## 4 Simulation Results  
In this section, the DRL-aided proposed PA methodology is applied to the experimental ARTEMIS time series data along with other heuristic, model-free strategies, i.e., DQN, Equal Power, and Random Power algorithms and the model-based supervised method. The ESA's data relay satellite mission ARTEMIS (Advanced Relay and Technology Mission Satellite) took place in 2003 when the spacecraft attained GEO orbit, and involved a variety of optical communication telescopes for satellite-to-ground and intersatellite bi-directional links [27; 28]. The experimental data to be utilized are recorded time series from the downlink transactions from the laser terminal (OPALE) onboard ARTEMIS to the reflector telescope (LUCE) installed on the Teide Observatory in Tenerife, 2400 m above sea level [27; 28]. The spacecraft's location and communication features as well as LUCE's and OGS's essential characteristics are given in Table 1.  
In Figure 1, the normalized PDFs of five experimental time series are illustrated vs. the normalized PDFs of synthesized data that are lognormally distributed [27; 28]. It is obvious that the PDFs derived from the retrieved ARTEMIS data accurately fit the lognormal PDFs, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Characteristic** & **Value** \\ \hline ARTEMIS & Longitude & 21.5\({}^{\circ}\) East \\ \hline \multirow{7}{*}{OPALE} & Latitude & 0.0\({}^{\circ}\)\(\pm\) 2.81\({}^{\circ}\) North \\  & Altitude & 35,787 km \\  & Elevation Angle & 37\({}^{\circ}\) \\  & Coverage & Europe, Africa, and the Middle East \\  & Wavelength & 819 nm \\  & Beam Diameter (1/e\({}^{2}\)) & 125 mm \\  & Transmitted Power & 10 mV \\  & Modulation Scheme & Intensity Modulation—Direct Detection \\  & Data Rate & 2 Mbps (downlink), 50 Mbps (uplink) \\ \hline LUCE & Aperture Diameter & 26 cm \\ \hline OGS & Altitude & 2.4 km \\ \hline \hline \end{tabular}
\end{table} 
Table 1: ARTEMIS, OPALE, LUCE, and OGS Characteristics. implying weak turbulence conditions, and that the channel model in (2) can be applied to find the exact solution which will be used as labeled data for the supervised approach, elaborated in Section 3.1. The channel samples are then employed to form a 5 \(\times\) 5 diagonal Multi-Input Multi-Output (MIMO) optical satellite-to-ground system. In general, the channels are assumed cloud-free but suffer from propagation losses and turbulence-induced scintillation. In Table 2, the experimental optical channels' mean powers and SIs are included. The lower the \(\langle P_{r}\rangle\) and the higher the SI, the worse the slant path conditions. The channels' correlation is negligible; hence, they are safely considered independent and will be denoted as ch.0, ch.1, ch.2, ch.3, and ch.4. To develop the proposed DRL-aided power allocation algorithm, the policy's DNN had to be accurately specified. In particular, the neural network's layers, nodes, and probability distribution must be chosen in a way to avoid overfitting, overhead, and high inference time. In Figure 2, the results of an investigation of the optimal number of hidden layers and neurons are shown. From Figure 2a, it is seen that one or two hidden layers are sufficient as they achieve the maximum average capacity and loss function. From Figure 2b, it is concluded that 256 neurons yield the best performance. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Channel** & **Experiment** & **Parameters** & **Values** \\ \hline
0 & 10/09/2003 20:10 & \(\langle P_{r}\rangle\), \(\sigma_{1}^{2}\) & \(-\)13.34 dBm, 0.0101 \\
1 & 10/09/2003 00:30 & \(\langle P_{r}\rangle\), \(\sigma_{1}^{2}\) & \(-\)15.79 dBm, 0.0142 \\
2 & 12/09/2003 00:30 & \(\langle P_{r}\rangle\), \(\sigma_{1}^{2}\) & \(-\)19.78 dBm, 0.0274 \\
3 & 13/09/2003 23:30 & \(\langle P_{r}\rangle\), \(\sigma_{1}^{2}\) & \(-\)20.94 dBm, 0.0485 \\
4 & 16/09/2003 20:10 & \(\langle P_{r}\rangle\), \(\sigma_{1}^{2}\) & \(-\)13.85 dBm, 0.0121 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optical Channels’ Parameters.