Reservoir computing-based signal compensation for laser inter-satellite communications

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 θ_s(t) of Sun radiation by using the following relation³⁰:

where E is the radiation strength from Sun; A is the aperture area of the receiving antenna, and θ_s(t) is the elevation angle with the function of time t. When the elevation angle θ_s(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 θ_s(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.

(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.

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 time^31,32. The typical emulator for the Doppler frequency shift is the optical modulator^33,34, 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.

Impact from the Doppler frequency shift on the signal quality.

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.

Impact of the power loss on signal quality.

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.

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

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.

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

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.

Signal compensation capability of ESN.

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.

(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.

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.

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

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.