser payload to improve the signal’s quality. Based on the optical parametric amplification in semiconductor optical amplifiers (SOAs), all-optical regenerator has been proposed to suppress the impact from the Sun radiation3. Based on this work, one can expect that other AO-SP methods9,10,11 could also be potentially applied into such scenario. Although the all-optical operation is attracted because of the fast operational as well as no optical/electrical/optical (O/E/O) conversion, the extra devices, such as SOA or other nonlinear devices are required in the satellite platform. Such requirement becomes the major issue to the weight-sensitive satellite systems. Moreover, the digital signal processing (DSP) approach is a powerful solution to the function of the signal compensation, which has been wildly used in the fiber-based coherent optical transmission systems12,13. The pre-selected algorithm flow is required for the particular communication scenario. The adaptability or intelligent operation is lack in the conventional DSP scheme. To bring the characteristics of the intelligent operation, the artificial intelligence (AI) approach has been introduced into the satellite communications14. To the particular task of the signal equalization, multiple AI methods, such as the echo state network (ESN)15, the neural network16, the transiently chaotic neural network17 and the deep neural network18 have been investigated. But most of works focus on the radio frequency (RF) communication. To the laser channel, the impacts from the laser-related distortions are still the challenge to the inter-satellite communications. In this paper, we introduce the reservoir computing (RC) operation into the laser inter-satellite communications, and investigate the compensation performance for the distortions originated from the Sun radiation, the Doppler frequency shift, and the vibration in the experiment.

The rest of the paper is organized as follows: in “Methods” section, we introduce the RC module for the compensation task of the laser inter-satellite communication systems, and, we also give the detail setup of the experimental platform to investigate the impacts from the Sun radiation, the Doppler frequency shift and the vibration, as well as the RC compensator at the receiver satellite end; in “Results and discussion” section, we discuss the experimental results from the three distortion sources, and perform the compensation behavior from RC module; finally, we draw the conclusions in “Conclusion” section.

Methods

The RC operation is one type of the machine learning concept which could be used to perform the compensation function as well as the hardware implementation with the less computing complexity. To deal with the scenario of laser inter-satellite communications with multiple distortion sources, the RC compensator has the potential to mitigate the impacts by using only one module. Therefore, the investigations on the RC operation could bring the intelligent signal processing into the satellite system with the advantages in cost, volume, weight, power consumption.

RC-based signal compensation

After the propagating between two satellites, the optical signal would be severely distorted by the Sun radiation, the Doppler frequency shift, the vibration of platform, etc. How to improve the signal quality at the receiver end is crucial to the laser inter-satellite communications. In this paper, we introduce the RC operation into the signal compensation in such satellite-communication scenario, depicted in Fig. 1. The RC19,20 has been successfully applied into different scenarios, e.g., the spoken-digit recognition21, the Mackey-Glass time series prediction22,23 and the nonlinear channel equations24,25. The RC module contains three layers: the input layer, the reservoir layer, and the output layer. In the input layer, the input data of the entire network is x(t)=[x1(t), x2(t), ., xK(t)]T at the moment of t, which are caputured at the receiving satellite. K indicates the latitude of the input layer.

Fig. 1
figure 1

RC operation used into the laser inter-satellite communications. [xi(t) indicates the signal distorted by the Sun radiation, the Doppler frequency shift, and the vibration. uj(t) denotes the node state of the reservoir-layer neuron, and yp(t) represents the signal after reservoir].

