## 6 Performance Evaluation
### Simulation Setup  
Our experiments were conducted on a laptop with 13 th Gen Intel(R) Core(TM) i7-13650 HX 2.60 GHz, 16.0 GB RAM, and NVIDIA GeForce RTX4060 Laptop GPU. All simulations were developed based on Python 3.11, the neural network method was designed based on PyTorch, and the solution of convex optimization problems was performed through CVXPY. We considered the following scenario: two LEO satellites are located in high-altitude orbits 200 km above the ground [27], while three HAP drones are positioned 20 km above the ground, randomly distributed within a square area with a side length of 2 km. On the ground, there are \(J\) randomly distributed terrestrial IoT devices. Both the IoT-HAP drone and HAP drone-LEO satellite links adopt the access strategy with maximum channel gain. In each time slot, we assume each terrestrial IoT device generates a task for processing. For each task, the default generated data size is in the range of \([1,1.2]\) Mbits. The number of CPU cycles required per bit is 1000 [40], and the maximum tolerable latency is \(T=3\) s [27]. In this paper, we assume that the available bandwidth for each wireless channel is 20 MHz, allocated evenly to each device. The maximum local computing capacity for each ground user is the same, set at 1 GHz. Both HAP drones and LEO satellites have a maximum computing capacity of 5 GHz. Other important simulation environment parameters are shown in Table 1.  
Choosing appropriate hyper parameters is crucial for the performance of DDPG. In this paper, we mainly focused on the following key hyper parameters: batch size, replay buffer size, learning rates of the actor network and critic network, the soft update factor for the actor network and critic network, and the discount factor.  
Our goal in selecting the batch size and replay buffer size was to ensure the stability and convergence speed of DDPG training while minimizing computational and memory resources. We chose a batch size of 64 and a replay buffer size of 100,000 as the hyperparameters for subsequent simulations. The soft update factor was chosen to control the update speed of the weights of the target network (including the actor target network and critic network). We chose \(\tau=0.0001\). A smaller value was chosen to increase the stability of training. Finally, we chose appropriate discount factors and learning rates to ensure the convergence, convergence speed, and performance of the DDPG algorithm in this scenario. In this regard, we designed comparative experiments with different discount factors ([0.95, 0.75, 0.55, 0.35]) and different learning rates (\([1\times 10^{-4},1\times 10^{-3},1\times 10^{-2},1\times 10^{-1}]\)). The experimental results are shown in Section 6.2. The specific parameters are shown in Table 2.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline AWGN spectral density (\(N_{0}\)) & \(-174\) dBm/Hz [34] \\ \hline Maximum transmit power of terrestrial IoT device (\(P_{j}\)) & 23 dBm \\ \hline Maximum transmit power of HAP drone (\(P_{n}\)) & 43 dBm \\ \hline Transmit antenna gain of HAP drone (\(G_{ts}\)) & 0 dB [34] \\ \hline Receive antenna gain of LEO satellite (\(G_{tr}\)) & 53 dB [34] \\ \hline Path loss (\(L_{as}\)) & 5.2 dB [34] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation environment settings.