*6.1.1 OEP simulation results for deterministic approach: OEP 1*

**Figure 6** shows the results for the deterministic prediction simulation results for a measured BER at 0.001. The results show that the predicted operating conditions with the lowest error are a temperature of 27°C with an IPBO value of 5. **Figure 6** presents the simulation results for the deterministic prediction when the measured BER is at 0.01 with a number of measured EbNo values of 2. These results show that only 35 out of 100 trials correctly predict both the operating temperature and IPBO.

**Figures 7** and **8** capture the simulation results for the deterministic prediction at a measured BER of 0.01 and 0.001, with a numerical measured value of 2 and 4, respectively. For the measured BER of 0.001, the results show that 96 out of 100 trials correctly predicted both operating temperature and IPBO. Thus, when the number of

**Figure 5.** *MORL-ANN implementation using combined DDPG-and-DQN.*

*Ground-Based HPA Pre-Distorter Using Machine Learning and Artificial Intelligent… DOI: http://dx.doi.org/10.5772/intechopen.110735*

**Figure 7.** *Deterministic prediction simulation results for BER = 0.01 with number of measured EbNo values of 2.*

measured EbNo increases, the probability of correctly identifying the operating conditions improves.

#### *6.1.2 OEP simulation results for Bayesian approach: OEP 2*

**Figure 9** provides the results on the probability of classification as a function of EbNo and BER obtained from the Naïve Bayesian classification model. **Figure 9** shows that the probability of classification is at its highest, about 0.3, when BER = 0.3 and operating system temperature and IPBO are at 27°C and 15 dB, respectively.

**Figure 9** presents simulation results using the Naïve Bayesian prediction approach.

The results were obtained using four measured BER values for predicting HPA's operating temperature and IPBO. **Figure 10** shows that the highest predicted

**Figure 8.** *Deterministic prediction simulation results for BER = 0.001 with number of measured EbNo values of 4.*

**Figure 9.** *Probability of classification.*

probability sum value is for 25°C with an IPBO value of 10, while the actual value is at 25°C with an IPBO value of 13.

**Table 1** summarizes the results for comparison between the two OEP approaches. As shown in **Table 1**, the deterministic approach achieves the best performance when the number of measurements is 4 or more and the BER is at 10E-3 or less. However, for the Bayesian classification approach, the probability of classification is inconclusive when increasing the number of measured BERs. Our team expects that the use of a "Kernel" can improve the probability of classification of the operating environment. *Ground-Based HPA Pre-Distorter Using Machine Learning and Artificial Intelligent… DOI: http://dx.doi.org/10.5772/intechopen.110735*

#### **Figure 10.**

*Probability of classification results for EbNo ranging from 0 to 8 dB.*


#### **Table 1.**

*Deterministic vs. Bayesian classification.*

#### **6.2 Ground-based MORL-ANN Predistorter simulation results**

**Figure 11** shows the simulation results for MORL-ANN PD using MATLAB's DDPG algorithm with the initial operating conditions prediction provided by OEP 1 approach. The results show that AM/AM (signal power curve) and AM/PM (signal

**Figure 11.** *MORL-ANN PD simulation results using existing DDPG in MATLAB.*

**Figure 12.** *MORL-ANN PD simulation results using the combined DDPG and DQN in MATLAB.*

phase curve) between the TX and RX signals are in good agreement, i.e., the PD provides an accurate prediction of AM/AM-AM/PM distortions and compensates for them. This means any inaccuracy associated with OEP eventually corrects itself through the MORL-ANN training and prediction processes. The results shown in **Figure 11** also show that there is a slight disagreement between the actual and predicted AM/AM distortion causing a discrepancy between the TX and RX signals between the Vector Index 150 and 200.

Our team has investigated the problem and learned that when using the combined deep Q-learning neural network (DQN) and DDPG during the learning and training process, the MORL-ANN PD performs better with the use of OEP. **Figure 12** presents the simulation results using the combined DQN-DPPG approach for mitigating the AM/AM discrepancy between the TX and RX signals.

*Ground-Based HPA Pre-Distorter Using Machine Learning and Artificial Intelligent… DOI: http://dx.doi.org/10.5772/intechopen.110735*

Based on the MATLAB implementation, our team has learned that the use of DDPG allowed to use a single, smaller neural network, so it uses much less memory. This implementation can feasibly take many small, discrete actions (due to the agent's smaller size), so it is more convenient for stabilization. However, given a bad initial state, the agent will take a long time (many steps) or never reach a desirable state. Thus, for our problem, we recognize that the DDPG can train faster and typically produces better results than DQN alone.

## **7. Conclusion and way forward**

This chapter provides a summary of the work performed by the CSUF-IFT team on an Industrial Collaboration Project during the 2019**–**2020 academic year. The project described in this chapter focuses on the MATLAB implementation and demonstration of the novel ground-based ML-AI framework presented in **Figure 1**. The proposed MATLAB implementation employs MORL-ANN combined with a deterministic OEP for predicting and compensating signal distortions caused by the ground terminal transmitter' HPA and satellite TXDER's HPA, and imperfect onboard signal processing. Preliminary results presented here have demonstrated the (i) feasibility of the proposed deterministic OEP for reducing operating environment uncertainties associated with unknown satellite TXDER's HPA operating temperature and IPBO, and (ii) use of MORL-ANN using DPPG and MORL-ANN using combined DQN-DPPG for compensating of AM-AM/AM-PM distortions caused by combined ground station's HPA and satellite TXDER's HPA.

Considering the preliminary OEP simulation results, it has been shown that the current proposed environment predictor using Bayesian approach is inconclusive. The CSUF-IFT team continues to investigate the use of ML-AI technology to improve the Bayesian OEP.

Last but not least, the chapter has proposed an approach to combine the data science and decision science to solve a challenging problem in satellite communication in the presence of unknown operational conditions. Our team has developed an endto-end SATCOM system model (E2E-SSM) emulator to generate a large amount of data for various practical operational conditions, including unknown IPBO, system operating temperature, HPA's AM-AM/AM-PM characteristics, and SNR. Using the data obtained from the emulator, the team has also developed an innovative ML-AI framework to (i) learn the behavior of amplitude and phase distortions of the received downlink signal, (ii) predict the amount of amplitude and phase of the transmitted uplink signal, and (iii) and adjust them accordingly for negating the effects of the HPA nonlinearity on the end-to-end communication signals. Our simulation results presented in this chapter has demonstrated the feasibility of these proposed combined technologies. Our team is also investigating the use of the proposed ML-AI pre-distorter for future Global Navigation Satellite System (GNSS) applications. The results of these investigations will be reported in the near future.

## **Acknowledgements**

IFT was awarded the SBIR Phase 1 in 2019, and contract number was FA9453-18- P-0233 from AFRL, entitled "Hybrid Low-Cost Predistortion Solutions for Next Generation Satellite Transponder," as the prime contractor. The results presented in this

chapter were done during Phase 1 (toward the end of Phase 1) through the Industrial Project for Graduate Program in Applied Mathematics (IPGPAM), which is a joint collaboration project between CSUF and IFT. Recently, IFT was awarded the SBIR Phase 2 contract, Contract No. FA9453-21-C-0539 from AFRL. Additionally, CSUF was awarded a subcontract from IFT, Subcontract Number: IFT083-02. The subcontract focused on maturing the proposed ML-AI technology enabler and OEP for future GNSS applications. The paper was cleared for public release, Case No. AFRL-2022-5077. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of AFRL.