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For the reservoir layer, the node state of reservoir-layer neurons is represented as u(t)=[u1(t), u2(t), ., uN(t)]T, where N represents the number of reservoir-layer neurons, and the u(t) could be expressed as follows26:

$$u(t)=f_{nl}(W_{in}x(t)+Wu(t - 1))$$
(1)

where Win represents the connection matrix from the input layer to the hidden layer with the dimension of \(N \times K\); the fnl(·) is the activation function, which is the tanh function of \(f_{nl}(x)=\frac{{{e^x} - {e^{ - x}}}}{{{e^x}+{e^{ - x}}}}\) in our case; \(W=\gamma \frac{{W_{0}}}{{\left| {\lambda_{\hbox{max}}} \right|}}\) represents the internal connection matrix between the hidden nodes, W0 is a randomly generated matrix with the value uniformly distributed between [-0.5, 0.5], \(\left| {\lambda \hbox{max} } \right|\) is the spectral radius of W0, γ is spectral radius27. Based on Eq. (1), it can be seen that the value of u(t) is related not only to the current input data xi(t), but also to the previous state u(t-1).

For the output layer, the output is represented by y(t)=[y1(t), y2(t),…, yL(t)]T, in which L is the dimension of the output layer:

$$y(t)=f_{out}(W_{out}u(t))$$
(2)

where fout(·) is an identity function, and Wout with the dimension of \(L \times N\) is the connection matrix from the reservoir layer to the output layer, called output matrix. During the training process, the input connection-matrix Win and the internal connection-matrix W of the neuron are randomly generated as initialization and kept unchanged for the whole computing process. The values of the output layer matrix Wout are continuously trained to achieve the best compensation performance through the ridge regression method28.

Experimental setup

To evaluate the compensation performance of the RC module, we set up an experimental platform to emulate the channel state of laser inter-satellite communications, as depicted in Fig. 2. There are three parts of the platform: the transmitter satellite, the channel emulator and the receiver satellite. In the transmitter satellite subsystem, the optical quadrature-phase-shift-keying (QPSK) signal was generated through an IQ modulator (IQM), which was driven by the 10Gbit/s NRZ electrical signals from an arbitrary waveform generator (AWG). The wavelength and linewidth of the continuous-wave (CW) laser were 1550.92 nm and 100 kHz, respectively. The single-polarization IQM has the bandwidth of 20 GHz. The polarization controller (PC-1) between laser and IQM was used to perform the polarization alignment, achieving the maximum optical output. We also utilized a 99:1 optical coupler (OC-1) to split 1% of modulated signals to monitor the status of IQM. An erbium-doped fiber amplifier was to restore the optical power after the modulation.

Fig. 2
figure 2

Experimental setup for laser inter-satellite communication with RC-based signal compensation.

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In the channel emulator, we considered three distortion sources, i.e., the Sun radiation, the Doppler frequency shift, and the vibration. In the Sun radiation emulator, a wideband optical source (CONQUER, KG-ASE) covering C-band was used to simulate the radiation impact3. The output power of the wideband optical source is up to 23dBm. The radiation strength was controlled by a variable optical attenuator (VOA-2). The power meter (PM) connected with the 50% port of the 3dB OC-2 was to monitor the power level of distorted signals. The optical spectrum was measured through the 1% port of the 99:1 OC-3. The optical multiplexer (MUX) with the bandwidth of 0.4 nm as the optical filter was to block the outside-band noise. In the Doppler frequency shift emulator, an acousto-optic modulator (AOM) produced by OVLINK could induce the 100 MHz or 200 MHz two-level frequency-shift by the electrical driver. The rising time and the insert loss are 12ns and 5dB, respectively. A C-band EDFA with the saturated output power of 23dBm was used to amplify the distorted signals. The noise figure (NF) of EDFA is 4dB. In the vibration emulator, we used an electrically controlled VOA-3 to simulate the power variation caused by the platform vibration. The loss range introduced by VOA-3 is from 2dB to 20dB.

In the receiver satellite subsystem, the detection was performed by a coherent receiver (Co-Rx) with the local laser of 1550.92 nm. The Co-Rx could support the dual-polarization modulated signals, and its bandwidth of Co-Rx is 25 GHz. The received I and Q data were captured by a real-time scope with the sampling rate of 50G Sample/s. These data were handled by the standard digital-signal-processing (DSP) algorithm as pre-processing, such as, IQ balance, time synchronization, frequency offset estimation and carrier recovery, etc. Then the pre-processed data was launched into the RC module as in Fig. 1 to perform the further compensation originated from the Sun radiation, the Doppler frequency shift, and the vibration.

