## 6 Space-Segment Optimization Aspects
### Applicable Optimization Methods for Space Segment
#### 6.8.4 Theoretical Modeling and ML-Based Approaches  
Technically, theoretical modeling can also be seen as an optimization technique because it is included in steps that relate to the optimization process as a whole, such as a necessity in methods and metrics as criteria, as we have briefly touched upon in this section. Alternatively, they can be used as a system model, typically within simulations (i.e., a brute-force approach, MC Optimization, solvers, etc.). Needless to say, it would not be possible for us to cover an extensive amount of models in detail, and covering examples makes little sense as they serve as optimization methods only for the particular case they model. Thus, we believe the models we include in our discussions with respect to the methods and metrics are sufficient to demonstrate the role of modeling in an optimization context related to the segments. Similarly, ML-based methods are tricky and difficult to explain briefly, as the networks themselves are designed in a case basis. The study we have cited in Table 2 with regards to ML is [22], where the authors utilize a DNN to modulate and demodulate the signal at terminal and relay nodes to optimize constellations in two-way relaying with physical-layer coding. Regarding their work, the details are complex and are not suited for overview in this paper. However, we will provide an overview about the general NN structure in its stead. An NN consists of layers, which are mathematical manipulations characterized by the neurons (or nodes) within the layer. A neuron is just a place where computation happens, inspired by the neurons in the human brain that fire when stimulated. In a neuron, input data matrix \(X\) is multiplied by the weight matrix \(W\) and is propagated through an activation function \(\Theta(\cdot)\) to generate the output matrix \(Y\):  
\[Y=\Theta(W^{T}X) \tag{16}\]  
This operation assigns significance to inputs with regard to the task the network is trying to learn and determines whether and to what extent that input should progress further through the network to affect the ultimate outcome. This process is called 'training'. While, in practice, it is limited by the available data, in theory, it does not terminate until the operation stops altering the weights used in the operation according to an optimality criterion (typically, a gradient descent is utilized for this purpose). An NN layer is a row of such neurons that turn on or off according to their activation functions, as the input is fed through the network. Each layer's output is simultaneously the subsequent layer's input, starting from an initial input layer receiving the data. An extremely simple NN with only one layer is shown in Figure 6 to serve as an example. A DNN, as the name suggests, is a type of NN. The adjective 'deep' refers to the use of multiple layers in the network. Typically, a DNN utilizes a very large number of layers but is a forward network. This means that the NN architecture does not loop or back-propagate. Other types of NNs utilize such architectures, such as a CNN or Recurrent Neural Network (RNN). We will cover the RNN variant in the ground segment; however, we will refrain from presenting an overview of the other ML-based optimization methods. In the context of data-driven approaches (which includes NN and its variants), online and offline optimization refer to their counterparts in learning theories, namely the online learning and offline learning. Online learning indicates that the learning takes place as the data come in, while the offline learning indicates the existence of a static dataset from which the learning is performed. ML-based methods can be constructed to operate with either of the two learning methods, or, in many cases, simultaneously, with both methods. The learning method imposes additional constraints to the feasibility of the method (the obvious example being the computation time constraint for online learning case, which operates in real-time).