Results and discussion

Distortion impacts

For the Sun radiation, it could be evaluated through the blackbody spectrum at the temperature T = 5777K29. In the lab environment, such wideband spectrum is hard to achieve. But focusing on the transmission window, i.e., C-band in the case, a C-band wideband optical source could bring the similar spectral behavior. Figure 3 (a) depicts the blackbody spectrum at the temperature T = 5777 K and the measurement results from the C-band wideband optical source. Therefore, the Sun radiation emulator employed a wideband optical source to induce the incoherent noise. The noise strength was controlled by tuning the VOA-2. To further reveal the impact of Sun radiation on the received signal, we converted the variation of noise strength P into the elevation angle θs(t) of Sun radiation by using the following relation30:

$$P=\frac{{E \cdot A \cdot \left\{ {\cos \left[ {\theta_{s}\left( t \right)} \right]+\left| {\cos \left[ {\theta_{s}\left( t \right)} \right]} \right|} \right\}}}{2}$$
(3)

where E is the radiation strength from Sun; A is the aperture area of the receiving antenna, and θs(t) is the elevation angle with the function of time t. When the elevation angle θs(t) of the Sun radiation changes, the noise strength P would be changed accordingly. Therefore, we could calculate the elevation angle from the noise strength. We suppose the maximum output from the Sun radiation emulator corresponding to the alignment propagation between the radiation light and the signal beam, resulting into the elevation angle θs(t) = 0 rad. When the noise strength decreased with VOA-2, the elevation angles could also be calculated through Eq. (3) accordingly. Figure 3 (b) depicts the impact from the Sun radiation on the signal quality. It can be clearly seen that the signal-to-noise (SNR) of detected signals after the distortion from Sun is decreased when the elevation angle gradually shifting from the π/2, where the perpendicular relation between the radiation light and the signal beam achieved. Over 3dB distortion was obtained for the testing case when the elevation angle changed from 1.57 to 0 rad.

Fig. 3
figure 3

(a) Radiation strength of the blackbody at 5777 K and the measured output from the wideband optical-source in the inset, (b) impact from the sun radiation on the signal quality.

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For the Doppler frequency shift, it brings the dynamic frequency shift for the receiving signals because of the relative motion. The value of the Doppler frequency shift is periodical change with the operational time31,32. The typical emulator for the Doppler frequency shift is the optical modulator33,34, which could introduce the extra frequency shift from the original carrier. In the experiment, an AOM was used to introduce the frequency shifting as the impact from the Doppler-frequency-shift effect. Due to the limitation of the driver board of AOM, only two frequency-shifting values could be generated, i.e., 100 MHz and 200 MHz. According to the previous investigations, these two values fall into the range of Doppler frequency shift between two laser satellites32. In Fig. 4, the signal quality of SNR and error vector magnitude (EVM) was tested. The frequency shifting of the detected signals away from the original carrier frequency would lead to the phase-rotation distortion, which severely degrades the signal’s quality. In the testing case, the EVM values increased from 10.15 to 11.64% because of Doppler frequency shift, leading to over 1dB-SNR distortion. It can be expected that the more degradation would be observed when the frequency-shift value further increases.

Fig. 4
figure 4

Impact from the Doppler frequency shift on the signal quality.

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The vibration of satellite platform is caused by both internal and external mechanisms. But most of them are located at the very low frequency35, which give the chance to emulate the vibration behavior through the electrically controllable VOA. The vibration of detected signals would cause the power variation. Although the vibration frequency is much lower than the data rate, the reduction on the average power of received signals still could degrade the quality35. We used an electrically controllable VOA-3 to introduce the extra loss into the receiving link, and detected the signal quality with the loss in Fig. 5. Very clear degradation was observed when the loss was increased, over 8dB-SNR reduction obtained in the testing case.

Fig. 5
figure 5

Impact of the power loss on signal quality.

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Based on the experimental testing, the distortions happened in the laser inter-satellite link could severely impacts on the optical signals. The compensation behavior is naturally expected for the real implementation in the laser satellite ends. In the paper, the RC-based compensation is introduced into the digital receiver to be against for the distortions from the Sun radiation, the Doppler frequency shift, and the vibration.

RC compensation

Firstly, the training operation is carried out to train the RC compensator for the task of the digital processing in the laser inter-satellite scenario. The data for the training and test are from the same transmission package. We focus on the two crucial parameters in RC, i.e., the training data-length and the number of neurons, see the results in Fig. 6. We increased the training data from 1000 to 12,000 with the step of 1000, and collected the SNR improvement (ΔSNR) of compensated signals as the monitoring, depicted in Fig. 6 (a). Significant improvement on ΔSNR could be observed when the training data increased from 1000 to 5000, suggesting the RC compensator with the sensitive to the data amount. A clear plateau was obtained in the range of 5000 to 11,000, and even decreased after the optimized data-length of 8000. Moreover, the number of neurons, as the parameter N in Eq. (1), also impacts the compensation performance. We tested the results with the increase of neuron number N from 100 to 2000 with the step of 100, depicted in Fig. 6 (b). The peak value was obtained when the N = 1500. Therefore, the optimized data-length and the neuron number was 8000 and 1500, respectively, also using in the following discussion. We chose the same testing length of 8000 for the quality evaluation.

Fig. 6
figure 6

The key parameters of the network are trained, (a) the length of training data; (b) the number of neurons.

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Before dealing with the multi-distortion sources, the case of the only one distortion is discussed. In Fig. 7 (a), we give the quality improvement ΔSNR versus the distortion strength. For the case of the Sun radiation, the elevation angle was changed from 0 rad to 1.57 rad, and the radiation strength reduced accordingly. The improvement was observed for the whole tested points. The maximum value of 5.74dB was obtained when the elevation angle of 1.57 rad. Moreover, the RC module handle with the impacts from the Doppler frequency shift, depicted in Fig. 7 (b). The 4.96dB and 4.2dB improvement were obtained for the frequency shift with 100 MHz and 200 MHz, respectively, confirming the capability with the mitigation on the Doppler frequency shift effect between two laser satellites. We measured the signal quality before and after RC module when the vibration emulator introducing extra loss from 0dB to 20dB in Fig. 7 (c). Because of the power reduction on the receiver end, the received SNR of signals was reduced accordingly. The RC compensator could improve the signal quality for each power loss, which is more than 2.4dB in the testing case. According to the testing results, the proposed RC compensator could mitigate the impact from the sole distortion in the laser inter-satellite communication systems, suggesting the possibility on the case of the multi-distortion sources.

Fig. 7
figure 7

Quality improvement on only one distortion source, (a) Sun radiation, (b) Doppler frequency shift and (c) vibration loss.

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Finally, we applied the three distortion sources into the laser inter-satellite communication systems simultaneously. In the discussion, the Doppler frequency shift of 200 MHz (the maximum value in the testing system), the vibration loss rang of 0 ~ 5dB and the elevation angle of 1.05 rad for the Sun radiation were investigated. We continuously measured 15 sets of experimental data to quantify the impacts from the distortions, and calculated the SNR results before and after the RC compensator. Figure 8 depicts the quality distribution within the 15 sets. After the DSP pre-processing, the distorted signals were in the range of 15.8dB to 18dB. By further compensating through RC, the signal quality was improved to 20.7dB ~ 22.4dB. A clear gap of over 4dB between before and after the RC compensation was observed. The results confirm the availability of the RC module to perform the compensation from the multi- distortion sources.

Fig. 8
figure 8

Signal compensation capability of ESN.

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To further investigate the compensation performance, we changed the elevation angle of the Sun radiation and collected the signal quality of compensated signals. In Fig. 9 (a), we depict the results-the SNR improvement versus the elevation angle (the radiation strength also changed accordingly). The other two distortion strengths were kept the same as the previous case. Each experiment data represents the average value of ΔSNR from 15 sets of collected results. The increasing trend was observed for the elevation angle away from 0 rad, where the strongest radiation was happened. But even in the worst case, the signal quality improvement ΔSNR = 4.14dB was still achieved. The maximum improvement ΔSNR = 5.59dB was obtained for our testing scenario. We also plot the typical constellation results before and after the RC compensation in Fig. 9 (b) and (c), confirming the quality improvement through the RC module.

Fig. 9
figure 9

(a) SNR improvement under three-distortion sources when elevation angle of the sun radiation changed, typical constellation results (b) before and (c) after the RC compensation.

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It should be noticed that although the RC module could handle with the signals distorted from multiple sources, the well-trained RC compensator could only improve the signal suffering from the same distortion as the training set. Therefore, the re-training is naturally expected when the channel state has changed, that is the different distortion applied in the experiment.

Results comparison

The proposed RC module performs the compensation function for the scenario of laser inter-satellite communications. The latest reported method in such application is the AO-SP approach to suppress the impacts from the Sun radiation3. To give the full comparison between two methods, we have built up the simulation platform based on the all-optical parametric process in a nonlinear SOA as the report3. Beside the distorted QPSK signals, the AO-SP regenerator requires the extra local-pump also input into the nonlinear SOA. In the simulation, the wavelength of the local pump was 1550.12 nm, 0.8 nm away from the input QPSK. And the optical power of QPSK signals was − 10dBm. The nonlinear SOA used in the simulation was from VPI as our previous work36, and the main parameters were: the length of the device section was 6.33*10− 4 m, the nonlinear index was 6.2*10− 19 m2/W, and the effective mode area was 10− 12 m2. The current to drive the nonlinear SOA was 539 mA. To achieve the best regeneration performance, the optimization on power-to-signal ratio (PSR) was carried out, the results depicted in Fig. 10 (a). The best signal quality improvement was achieved by PSR = 16dB, the same value reported in3, confirming the validation of the AO-SP regenerator simulation. Then, we input the distorted QPSK signal as measured in experiment, and collected the improvement results in Fig. 10 (b). Although the compensation has been observed for the whole testing range, the improvement was clearly reduced over 3dB when increasing the elevation angle of the Sun radiation. The reduction might come from the limitation on the regeneration range.

Fig. 10
figure 10

(a) PSR optimization for SOA-based AO-SP, (b) results comparison between RC module and AO-SP.

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According to the comparison between the proposed RC module and the latest AO-SP approach, the more equalized compensation performance was achieved through RC with the changes of the distortion strength. It could support to achieve the stable output from the operational module. Moreover, no extra devices, such as the SOA and the local pump that are important to the AO-SP, are necessary in the proposed RC module, which would help to reduce the requirement of the power assumption, the weight, and the volume of the signal compensation unit.

Conclusion

We used only one RC compensator to mitigate the impacts from the Sun radiation, the Doppler frequency shift, and the vibration. We built an experimental platform to investigate the compensation performance of RC module for the case of laser inter-satellite communication. The impacts from the three distortion sources were quantified, and the quality improvement was tested for QPSK signals. When the optimized training length of 8000 and the number of neurons of 1500 were used, the significant improvement of 5.59dB was experimentally achieved. To the best of our knowledge, this is the first experimental demonstration to perform the compensation task by using RC module in the laser inter-satellite communication scenario. The capability of the mitigation on the multi-distortion sources shows the potential application of the RC module into the signal compensation for the laser satellite networks.